influence of mechanical and geometrical parameters
on the static behavior of a violin bow
in playing situation
Frederic Ablitzer
Laboratoire d’Acoustique de l’Universite du Maine – UMR CNRS 6613
PhD defence
Le Mans, France – December 5th, 2011
Examining committee
A. Askenfelt | KTH, Stockholm (Examiner) B. Cochelin | LMA, Marseille (Reviewer)R. Causse | IRCAM, Paris (Reviewer) J.P. Dalmont | LAUM, Le Mans (Supervisor)
A. Chaigne | ENSTA ParisTech, Palaiseau (Chairman) N. Dauchez | SUPMECA, Saint-Ouen (Supervisor)
G. Chevallier | SUPMECA, Saint-Ouen (Examiner) N. Poidevin | Bow maker, Dinan (Invited)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 1 / 50
Introduction
Paganini’s 24th Caprice (1819)
played by Alexander Markov
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 2 / 50
Introduction
Paganini’s 24th Caprice (1819)
played by Alexander Markov
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 2 / 50
Introduction
Evolution of the bow
Renaissance
Baroque
Classique
Moderne
c© N. Poidevin
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 3 / 50
Introduction
Evolution of the bow
Renaissance
Baroque
Classique
Moderne
c© N. Poidevin
stickbaguette
lengthening of the stick
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 3 / 50
Introduction
Evolution of the bow
Renaissance
Baroque
Classique
Moderne
c© N. Poidevin
headtete
stickbaguette
lengthening of the stick
development of a head
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 3 / 50
Introduction
Evolution of the bow
Renaissance
Baroque
Classique
Moderne
c© N. Poidevin
headtete
stickbaguette
buttonbouton
hairmeche
froghausse
lengthening of the stick
development of a head
mechanism to adjust hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 3 / 50
Introduction
Evolution of the bow
Renaissance
Baroque
Classique
Moderne
c© N. Poidevin
headtete
stickbaguette
buttonbouton
hairmeche
froghausse
lengthening of the stick
development of a head
mechanism to adjust hair tension
inversion of the curvature
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 3 / 50
Introduction
The modern bow
Almost the same bow for 200 years
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 4 / 50
Introduction
The modern bow
Almost the same bow for 200 years
Francois-Xavier Tourte(1747-1835)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 4 / 50
Introduction
The modern bow
Almost the same bow for 200 years
Francois-Xavier Tourte(1747-1835)
Pernambuco wood
standardized design
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 4 / 50
Introduction
The modern bow
Almost the same bow for 200 years
Francois-Xavier Tourte(1747-1835)
Pernambuco wood
standardized design
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 4 / 50
Introduction
The modern bow
Almost the same bow for 200 years
Francois-Xavier Tourte(1747-1835)
Pernambuco wood
standardized design
An achieved compromise
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 4 / 50
Introduction
Why study the bow?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 5 / 50
Introduction
Why study the bow?
Little scientific studies on the bow
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 5 / 50
Introduction
Why study the bow?
Little scientific studies on the bow
Questions from bow makers about the physics behind the bowduring “Journees Facture Instrumentale et Sciences”(ITEMM, Le Mans)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 5 / 50
Introduction
Why study the bow?
Little scientific studies on the bow
Questions from bow makers about the physics behind the bowduring “Journees Facture Instrumentale et Sciences”(ITEMM, Le Mans)
Pernambuco listed as endengered species since 2007in CITES, Appendix II
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 5 / 50
Introduction
Why study the bow?
Little scientific studies on the bow
Questions from bow makers about the physics behind the bowduring “Journees Facture Instrumentale et Sciences”(ITEMM, Le Mans)
Pernambuco listed as endengered species since 2007in CITES, Appendix II
Supply makers with dedicated characterization and simulation toolswithin the project PAFI supported by ANR (2009-2012)(“Plateforme d’Aide a la Facture Instrumentale”)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 5 / 50
Introduction
3 points of view
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 6 / 50
Introduction
3 points of view
The player
What does he need?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 6 / 50
Introduction
3 points of view
The player
What does he need?
The bow maker
How does he meetthe player’s demand?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 6 / 50
Introduction
3 points of view
The player
What does he need?
The bow maker
How does he meetthe player’s demand?
The scientist
How can he helpthe maker?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 6 / 50
Introduction
Player’s point of view
What does the player need?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 7 / 50
Introduction
Player’s point of view
What does the player need?
playability= allows to play a variety of bow strokes
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 7 / 50
Introduction
Player’s point of view
What does the player need?
playability= allows to play a variety of bow strokes
tonal qualities= allows to achieve a good tone
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 7 / 50
Introduction
Player’s point of view
What does the player need?
playability= allows to play a variety of bow strokes
tonal qualities= allows to achieve a good tone
aesthetics
price
...
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 7 / 50
Introduction
Bow maker’s point of view
How does the maker meet the player’s demand?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 8 / 50
Introduction
Bow maker’s point of view
How does the maker meet the player’s demand?
wood
density
elasticity
damping
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 8 / 50
Introduction
Bow maker’s point of view
How does the maker meet the player’s demand?
wood
density
elasticity
damping
tapering
↓distribution of mass and stiffness
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 8 / 50
Introduction
Bow maker’s point of view
How does the maker meet the player’s demand?
wood
density
elasticity
damping
tapering
↓distribution of mass and stiffness
camber
↓adjustment of playing
and tonal qualities
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 8 / 50
Introduction
Bow maker’s point of view
Making and adjustment mainly empirical...
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 9 / 50
Introduction
Bow maker’s point of view
Making and adjustment mainly empirical...
...sometimes combined with a scientific approach
measuring stiffnessLucchimeter
Lutherie Tools
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 9 / 50
Introduction
Scientist’s point of view
How to characterize or model a bow?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 10 / 50
Introduction
Scientist’s point of view
How to characterize or model a bow?
For the acoustician: bow = vibrating structure
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 10 / 50
Introduction
Scientist’s point of view
How to characterize or model a bow?
For the acoustician: bow = vibrating structure
eigenmodes(modal analysis, FE model)[Bissinger 1993, Causse et al. 2001,
Pickering 2002, Ravina et al. 2008]
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 10 / 50
Introduction
Scientist’s point of view
How to characterize or model a bow?
For the acoustician: bow = vibrating structure
eigenmodes(modal analysis, FE model)[Bissinger 1993, Causse et al. 2001,
Pickering 2002, Ravina et al. 2008]
admittance presented to the string[Schumacher 1975, Askenfelt 1995]
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 10 / 50
Introduction
Scientist’s point of view
How to characterize or model a bow?
For the acoustician: bow = vibrating structure
eigenmodes(modal analysis, FE model)[Bissinger 1993, Causse et al. 2001,
Pickering 2002, Ravina et al. 2008]
admittance presented to the string[Schumacher 1975, Askenfelt 1995]
vibrations during playing[Askenfelt 1993]
→ may help to better understand and model the bow/string interaction
however, difficult to relate to bow maker’s adjustment and player’s perception
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 10 / 50
Introduction
Axes of investigation
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
bow = prestressed structure
→ consequences on the behavior?
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
bow = prestressed structure
→ consequences on the behavior?
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
bow = prestressed structure
→ consequences on the behavior?
risk of buckling?
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
offer a certain compliance
bow = prestressed structure
→ consequences on the behavior?
risk of buckling?
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
offer a certain compliance
bow = prestressed structure
→ consequences on the behavior?
risk of buckling?
Introduction
Axes of investigation
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
offer a certain compliance
bow = prestressed structure
→ consequences on the behavior?
risk of buckling?
how to control compliance?
Introduction
Axes of investigation
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 11 / 50
function of the bow:maintain the hair under tension
resist to player’s action
offer a certain compliance
bow = prestressed structure
→ consequences on the behavior?
risk of buckling?
how to control compliance?
Introduction
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 12 / 50
Modelling
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 13 / 50
Modelling
Modelling
������������������������������������
bow without hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������������������������
bow without hair tension
Assumptions
stick = Euler-Bernoulli beam
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������������������������
bow without hair tension
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������������������������
������������������������������������
T0
bow without hair tension
(i) ↓
tightened at playing tension T0
prestressed state
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������
������������������������������������
������������������������������������
T0
T
F
bow without hair tension
(i) ↓
tightened at playing tension T0
prestressed state
(ii) ↓
loaded by a force F on the hairplaying situation
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������
������������������������������������
������������������������������������
T0
T
F
bow without hair tension
(i) ↓
tightened at playing tension T0
prestressed state
(ii) ↓
loaded by a force F on the hairplaying situation
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
hair has longitudinal stiffness
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������
������������������������������������
������������������������������������
T0
T
F
bow without hair tension
(i) ↓
tightened at playing tension T0
prestressed state
(ii) ↓
loaded by a force F on the hairplaying situation
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
hair has longitudinal stiffness
material is elastic
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Modelling
������������������
������������������������������������
������������������������������������
T0
T
F
bow without hair tension
(i) ↓ (i)
tightened at playing tension T0
prestressed state
(ii) ↓ (ii)
loaded by a force F on the hairplaying situation
Assumptions
stick = Euler-Bernoulli beam
stick oriented along the grain of the wood: longitudinal Young’s modulus is considered
hair has longitudinal stiffness
material is elastic
(i) and (ii) are large transformations → geometric non-linear model
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 14 / 50
Modelling
Corotationnal approach: Illustration
Cantilever beam subject to end moment
M =2π E I
L
M
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 15 / 50
Modelling
Corotationnal approach: Illustration
Cantilever beam subject to end moment
M =2π E I
L
M
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 15 / 50
Modelling
Corotationnal approach: Illustration
Cantilever beam subject to end moment
M =2π E I
L
M
Local deformation (small)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 15 / 50
Modelling
Corotationnal approach: Illustration
Cantilever beam subject to end moment
M =2π E I
L
M
Rigid body-motion (large)
Local deformation (small)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 15 / 50
Modelling
2D model
Finite element model of the stick
2D Euler-Bernoulli beam elements,corotational formulation
external load : force T =[Tx Ty
]T
→ follower force→ amplitude depends ondisplacements
Lh
βhx
y
Tx
Ty
Rh
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 16 / 50
Modelling
2D model
Finite element model of the stick
2D Euler-Bernoulli beam elements,corotational formulation
external load : force T =[Tx Ty
]T
→ follower force→ amplitude depends ondisplacements
Lh
βhx
y
Tx
Ty
Rh
Model of the hair
equivalent single hair
compliance per unit length ch
relationship between T and playingforce Fy at relative abscissa γ
Ty = γFy
f (Tx , Fy , Lh, · · · ) = 0
T′
0 T0
γL0 L0
Rh
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 16 / 50
Modelling
2D model
Finite element model of the stick
2D Euler-Bernoulli beam elements,corotational formulation
external load : force T =[Tx Ty
]T
→ follower force→ amplitude depends ondisplacements
Lh
βhx
y
Tx
Ty
Rh
Model of the hair
equivalent single hair
compliance per unit length ch
relationship between T and playingforce Fy at relative abscissa γ
Ty = γFy
f (Tx , Fy , Lh, · · · ) = 0
Lh
Fx
Fy F
Tx
Ty
T′
T
Rh
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 16 / 50
Modelling
2D model
Finite element model of the stick
2D Euler-Bernoulli beam elements,corotational formulation
external load : force T =[Tx Ty
]T
→ follower force→ amplitude depends ondisplacements
Lh
βhx
y
Tx
Ty
Rh
Model of the hair
equivalent single hair
compliance per unit length ch
relationship between T and playingforce Fy at relative abscissa γ
Ty = γFy
f (Tx , Fy , Lh, · · · ) = 0
Lh
Fx
Fy F
Tx
Ty
T′
T
Rh
K(u)u = f(u)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 16 / 50
Modelling
3D model
Why a 3D model?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 17 / 50
Modelling
3D model
Why a 3D model?
player frequently tilts the bow→ lateral bending of the stick during playing
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 17 / 50
Modelling
3D model
Why a 3D model?
player frequently tilts the bow→ lateral bending of the stick during playing
bow maker adjusts the lateral compliance of the bow(tapering, camber)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 17 / 50
Modelling
3D model
Why a 3D model?
player frequently tilts the bow→ lateral bending of the stick during playing
bow maker adjusts the lateral compliance of the bow(tapering, camber)
stick
hair
}
3D Euler-Bernoulli beam
corotationnal formulation
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 17 / 50
Experimental characterization
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 18 / 50
Experimental characterization
Measurement of bow shape
Method to determine the shape of the bow in a given state
Example: determination of camber
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 19 / 50
Experimental characterization
Measurement of bow shape
Method to determine the shape of the bow in a given state
Example: determination of camber
picture of the bow
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 19 / 50
Experimental characterization
Measurement of bow shape
Method to determine the shape of the bow in a given state
Example: determination of camber
picture of the bow
detect lower and upper edges along the bow
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 19 / 50
Experimental characterization
Measurement of bow shape
Method to determine the shape of the bow in a given state
Example: determination of camber
picture of the bow
detect lower and upper edges along the bow
approximate neutral curve with polynom of appropriate order
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 19 / 50
Experimental characterization
Determination of bow properties: Step 1
Procedure in 4 steps
1 Geometry
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 20 / 50
Experimental characterization
Determination of bow properties: Step 1
Procedure in 4 steps
1 Geometry
Tapering
measurement with digital caliper
����������������
����������������
lateralvertical
dia
met
er(m
m)
x (mm)
0 100 200 300 400 500 600 7005
6
7
8
9
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 20 / 50
Experimental characterization
Determination of bow properties: Step 1
Procedure in 4 steps
1 Geometry
Tapering
measurement with digital caliper
����������������
����������������
lateralvertical
dia
met
er(m
m)
x (mm)
0 100 200 300 400 500 600 7005
6
7
8
9
Camber
image processing
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 20 / 50
Experimental characterization
Determination of bow properties: Step 2
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
bow without hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 21 / 50
Experimental characterization
Determination of bow properties: Step 2
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
bow without hair tension
force Fz at the tip
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 21 / 50
Experimental characterization
Determination of bow properties: Step 2
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
bow without hair tension
force Fz at the tip
find E that minimizes difference betweenmeasured and simulated deformed shape
modelmeasurementFz = 0 N
y(m
m)
x (mm)
E = 26.7 GPa — Eh = 0.0 GPa — T0 = 0.0 N
0 650
0
20
comparison in the hair reference frame↓
elimination of rigid body motion
E = 26.7± 0.7 GPa (3%)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 21 / 50
Experimental characterization
Determination of bow properties: Step 3
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
bow without hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 22 / 50
Experimental characterization
Determination of bow properties: Step 3
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
T0
bow without hair tension
tighten the bow
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 22 / 50
Experimental characterization
Determination of bow properties: Step 3
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
T0
bow without hair tension
tighten the bow
find T0 that minimizes difference betweenmeasured and simulated deformed shape
modelmeasurementT0 = 0 N
y(m
m)
x (mm)
E = 26.7 GPa — Eh = 0.0 GPa — T0 = 66.7 N
0 650
0
20
T0 = 66.7± 3.9 N (6%)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 22 / 50
Experimental characterization
Determination of bow properties: Step 4
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
T0
4 Stiffness of the hair Eh
T0
bow under hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 23 / 50
Experimental characterization
Determination of bow properties: Step 4
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
T0
4 Stiffness of the hair Eh
Fz
T
bow under hair tension
force Fz at the tip
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 23 / 50
Experimental characterization
Determination of bow properties: Step 4
Procedure in 4 steps
1 Geometry
2 Young’s modulus of the stick E
Fz
3 Hair tension T0
T0
4 Stiffness of the hair Eh
Fz
T
bow under hair tension
force Fz at the tip
find Eh that minimizes difference betweenmeasured and simulated deformed shape
modelmeasurementFz = 0 N
y(m
m)
x (mm)
E = 26.7 GPa — Eh = 7.2 GPa — T0 = 66.7 N
0 650
0
20
Eh = 7.2± 1.7 GPa (24%)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 23 / 50
Experimental characterization
Validation: Measurement of compliance
Distribution of compliance along the bow?
→ simultaneous measurement of force anddeflection at several abscissas
u
F
γ = 0 γ = 1
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 24 / 50
Experimental characterization
Validation: Measurement of compliance
Distribution of compliance along the bow?
→ simultaneous measurement of force anddeflection at several abscissas
u
F
γ = 0 γ = 1
linear2nd order polynommeasured data
γ = 0.5
γ = 1
defl
ecti
on
(mm
)force (N)
0 0.5 1 1.50
5
10
15
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 24 / 50
Experimental characterization
Validation: Measurement of compliance
Distribution of compliance along the bow?
→ simultaneous measurement of force anddeflection at several abscissas
u
F
γ = 0 γ = 1
linear2nd order polynommeasured data
γ = 0.5
γ = 1
defl
ecti
on
(mm
)force (N)
0 0.5 1 1.50
5
10
15
20
compliance c =∂u
∂Fat F = 1 N
measurement in vertical and lateraldirections
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 24 / 50
Experimental characterization
Comparison between measured and simulated compliance
measurement - lateralmeasurement - vertical
bow B2
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 25 / 50
Experimental characterization
Comparison between measured and simulated compliance
simulation - verticalmeasurement - lateralmeasurement - vertical
bow B2
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 25 / 50
Experimental characterization
Comparison between measured and simulated compliance
simulation - lateralsimulation - verticalmeasurement - lateralmeasurement - vertical
bow B2
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Good agreement between numerical and experimental results → predictive model
[Ablitzer, Dauchez, Dalmont, submitted to Acta Acustica]
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 25 / 50
Results
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 26 / 50
Results Static behavior
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 27 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Adjustment of a bow
a0
T0T0
Hair tension T0 vs hair-stick distance a0
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Shape of the bow
(κ initial distance)
κ = 0 mm
y(m
m)
x (mm)0 650
0
20
κ = −2 mmy
(mm
)
x (mm)0 650
0
20
Adjustment of camber allows to reach another hair tension for the same distance
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 28 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 0 N
total
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 0 N
stickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 0 N
stickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Pitteroff’s model [Pitteroff 1995]
c =γ (1− γ) L0
T0︸ ︷︷ ︸
hair
+γ2
Kb︸︷︷︸
stick
hair length L0
hair tension T0
stiffness of the stick at the tip Kb
Kb
F
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 0 N
Pitteroff’s modelstickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Pitteroff’s model [Pitteroff 1995]
c =γ (1− γ) L0
T0︸ ︷︷ ︸
hair
+γ2
Kb︸︷︷︸
stick
hair length L0
hair tension T0
stiffness of the stick at the tip Kb
Kb
F
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 0.5 N
Pitteroff’s modelstickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Pitteroff’s model [Pitteroff 1995]
c =γ (1− γ) L0
T0︸ ︷︷ ︸
hair
+γ2
Kb︸︷︷︸
stick
hair length L0
hair tension T0
stiffness of the stick at the tip Kb
Kb
F
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 1.0 N
Pitteroff’s modelstickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Pitteroff’s model [Pitteroff 1995]
c =γ (1− γ) L0
T0︸ ︷︷ ︸
hair
+γ2
Kb︸︷︷︸
stick
hair length L0
hair tension T0
stiffness of the stick at the tip Kb
Kb
F
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow
Vertical compliance along the bow c =∂u
∂FFz = 1.5 N
Pitteroff’s modelstickhairtotal
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Two contributions:
compliance of the hair
compliance of the stick
Pitteroff’s model [Pitteroff 1995]
c =γ (1− γ) L0
T0︸ ︷︷ ︸
hair
+γ2
Kb︸︷︷︸
stick
hair length L0
hair tension T0
stiffness of the stick at the tip Kb
Kb
F
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 29 / 50
Results Static behavior
Compliance of the tightened bow: Non-linearity
Vertical compliance along the bow c =∂u
∂F
high forcelow force
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Consider compliance at low forces (0 N)and high forces (1.5 N)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 30 / 50
Results Static behavior
Compliance of the tightened bow: Non-linearity
Vertical compliance along the bow c =∂u
∂F
high forcelow force
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
γ = 0 γ = 1
Consider compliance at low forces (0 N)and high forces (1.5 N)
near the middle
→ stiffening behavior
near the tip
→ softening behavior
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 30 / 50
Results Static behavior
Compliance of the tightened bow: Effect of hair tension and camber
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 31 / 50
Results Static behavior
Compliance of the tightened bow: Effect of hair tension and camber
◦ low tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
• high tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 31 / 50
Results Static behavior
Compliance of the tightened bow: Effect of hair tension and camber
◦ low tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
• high tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
◦ little camber
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
• much camber
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 31 / 50
Results Static behavior
Compliance of the tightened bow: Effect of hair tension and camber
◦ low tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
• high tension
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
◦ little camber
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
• much camber
vert
ical
com
plia
nce
(mm
/N
)
relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
Adjustment of camber strongly affects compliance
[Ablitzer, Dalmont, Dauchez, J. Acoust. Soc. Am. 123 (2012)]
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 31 / 50
Results Static behavior
Effect of bow tilt
Bow frequently tilted in playing(up to about 30◦)
F
ψ
axis of the string
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 32 / 50
Results Static behavior
Effect of bow tilt
Bow frequently tilted in playing(up to about 30◦)
F
ψ
axis of the string
Evolution of compliance with tilt angle ψ
F = 1 N | κ = 0 mm
0◦
com
plia
nce
(mm
/N
)relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
γ = 0 γ = 1
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 32 / 50
Results Static behavior
Effect of bow tilt
Bow frequently tilted in playing(up to about 30◦)
F
ψ
axis of the string
Evolution of compliance with tilt angle ψ
F = 1 N | κ = 0 mm
30◦
0◦
com
plia
nce
(mm
/N
)relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
γ = 0 γ = 1
Lateral compliance is higher than vertical compliance
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 32 / 50
Results Static behavior
Effect of bow tilt
Bow frequently tilted in playing(up to about 30◦)
F
ψ
axis of the string
Evolution of compliance with tilt angle ψ
F = 1 N | κ = −2 mm (more camber)
30◦
0◦
30◦
0◦
com
plia
nce
(mm
/N
)relative abscissa γ
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
35
40
γ = 0 γ = 1
Lateral compliance is higher than vertical compliance
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 32 / 50
Results Stability
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 33 / 50
Results Stability
Stability of the bow
Load case
x
y
z Fz
εFy
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 34 / 50
Results Stability
Stability of the bow
Load case
x
y
z Fz
εFy
❶ without perturbation force (Fz only)
❷ with perturbation force (Fz + εFy )
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 34 / 50
Results Stability
Stability of the bow
Load case
x
y
z Fz
εFy
The bow may be unstable in two ways:
1 limit point instability(snap-through)
2 bifurcation instability(lateral buckling)
❶ without perturbation force (Fz only)
❷ with perturbation force (Fz + εFy )
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 34 / 50
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Limit point instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 35 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Bifurcation instabilityfo
rce
Fz
(mm
)
displacements (mm)0 20 40 60 80 100 120
0
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 20 40 60 80 100 120
0
20
40
60
80
100
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 36 / 50
— uz (vertical)- - uy (lateral)
Results Stability
Critical buckling loadsfo
rce
Fz
(mm
)
displacements (mm)
Fc
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
hai
rte
nsi
on
T(N
)
displacement uz (mm)
Tc
0 20 40 60 80 100 1200
20
40
60
80
100
Buckling occurs
when T = Tc
critical hair tension
when Fz = Fc
critical playing force
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 37 / 50
Results Stability
Influence of hair tension
forc
eF
z(N
)
displacements (mm)0 50 100 150
0
1
2
3
4
5
Tc
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 50 100 150
0
20
40
60
80
100
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 38 / 50
Results Stability
Influence of hair tension
forc
eF
z(N
)
displacements (mm)0 50 100 150
0
1
2
3
4
5
Tc
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 50 100 150
0
20
40
60
80
100
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
same critical tension Tc
critical force Fc not very sensitive to hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 38 / 50
Results Stability
Influence of camber
forc
eF
z(N
)
displacements (mm)0 50 100 150
0
1
2
3
4
5
Tc
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 50 100 150
0
20
40
60
80
100
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 39 / 50
Results Stability
Influence of camber
forc
eF
z(N
)
displacements (mm)0 50 100 150
0
1
2
3
4
5
Tc
hai
rte
nsi
on
T(N
)
displacement uz (mm)0 50 100 150
0
20
40
60
80
100
hai
r-st
ick
dis
tance
(mm
)
hair tension T0 (N)0 10 20 30 40 50 60 70
−5
0
5
10
15
20
same critical tension Tc
increasing camber ⇒ critical force Fc decreases
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 39 / 50
Playing tests
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 40 / 50
Playing tests
Selection and adjustment of bows
Idea: vary only 2 parameters: camber and hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 41 / 50
Playing tests
Selection and adjustment of bows
Idea: vary only 2 parameters: camber and hair tension
❶ Selection of 3 bows
same properties (stiffness, mass, center of inertia...)
same aspect
high-quality bows in Pernambuco after Tourte model
×3
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 41 / 50
Playing tests
Selection and adjustment of bows
Idea: vary only 2 parameters: camber and hair tension
❶ Selection of 3 bows
same properties (stiffness, mass, center of inertia...)
same aspect
high-quality bows in Pernambuco after Tourte model
❷ Adjustment of the bows
one bow with more camber (κ = −3 mm)
one bow with less camber (κ = 2 mm)
— camber +
— camber −
— reference
selection and adjustment by bow maker Jean-Grunberger
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 41 / 50
Playing tests
Selection and adjustment of bows
Idea: vary only 2 parameters: camber and hair tension
❶ Selection of 3 bows
same properties (stiffness, mass, center of inertia...)
same aspect
high-quality bows in Pernambuco after Tourte model
❷ Adjustment of the bows
one bow with more camber (κ = −3 mm)
one bow with less camber (κ = 2 mm)
❸ Characterization of the bows
— camber +
— camber −
— reference
selection and adjustment by bow maker Jean-Grunberger
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 41 / 50
Playing tests
Selection and adjustment of bows
Idea: vary only 2 parameters: camber and hair tension
❶ Selection of 3 bows
same properties (stiffness, mass, center of inertia...)
same aspect
high-quality bows in Pernambuco after Tourte model
❷ Adjustment of the bows
one bow with more camber (κ = −3 mm)
one bow with less camber (κ = 2 mm)
❸ Characterization of the bows
dis
tance
crin
-bag
uet
tea
0(m
m)
tension du crin T0 (N)0 20 40 60 80 100
−5
0
5
10
15
20
− +ref
— camber +
— camber −
— reference
selection and adjustment by bow maker Jean-Grunberger
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 41 / 50
Playing tests
Verbalization
Expert 1 Expert 2
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
Expert 2
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Attack (consonants) (few ←→ many)timbre of transients
Expert 2
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Attack (consonants) (few ←→ many)timbre of transients
3 Playing at the frog (difficult ←→ easy)ease to play at the frog
4 String crossings (difficult ←→ easy)ease to make smooth string crossings
Expert 2
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Attack (consonants) (few ←→ many)timbre of transients
3 Playing at the frog (difficult ←→ easy)ease to play at the frog
4 String crossings (difficult ←→ easy)ease to make smooth string crossings
Expert 2
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Spectrum (less rich ←→ more rich)timbre on long notes
3 Consonant (softer ←→ harder)timbre of transients
4 Reactivity (slow ←→ rapid)time necessary to produce the tone
5 Spring (little ←→ much)ability to separate notes
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Attack (consonants) (few ←→ many)timbre of transients
3 Playing at the frog (difficult ←→ easy)ease to play at the frog
4 String crossings (difficult ←→ easy)ease to make smooth string crossings
Expert 2
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Spectrum (less rich ←→ more rich)timbre on long notes
3 Consonant (softer ←→ harder)timbre of transients
4 Reactivity (slow ←→ rapid)time necessary to produce the tone
5 Spring (little ←→ much)ability to separate notes
descriptors relative to playability and tonal qualities
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Verbalization
Expert 1
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Attack (consonants) (few ←→ many)timbre of transients
3 Playing at the frog (difficult ←→ easy)ease to play at the frog
4 String crossings (difficult ←→ easy)ease to make smooth string crossings
Expert 2
1 Stability (unstable ←→ stable)bow doesn’t tremble on long notes
2 Spectrum (less rich ←→ more rich)timbre on long notes
3 Consonant (softer ←→ harder)timbre of transients
4 Reactivity (slow ←→ rapid)time necessary to produce the tone
5 Spring (little ←→ much)ability to separate notes
descriptors relative to playability and tonal qualities
2 descriptors common to both experts: stability and attack
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 42 / 50
Playing tests
Pair-wise comparison task
For each configuration to be tested
prepare the bow
picture
play & compareagainst reference bow
evaluate
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 43 / 50
Playing tests
Pair-wise comparison task
For each configuration to be tested
After the test
prepare the bow
picture
objective data subjective data
play & compareagainst reference bow
evaluate
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 43 / 50
Playing tests
Pair-wise comparison task
For each configuration to be tested
After the test
prepare the bow
picture
objective data subjective data
play & compareagainst reference bow
evaluate
correlations?
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 43 / 50
Playing tests
Results
Significant correlations
Expert 1 | r = −0.83
atta
ques
(conso
nnes
)
jeu au talon−1 0 1
−1
0
1
playing at the frog | attack
(subjective – subjective)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 44 / 50
Playing tests
Results
Significant correlations
Expert 1 | r = −0.83
atta
ques
(conso
nnes
)
jeu au talon−1 0 1
−1
0
1
Expert 2 | r = 0.91
tensi
on
T0
(N)
reactivite au geste−1 0 1
30
40
50
60
70
80
playing at the frog | attack
(subjective – subjective)
hair tension | reactivity
(objective – subjective)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 44 / 50
Playing tests
Results
Significant correlations
Expert 1 | r = −0.83
atta
ques
(conso
nnes
)
jeu au talon−1 0 1
−1
0
1
Expert 2 | r = 0.91
tensi
on
T0
(N)
reactivite au geste−1 0 1
30
40
50
60
70
80
Expert 1 | r = 0.78
tensi
on
T0
(N)
attaques (consonnes)−1 0 1
30
40
50
60
70
80
playing at the frog | attack
(subjective – subjective)
hair tension | reactivity
(objective – subjective)
hair tension | attack
(objective – subjective)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 44 / 50
Playing tests
Results
Significant correlations
Expert 1 | r = −0.83
atta
ques
(conso
nnes
)
jeu au talon−1 0 1
−1
0
1
Expert 2 | r = 0.91
tensi
on
T0
(N)
reactivite au geste−1 0 1
30
40
50
60
70
80
Expert 1 | r = 0.78
tensi
on
T0
(N)
attaques (consonnes)−1 0 1
30
40
50
60
70
80Expert 2 | r = 0.82
tensi
on
T0
(N)
consonne−1 0 1
30
40
50
60
70
80
playing at the frog | attack
(subjective – subjective)
hair tension | reactivity
(objective – subjective)
hair tension | attack
(objective – subjective)→ result common to both players
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 44 / 50
Playing tests
Playing tests: Conclusions
✔ Influence of hair tension on player’s peception
reactivity
attacksր with hair tension
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 45 / 50
Playing tests
Playing tests: Conclusions
✔ Influence of hair tension on player’s peception
reactivity
attacksր with hair tension
✘ Stability
instability = trembling bow? → find relevant dynamic property
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 45 / 50
Playing tests
Playing tests: Conclusions
✔ Influence of hair tension on player’s peception
reactivity
attacksր with hair tension
✘ Stability
instability = trembling bow? → find relevant dynamic property
instability = buckling? → tests with bows of lower stiffness
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 45 / 50
Playing tests
Playing tests: Conclusions
✔ Influence of hair tension on player’s peception
reactivity
attacksր with hair tension
✘ Stability
instability = trembling bow? → find relevant dynamic property
instability = buckling? → tests with bows of lower stiffness
✔ Characterization of bows for the test
differences in bow properties
state in which the bow is played
}
are well determined
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 45 / 50
Conclusions & perspectives
Introduction
1 Modelling
2 Experimental characterization
3 ResultsStatic behaviorStability
4 Playing tests
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 46 / 50
Conclusions & perspectives
Conclusion
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 47 / 50
Conclusions & perspectives
Conclusion
static behavior of the bow strongly depends on prestress
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 47 / 50
Conclusions & perspectives
Conclusion
static behavior of the bow strongly depends on prestress
bow played near its limit of stability
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 47 / 50
Conclusions & perspectives
Conclusion
static behavior of the bow strongly depends on prestress
bow played near its limit of stability
camber has a strong influence on
{playing hair tensioncompliancelimit of stability
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 47 / 50
Conclusions & perspectives
Conclusion
static behavior of the bow strongly depends on prestress
bow played near its limit of stability
camberր
has a strong influence on
{playing hair tension րcompliance րlimit of stability ց
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 47 / 50
Conclusions & perspectives
Perspectives
NUMERICAL MODELS + PROCEDURE TO DETERMINE BOW PROPERTIES
predictive using affordable and easy-to-use equipment
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 48 / 50
Conclusions & perspectives
Perspectives
NUMERICAL MODELS + PROCEDURE TO DETERMINE BOW PROPERTIES
predictive using affordable and easy-to-use equipment
Assistance to bow making
Characterization in workshop
Prediction upstream from fabrication or adjustment
Looking for alternative woods
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 48 / 50
Conclusions & perspectives
Perspectives
NUMERICAL MODELS + PROCEDURE TO DETERMINE BOW PROPERTIES
predictive using affordable and easy-to-use equipment
Assistance to bow making
Characterization in workshop
Prediction upstream from fabrication or adjustment
Looking for alternative woods
Organology
Categorization of bows in museums
Information on bows in playing situation
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 48 / 50
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Perceptive studies+
Measurement of gesture
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Perceptive studies+
Measurement of gesture
Dynamic properties
How do they affect the tone?
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Perceptive studies+
Measurement of gesture
Dynamic properties
How do they affect the tone?
Influence on string motion?
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
static & dynamic properties
transient & spectrum
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Perceptive studies+
Measurement of gesture
Dynamic properties
How do they affect the tone?
Influence on string motion?
Identify “signature” of the bow
Conclusions & perspectives
Perspectives
playability
tonal qualities
TT
?
?
static & dynamic properties
transient & spectrum
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 49 / 50
Dynamic properties
How do they affect playability?
Perceptive studies+
Measurement of gesture
Dynamic properties
How do they affect the tone?
Influence on string motion?
Identify “signature” of the bow
Role of damping?
Conclusions & perspectives
influence of mechanical and geometrical parameters
on the static behavior of a violin bow
in playing situation
Frederic Ablitzer
Laboratoire d’Acoustique de l’Universite du Maine – UMR CNRS 6613
PhD defence
Le Mans, France – December 5th, 2011
Examining committee
A. Askenfelt | KTH, Stockholm (Examiner) B. Cochelin | LMA, Marseille (Reviewer)R. Causse | IRCAM, Paris (Reviewer) J.P. Dalmont | LAUM, Le Mans (Supervisor)
A. Chaigne | ENSTA ParisTech, Palaiseau (Chairman) N. Dauchez | SUPMECA, Saint-Ouen (Supervisor)
G. Chevallier | SUPMECA, Saint-Ouen (Examiner) N. Poidevin | Bow maker, Dinan (Invited)
Frederic Ablitzer (PhD defence) Universite du Maine December 5th, 2011 50 / 50