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Penn State Center for Acoustics and Vibration (CAV)
Structural Vibration and Acoustics Group Presented as part of the 2015 CAV Spring workshop Stephen Hambric, Group Leader May 2015 Robert Campbell James Chatterley Stephen Conlon Tyler Dare John Fahnline Sabih Hayek
Tony Jun Huang Kevin Koudela Dan Russell Micah Shepherd Alok Sinha
2/12 April 2015
CAV Today’s topics
• Panel vibration and stress induced by supersonic jet flow • Matt Shaw, PhD student, and Dr. Steve Hambric
• Acoustic Tweezers • Li Peng, PhD student, and Dr. Tony Jun Hwang
• Turbine blade mistuning and friction damping • Dr. Alok Sinha
3/12 April 2015
CAV Other Student Projects
• Student posters: – Offshore wind turbine flow-induced vibration and structural
integrity • Javier Motta-Mena, MS; Dr. Robert L. Campbell, advisor
– Fluid-structure interaction modeling of blood clot migration and entrapment in the inferior vena cava
• Key Aycock, PhD, Dr. Rob Campbell, advisor
– Quiet structure design using embedded acoustic black holes • Phil Feurtado, PhD, Dr. Steve Conlon, advisor
• Just starting out: – Accelerated fatigue testing of composites
• Chet Kupchella, MS; Drs. Hambric and Campbell, advisors
– Nonlinear flow-induced structural damping • Trevor Jerome, PhD. Drs. Hambric and Shepherd, advisors
4/12 April 2015
CAV
Flow-excited ribbed panel optimization1
Principal Investigator: Matt Shaw, PhD student, Acoustics Dr. S.A. Hambric and Dr. R.L. Campbell, Advisors
Sponsor:
5/12 April 2015
CAV
6/12 April 2015
CAV Supersonic Nozzle Discharge Flow
7/12 April 2015
CAV CFD LES Simulations
8/12 April 2015
CAV Simulated Structural Response
9/12 April 2015
CAV Simulated vs. Measured Structural Displacement
10/12 April 2015
CAV Wavenumber Analysis
11/12 April 2015
CAV Wavenumber Analysis – Streamwise Excitation
12/12 April 2015
CAV Wavenumber Analysis – Negative Streamwise Excitation
Vibration of a Bladed Rotor : Mistuning and Friction
Damping
by
Alok Sinha Professor of Mechanical Engineering,
The Pennsylvania State University, University Park, 16802
http://en.wikipedia.org/wiki/File:Jet_engine.svg
Cyclic Symmetry is lost. Sector Analysis is not applicable
Variations in Blades Properties: Random Variables
Need to determine probability distribution functions of vibratory amplitudes
Monte Carlo Simulation
Importance of Mistuning Forced Vibratory amplitude of one blade can be 2-3 times amplitudes of other blades
Mode Localization: Connection with Anderson Localization
Analytical Complexities caused by Mistuning
Reduced Order Models are required which can accurately analyze a mistuned system without incurring the costs of full order model.
Eigenvectors are not unique for repeated eigenvalues
)()( −− +=+ ntnt mK pppp βαλβα
In case of mistuning, repeated eigenvalues split, and there are unique eigenvectors.
Mode Localization Nodal Diameter Map
Mode# 5 Mode# 19
Integrally Bladed Rotors (IBR) or Blisk
Blade to Blade Geometry Variations
Very Low Damping
Aerodynamically Efficient
Reduced number of parts
Damage in one blade may lead to replacement of the whole IBR
http://en.wikipedia.org/wiki/Blisk
A Major Breakthrough in Mistuning Research
MMDA (Modified Modal Domain Analysis) – proper orthogonal decomposition of
Coordinate Measurement Machine (CMM) data on blades’geometries
– sector analyses using ANSYS and UNIGRAPHICS.
– Validated on an academic rotor at P&W
A. Sinha, “Reduced Order Modeling of a Bladed Rotor with Geometric Mistuning,” ASME Journal of Turbomachinery, Vol. 131, July 2009
6
Continued…..
POD # 0-6 POD # 0-9
POD # 0-12 POD # 0-15
POD# 0 to 17
All POD used in MMDA
7
Transonic Rotor Random Permutation/Monte Carlo test
Computation of the Optimal Normal Load for a Mistuned and Frictionally Damped Bladed Disk Assembly
under Different Types of Excitation
Deterministic Sinusoidal Excitation
White Noise
Narrow Band Random Excitation
Sinusoidal Excitation with Random Amplitudes
Blade
Ground
Idealized damper
Blade-to-Ground damper
Idealized damper
Ground
Blade
Blade-to-Blade damper
x
damper force
µ f NF
−µ f NF
xc
slip
slip
stuckstuck
stuck
cx = slip distance,
stx = response of the tuned system when the friction dampers are fully stuck
][ 2stst xER = stst R=σ
tBtAx ststststst ωω cossin +=
][ 22ststst BAERa += ( ) stst Raxrms 5.0=
the mean and standard deviation of response variance
Rµ Rσ, :
,
the mean and standard deviation of mean-square amplitude
, aRµ aRσ
Friction Damping of Flutter
00 =f
Point 2
Point 1
CONCLUDING REMARKS
MMDA: Accurate Reduced- Order Model for a Mistuned Bladed Rotor
Reduced Order Model of a Multi-stage Bladed Rotor with Geometric Mistuning
Design of Friction Dampers to Reduce Resonant Vibratory Stresses of Blades
Design of Friction Dampers to Mitigate Flutter in a Bladed Rotor
Statistics of Forced Vibration Amplitudes via Random Permutations A Major Breakthrough in Mistuning Research
Sinusoidal Excitation and Random Excitations.
Non-dimensional Slip Load is almost invariant to nature of excitation.