Random Vibrations in Spacecraft Structures Design (eBook)

Theory and Applications

J. Jaap Wijker (Autor)

eBook Download: PDF

2009 | 2009
XIV, 516 Seiten
Springer Netherland (Verlag)
978-90-481-2728-3 (ISBN)

Infos

Random Vibration in Spacecraft Structures Design is based on the lecture notes 'Spacecraft structures' and 'Special topics concerning vibration in spacecraft structures' from courses given at Delft University of Technology. The monograph, which deals with low and high frequency mechanical, acoustic random vibrations is of interest to graduate students and engineers working in aerospace engineering, particularly in spacecraft and launch vehicle structures design.

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Random Vibration in Spacecraft Structures Design is based on the lecture notes "e;Spacecraft structures"e; and "e;Special topics concerning vibration in spacecraft structures"e; from courses given at Delft University of Technology. The monograph, which deals with low and high frequency mechanical, acoustic random vibrations is of interest to graduate students and engineers working in aerospace engineering, particularly in spacecraft and launch vehicle structures design.

Inhalt

Preface 7
Contents 8
Introduction 14
General 14
Random Mechanical Vibration 18
Random Acoustic Vibration 18
Statistical Energy Analysis 19
Fokker-Planck-Kolmogorov Equation 19
Part I Random Mechanical Vibration 20
Linear Random Vibration Systems 21
Introduction 21
Probability 21
Characteristic Function 25
Problems 26
Random Process 28
Power Spectral Density 32
White Noise 40
Measurement of PSD 42
Discrete Fourier Transform 43
Evaluation of the Autocorrelation Function 44
Evaluation of the PSD 44
Digital Simulation of a Random Process 47
Problems 47
Deterministic Linear Dynamic Systems 49
Force Loaded SDOF System 51
Problems 57
SDOF with Enforced Acceleration 58
Multi-Inputs and Single Output (MISO) 64
Unit Load Random Vibration Responses 65
Problems 66
Deterministic MDOF Linear Dynamic Systems 68
Random Forces 68
MDOF System Loaded by Random Enforced Acceleration 71
Random Forces and Stresses 74
Problems 80
Complex Modal Analysis, Lyapunov's Equation 82
State-Space Equation 82
Left Eigenvectors 86
Enforced Acceleration 86
Modal Reduction 90
Derivation of Miles' Equation 94
Power Transfer Between Two Oscillators 95
Augmented State-Space Equation under Non-White Excitation 99
First Companion Form 102
Problems 110
Limit Load Factors 116
Introduction 116
Equations of Motion 2 SDOF System 117
Frequency Transfer Function 119
Random Responses 120
Feedback Factor 121
Limit Load Factors 123
Force-Limit Prediction Methods 124
Introduction 124
Simple Coupled 2DOF System 125
Complex Coupled Two-SDOF System 132
Selection Modal Effective Mass and Residual Mass 139
Semi-Empirical Method 141
Problems 143
Analysis of Narrow-Band Processes 145
Crossings 146
Peaks 150
Fatigue Damage due to Random Loads 152
Problems 155
Wide-Band Fatigue Damage 158
Problems 161
Practical Aspects Enforced Acceleration 162
Spectrum with a Positive Slope 165
Flat Spectrum 165
Spectrum with a Negative Slope 165
Problems 167
3-Sigma Strength Verification 168
Strength Verification 169
Estimation of Payload Random Vibration Load Factors for Structure Design 172
Miles' Equation 172
Vibration Specifications 172
PSD integration over the Full Bandwidth 173
Half Power Point Approach 173
Mass Participation Approach 173
PSD Integration over a Reduced Bandwidth 174
Random Vibration Input Reduction 179
Acceleration Response Curve 182
Random Response Spectrum 183
Relating Random to Sinusoidal Vibration 184
Method for Calculating rms Von Mises Stress 187
Problems 195
Random Vibration Component Test Specification 197
Random Responses Analysis in the Time Domain 197
Introduction 197
Simulation of the Random Time Series 198
Problems 211
Part II Acoustic Random Vibration 213
Low Frequency Acoustic Loads 214
Introduction 214
Acoustic Loads 214
Problems 217
Response Analysis 218
Problems 228
Modal Damping 231
Simplified Acoustic Response Analysis 232
Introduction 232
Acoustic Loads Transformed into Mechanical Random Vibrations 232
The Stress in an Acoustically Loaded Panel 236
Acoustic and Random Vibration Test Tailoring 237
Base Excited SDOF System 239
Pressure Loaded SDOF System 240
Synthesis 242
Problems 243
Fluid Structure Interaction 244
Introduction 244
Wave Equation 244
Spherical Radiator 249
Pressure Structure Interaction 251
Structural Responses 252
Part III Statistical Energy Analysis 259
Statistical Energy Analysis 260
Introduction 260
Some Basics about Averaged Quantities 260
Two Coupled Oscillators 265
Multimode Systems 273
SEA Parameters 278
Dissipation Loss Factor 278
Plates 280
Sandwich Panels 280
Cylinders 281
Acoustic Room 281
Coupling Loss Factor 281
L-beam Structures Coupling Loss Factors 282
Plate-to-Plate Coupling Loss Factors 283
Acoustic Radiation 284
General 284
Plates 285
Stiffened Panels 288
Unstiffened Cylinder 289
Critical Frequency 290
Modal Densities 292
General 292
Composite Structure 292
General Structure 293
Bending Beam 293
Plates 294
Sandwich Panels 296
Unstiffened Cylinders 297
Acoustic Chamber 299
Modal Overlap 299
Subsystem Energies 300
Mechanical Subsystem 300
Acoustic Room 302
Source Power Inputs 303
Stresses and Strains 304
Non-resonant Response 306
Applications 308
Panel in an Acoustic Field 308
Sandwich Panels 308
Test-Based SEA Equations 313
Properties of Subsystem 2 (Panel) 317
Subsystems 1 and 3, Space 1 and Space 2 317
Coupling Loss Factors 318
Loss Factor 318
Experimental Determination of the Radiation Efficiency 318
SEA Strategy 321
Problems 322
Part IV Fokker-Planck-Kolmogorov Method or Diffusion Equation Method 330
Fokker-Planck-Kolmogorov Method or Diffusion Equation Method 331
Introduction 331
Probability Theory 332
Markoff Process 333
Smoluchowki or Chapman-Kolmogorov Equation 334
Derivation of the Fokker-Planck-Kolmogorov Equation 335
Stationary Solution 338
Calculation of FPK Equation Coefficients 343
Exact Stationary Response Solutions of Nonlinear Dynamic Systems 346
Stationary Solution FPK Equation of Conservative Systems 350
Second-Order System (SDOF) 350
High-Order System (MDOF) 352
Itô-Stratonovich Dilemma in Stochastic Processes 354
Itô and Stratonovich Approach for Integration 358
Itô Approach 358
Stratonovich Approach 358
Fokker-Planck-Kolmogorov Equation 360
MDOF Stochastic Differential Equations 362
Behavior of Linear Systems with Random Parametric Excitation 365
Moments and Autocorrelation 367
Mean 367
Autocorrelation Function 368
Second Moments and the Variance 368
Generation FPK Equation for MDOF Systems 370
Problems 373
Numerical Solution of the FPK Equation 381
Solution of the FPK Equation by the Finite Element Method 381
General Finite Element Approach 381
Solution 1-D Problem 388
Problems 392
Solution of the FPK Equation by the Finite Difference Method 394
Boundary Conditions Numerical Solution FPK Equation 398
Problems 400
Applications 402
Vibrating Thin Plates Exposed to Acoustic Loads 402
Introduction 402
Vibration Theory Thin Plates 402
Random Pressure Load 405
A SDOF Vibro-Impact System 407
Simulation of the Random Time Series 412
Problems 415
Tables of Integrals 416
Approximations of Inverse Transform of the Standard Normal 418
Integrals of Probability Density Functions 418
Some Fourier Transforms 420
Problems 423
Modal Effective Mass 424
Problems 428
Thevenin's and Norton's Theorems for Equivalent Linear Mechanical 431
Problems 434
Lyapunov's Equation 435
Correlation Coefficients 441
Approximations for the Joint Acceptance and Acoustic Response Analysis 444
Theory 444
Problems 451
Simplification of Conductance 454
Modal Density of Composite Sandwich Panels 456
Equation of Motion 456
Modal Density 458
Wave Propagation and Group Velocity 463
Relationship Modal Energy and Energy Striking the Boundary 468
Finite Difference Approximations for Various Orders 470
Introduction 470
Second Order Approximation 470
Fourth Order Approximation 471
Sixth Order Approximation 471
Eighth Order Approximation 471
Tenth Order Approximation 471
Stability 472
Problems 473
The Galerkin Method 474
Problems 478
Wiener Process, Stochastic Integrals, Stochastic Differential Equations 483
Wiener Process 483
Simulation of White Noise 484
Itô versus Stratonovich 485
Stochastic Integrals 490
Correlation Function 492
Problems 493
Glossary 495
References 500
Index 
514 

Produkt-Details

• Erscheint lt. Verlag: 19.8.2009
• Reihe/Serie: Solid Mechanics and Its Applications
• Reihe/Serie: Solid Mechanics and Its Applications
• Zusatzinfo: XIV, 516 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Fahrzeugbau / Schiffbau
• Themenwelt: Technik ► Luft- / Raumfahrttechnik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Aerospace • Aerospace Engineering • Design • Fokker-Planck-Kolgomorov Equation • random mechanical vibrations • random vibrations • spacecraft • space engineering • space instrument design • statistical energy analysis • Structures • vehicle structures • Vibration
• ISBN-10: 90-481-2728-9 / 9048127289
• ISBN-13: 978-90-481-2728-3 / 9789048127283