Interrogative Simulation and Uncertainty Quantification of Multi-Disciplinary Systems

Transcription

1 Interrogative Simlation and Uncertainty Qantification of Mlti-Disciplinary Systems Ali H. Nayfeh and Mhammad R. Hajj Department of Engineering Science and Mechanics Virginia Polytechnic Institte and State University Blacksbrg, VA 406 Bifrcation and Model Redction Techniqes for Large Mlti-Disciplinary Systems University of Liverpool 6-7 Jne, 008

2 Backgrond Simlation, testing and prediction of the responses of mltidisciplinary systems are extremely difficlt - Nonlinear competing mechanisms (e.g. aeroelastic phenomena - Mltiple coexisting attractors, spercritical and sbcritical bifrcations, limit cycles, etc. Global Metrics - Fltter speed, LCO amplitde - Lift and drag forces on blff bodies - Pll-in voltage and displacement of MEMS - Dependence on physical parameters is not straightforward. Jne 008 A. H. Nayfeh & M. R. Hajj

3 Motivation Difficlt and expensive to se brte- force comptations to relate global response metrics to system parameters Need for redced-order models - Reprodce reslts of high-fidelity simlations or experiments - Relate global metrics to system parameters - Qantify system response ncertainties - Implement control strategies (flow control Physically motivated models - Make se of scientific principles, feasible for certain systems (simple strctres, Black-box models - No clear relation between physics and system (networks, - Match the behavior with that of a mathematical model Jne 008 A. H. Nayfeh & M. R. Hajj

4 Objective Interrogative Testing/Simlation and Uncertainty Qantification of Mlti-Disciplinary Systems Approach - Design the experiment/simlation to - Exploit specific behavior - Draw more information from data - Relate model featres to system dynamics Examples - System identification - Global metrics - Uncertainty qantification - Control (flow control Jne 008 A. H. Nayfeh & M. R. Hajj 4

5 System Identification HSCT FSM Test points and instability regions of the FSM Chimney region Sweep and dwell tests Jne 008 A. H. Nayfeh & M. R. Hajj 5

6 System Identification HSCT FSM M=0.7 Wing response to sweep excitation of control srface M=0.95 M=.0 Response is different in sbsonic, transonic and spersonic flow regimes. Exploitation of specific behavior in different regimes Jne 008 A. H. Nayfeh & M. R. Hajj 6

7 Exploitation of Nonlinearities Nonlinear Response Data Linear ID Nonlinear Parameters (Sensitivity & Physics Nonlinear Model Higher-Order Spectra Approximate Soltions Characterization Redced-Order Model Strctre Vibrations, Ship Motions, Lift and Drag on Cylinders Jne 008 A. H. Nayfeh & M. R. Hajj 7

8 System Identification F-5 tail Assembly Model Model - /6 dynamically scaled model m x 0.8 m x 0.48 m - Series of alminm channels, brass rings, composite plates, metal masses,... - Excitation - Monted on a 50-lb shaker - Exploit parametric resonance to maximize inflence of nonlinearities Identification Procedre - Series of experiments - Combination of approximate soltions for governing eqations and data analysis Control and effects of ncertainties Jne 008 A. H. Nayfeh & M. R. Hajj 8

9 System Identification Governing Eqations, : modal coordinates ( micro strains ( s, : natral freqencies (radian / s, : linear damping coefficients (radian / s, 4 : aerodynamic damping coefficients.(/ s, : coefficients of cbic nonlinearity (/ s^*s^, : transmissibility terms (/g*s^ k : copling term. (/s^ - k F cos Ω t τ 4 - k F cos Ω t τ Linear Identification: Freqency Response Fnctions f, f : 9.5 Hz, 9.05 Hz damping ratios: 0.04 and will also be identified from parametric excitation experiments Jne 008 A. H. Nayfeh & M. R. Hajj 9

10 System Identification Nonlinear Identification - k F cos Ω t τ 4 - k F cos Ω t τ Uncopled experiments one tail fixed (k=0; Mltiple scales a a a ' ' ' 8 T a 0 and a 4 ' 0 Fa 4 Steady state soltion a cos i t A( t e ( cc A Fa sin 4 ς α ς α , μ , μ 0 4 s s 57. με με, η 9588., η 0 ae i με 654. gs με,, 75. gs Jne 008 A. H. Nayfeh & M. R. Hajj 0

11 Jne 008 A. H. Nayfeh & M. R. Hajj System Identification Nonlinear Identification 4 cos - cos - Ω t τ F k Ω t τ F k K = 87 /s

12 Three-beam Frame Jne 008 cos( cos( e e t f t f A. H. Nayfeh & M. R. Hajj

13 Roll Instabilities in Ship Motions Data Sorce: Large-Amplitde-Motions Program ( LAMP Nonlinear Model: DOF: heave, pitch, roll Approximate Soltion: Method of Mltiple Scales Higher-order spectral analysis: spectral parameters and in particlar phase measrement Accont for mltiple phase qantities Jne 008 A. H. Nayfeh & M. R. Hajj

14 Roll Instabilities in Ship Motions m m 5 z z m m 5 55 m 44 [R k k 44 5 z z z k 44 k k 5 55 R c ] c c 5 z z f p c c [ V 5 55 cos( 4444 f f p zp t p X cos( cos( 4444 p ] p p t t zp p Jne 008 A. H. Nayfeh & M. R. Hajj 4

15 Lift on Stationary Circlar Cylinders Data Sorce: Nmerical simlation Nonlinear Model Represent response behavior Spectrm Lift Approximate Soltion: Method of Mltiple Scales Higher-order spectral analysis (trispectrm: spectral parameters and in particlar phase measrement Jne 008 A. H. Nayfeh & M. R. Hajj 5

16 Lift on Stationary Circlar Cylinders Jne 008 Lift Modeling and Approximate Soltion Rayleigh Eqation van der Pol Eqation / ( ( s s / ( ( s s 0 l l l l r r s 0 l l l l l v v s cos( cos( t a t a l s s r s cos( cos( t a t a l s s v s 6 A. H. Nayfeh & M. R. Hajj

17 F6 flight testing Relate global metrics to system parameters Amplitde (g LCO amplitde vs. Mach nmber Mach no. Constant α=0. α=0 α=.04 α=.04 Jne 008 A. H. Nayfeh & M. R. Hajj 7

18 Goland wing with Store Fltter Speed Beran et al, Nonlinear Dynamics 7: -9, The complex conjgate representing the second mode cross the imaginary axis transversely, and the instability is de to a Hopf bifrcation. Jne 008 A. H. Nayfeh & M. R. Hajj 8

19 Goland wing with Store Fltter speed variations with ncertainties in damping Variations in fltter speed de to ncertainties in the damping parameters k and k Jne 008 A. H. Nayfeh & M. R. Hajj 9

20 Goland wing with Store Nonlinear parameter ncertainty Variations in the fltter speed de to ncertainties in other parameters Parameters Uncertainty and Effects on Global Measres Nonlinear analysis Jne 008 A. H. Nayfeh & M. R. Hajj 0

21 ROM of the Velocity Field Project Navier-Stokes eqation onto the POD modes ROM (M =0, Re=00 Ordinary-differential eqations Nonlinear system Linear stability eigenvales Pair in right-half plane Hopf bifrcation Im Re

22 Actators Placement Pressre POD - Eigenvales Use dominant mode Optimm location Re=00

23 Control of vortex shedding Jne 008 A. H. Nayfeh & M. R. Hajj

24 Smmary System characterization and ROM development throgh exploitation of physical behavior Flight testing: Combination of nderstanding of physical behavior and data analysis to develop a model with parameters that depend on system variables and system characterization Goland wing store Modeling stages Uncertainty qantification framework Use of ROM derived physical characteristics to control vortex shedding Jne 008 A. H. Nayfeh & M. R. Hajj 4