elastic wave

High Frequency Pyroshock ResponseHigh Frequency Pyroshock Response Predictions Using Elastic Wave Propagation FormulationFormulation

Shyh-Shiuh Mike Lih and Ali R. Kolainiy

Jet Propulsion Laboratory, California Institute of Technology June 2010

© The Aerospace Corporation 2010© The Aerospace Corporation 2010

IntroductionR li bl t l t t l di t th h k th ti Sh k• Reliable tools to accurately predict the shock responses over the entire Shock Response Spectrum (SRS) frequency are lacking

• Some methods of predictions used by the community are:Normal mode and finite element analysis– Normal mode and finite element analysis

• not effective for high frequency predictions– Empirical models

H it d t t ki i t t th tt ti d t di t d j i t• Heritage data taking into account the attenuation due to distance and joints– Statistical Energy Analysis

• Power and subsystem energy assumed to be time-dependent, accuracy not validatedvalidated

• An attempt is being made to develop a new method using the elastic wave propagation to model the high frequency pyroshock responses

– A linear elastic plate is used in the modeling to simulate the guided wave– A linear elastic plate is used in the modeling to simulate the guided wave propagation due to the pyroshock

– The predicted results are used to correlate with a series of shock data obtained using the JPL tunable beam shock simulation systemg y

– The preliminary predicted results indicate satisfactory correlations with the measured data

• The applicability of the elastic wave propagation method of analysis to the aerospace

2e-mail addressDepartment/subdivision name

structures will be discussed in some detail.

The Test Setup

JPL Resonant Beam

– The tunable beam consists of a 4-inch thick beam clamped at two ends, the span of which can be changed to obtain the desired knee frequencies

– The beam sits on a massive support structure anchored to several feet of concrete floor

– One quarter inch square steel rods are sandwiched between the clamp plates and the beam at all interfaces with damping pads sandwiched between the beam and rods. The square rods are used to minimize the beam and clamp contacts for better calibrating the knee frequencies

– Pads are used to damp out the high frequency shock waves – The robustness of the system is in generating shock signatures that produce

the desired knee frequencies ranging from a few hundred Hz to about 3000 Hz, with levels ranging from a few hundred peak g’s to more than 40k g’s,

d t i t tl ti d ibl h kand most importantly, generating re-producible shocks

A 1-inch Aluminum plate was used for shock testing and model correlation

Details of the setup can be found in Ref. 4.


Experimental Tunable BeamExperimental Tunable Beam

Projectile Tube

Test Area Strike Plate Sacrificial Strike Plate

Tube

Adjustable

Clamps

Adjustable Resonant Beam

Slugs


The Test DATA

East Vertical (4”x1”)

S Y

W

East Vertical (4 x1 )West North Vertical (6”x9”)North Vertical (0”x5”)South Vertical (9”x5 5/8”)Central Vertical (4”x5”) S

Center

N( )

E X

•5 Accelerometers used to acquire shock signatures on an aluminum plate

•Piranha II 32 channel system with a 200 kHz sampling rate used

•The data acquisition system consisted of a built-in analog filter that


The data acquisition system consisted of a built in analog filter that rolled off at 20 kHz

Formal Solution of the Dynamic Surface Load Problem Based on Linear Elastodynamic Model

The Surface Point Load Problem


Constitutive Equations

Frequency depend damping parameters


Multiple Fourier Transforms

are the horizontal wave numbers


Six-dimensional stress-displacement pvector {S} is introduced in the transformed domain.

{C+/ } are complex constants related to{C+/-} are complex constants related to the down going (+) and up going (-) waves within the plate.

th ti l bare the vertical wave numbers


The 12 unknowns will be determined from:

Details please see references 1-3.


Shock Source Signature Estimate Used in the Model

The impact loading input to the Linear Elastodynamic Model was estimated using• The time history of the measured acceleroemter placed at the center of the plate (slide 5) as shown below

•Assumed to be near the impact load •Only 1-msec data was used to eliminate the late wave arrivals and structural oscillation

7

108

109

1010

ctru

m1

2

3x 10

7

N)

106

107

10

Sou

rce

Forc

e Sp

ec

-3

-2

-1

0

Sou

rce

Forc

e(N

0 10 20 30 40 5010

4

105

Freq (KHz)0 50 100 150 200

-5

-4

Time (microsec)


source time history and spectrum

C l ti f th P di t d d M d Ti Hi t dCorrelation of the Predicted and Measured Time History and Spectral Levels

105

106East

6000

8000East

calculatedmeasured

103

104

c. S

pect

rum

0

2000

4000

AC

C. (

g)

0

101

102Acc

-6000

-4000

-2000

A

100 101100

Freq (KHz)

0 100 200 300 400 500 600-8000

Time (microsec)

(East Accelerometer)



105

106North

6000

8000North

calculatedmeasured

103

104

10

Spe

ctru

m

0

2000

4000

CC

. (g)

101

102Acc

. S

-6000

-4000

-2000

AC

100 101100

Freq (KHz)

0 100 200 300 400 500 600-8000

Time (microsec)

(North Accelerometer)



105

106South

6000

8000South

calculatedmeasured

103

104

Spe

ctru

m

0

2000

4000

CC

. (g)

101

102Acc

.

-6000

-4000

-2000

AC

100 101100

Freq (KHz)

0 100 200 300 400 500 600-8000

Time (microsec)

(South Accelerometer)



106West-N

8000West-N

calculated

104

105

trum2000

4000

6000

g)

measured

1

102

103

Acc

. Spe

ct

-4000

-2000

0

AC

C. (

g

100 101100

101

Freq (KHz)

0 100 200 300 400 500 600-8000

-6000

Time (microsec)

(West Accelerometer)


Correlation of the Predicted and Measured Time History and SRSCorrelation of the Predicted and Measured Time History and SRS (50 kHz filter applied to the data)

104

103

cele

ratio

n, g

102Acc

102 103 104101

Frequency, Hz

(South Accelerometer)


Correlation of the Predicted and Measured Time History and SRS (50 kHz filter applied to the data)

104

103

cele

ratio

n, g

102Acc

102 103 104101

Frequency, Hz

(North Accelerometer)


Concluding Remarks

1. Preliminary results correlating the predicted shock responses using the wave propagation linear elastodynamic theory and p p g y ymeasurements were obtained• First attempt provided reasonable correlation with the

measured data• This method is applicable to high frequency regime

2. Future investigation is needed to firm up the applicability of this method to the aerospace structures • Controlled experiments with proper selections of test articles

with different configurations, boundary conditions, materials, d i h k t id tif b fit fand various shock sources are necessary to identify benefits of

this method

3 A bi d FEM t t f l f t t l it ti3. A combined FEM to account for low-frequency structural excitation and linear elastodynamics to account for high-frequency wave propagation will result from this effort


References

1. Mal, A.K., and Lih, S.-S., "Elastodynamic Response of a Unidirectional Composite Laminate to Concentrated Surface Loads: Part I", J. Appl. Mech., Vol. 59, pp. 878-886, December 1992., pp ,

2. Lih, S.-S., and Mal, A.K., "Elastodynamic Response of a Unidirectional Composite Laminate to Concentrated Surface Loads: Part II", J. Appl. Mech., Vol 59 pp 887 892 December 1992Vol. 59, pp. 887-892, December 1992.

3. Lih, S.-S., and Mal, A.K., "Elastic Waves From a Distributed Surface Source in a Unidirectional Composite Laminate", in Impact, Fracture and Waves, ASME-p , p , ,AMD-Vol. 205, pp. 209-219, 1995.

4. Ali Kolaini and Juan Fernandez, “JPL Tunable Beam Pyroshock Simulation System” The 2007 Spacecraft & Launch Vehicle Dynamic EnvironmentsSystem , The 2007 Spacecraft & Launch Vehicle Dynamic Environments Workshop, JUNE 26, 2007 , El Segundo, CA.

5. M. Gherlone, D. Lomario, M. Mattone, R. Ruotolo, “Application of wave pppropagation to pyroshock analysis,” Shock and Vibrations, Volume 11, Numbers 3-4/2004, pp. 1070-9622


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