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.