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
Today s topics CAV 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 April 2015 2/12
Other Student Projects CAV 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 April 2015 3/12
CAV Flow-excited ribbed panel optimization 1 Principal Investigator: Matt Shaw, PhD student, Acoustics Dr. S.A. Hambric and Dr. R.L. Campbell, Advisors Sponsor: April 2015 4/12
CAV April 2015 5/12
Supersonic Nozzle Discharge Flow CAV April 2015 6/12
CFD LES Simulations CAV April 2015 7/12
Simulated Structural Response CAV April 2015 8/12
Simulated vs. Measured Structural Displacement CAV April 2015 9/12
Wavenumber Analysis CAV April 2015 10/12
Wavenumber Analysis Streamwise Excitation CAV April 2015 11/12
Wavenumber Analysis Negative Streamwise Excitation CAV April 2015 12/12
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
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 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 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 Kt ( αp + βpn ) = λ mt ( αp + βpn ) In case of mistuning, repeated eigenvalues split, and there are unique eigenvectors. Nodal Diameter Map Mode Localization Mode# 5 Mode# 19
Integrally Bladed Rotors (IBR) or Blisk Aerodynamically Efficient Reduced number of parts Blade to Blade Geometry Variations Very Low Damping 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
POD # 0-6 POD # 0-12 POD # 0-9 POD # 0-15 Continued.. 6
All POD used in MMDA POD# 0 to 17 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
damper force µ f F N stuck slip Blade Blade stuck x c stuck x slip µ f F N Idealized damper Idealized damper Ground Ground Blade-to-Ground damper Blade-to-Blade damper
x c x st = slip distance, = response of the tuned system when the friction dampers are fully stuck : R st = E[ xst 2 ] σ st = R st xst = Ast sin ωstt + Bst cosωstt 2 2 Ra st E[ Ast + Bst ], rms x st = 0. 5Ra µ R σ, R µ Ra σ, R a = ( ) st the mean and standard deviation of response variance the mean and standard deviation of mean-square amplitude
Friction Damping of Flutter Point 2 f 0 = 0 Point 1
CONCLUDING REMARKS MMDA: Accurate Reduced- Order Model for a Mistuned Bladed Rotor A Major Breakthrough in Mistuning Research Statistics of Forced Vibration Amplitudes via Random Permutations Reduced Order Model of a Multi-stage Bladed Rotor with Geometric Mistuning Design of Friction Dampers to Reduce Resonant Vibratory Stresses of Blades Sinusoidal Excitation and Random Excitations. Non-dimensional Slip Load is almost invariant to nature of excitation. Design of Friction Dampers to Mitigate Flutter in a Bladed Rotor