Random Vibrations in Spacecraft Structures Design

1 Introduction; 1.1 General; 1.2 Mechanical Random Vibration; 1.3 Acoustic Random Vibration; 1.4 Statistical Energy Analysis; 1.5 Fokker-Planck-Kolgomorov Equation; Part I Mechanical Random Vibration; 2 Random Vibration Linear Systems; 2.1 Introduction; 2.2 Probability; Problems; 2.3 Random Proces; 2.3.1 Power Spectral Density; 2.3.2 Measurement PSD; 2.3.3 Discrete Fourier Transform; 2.3.4 Evaluation of Autocorrelation Function; 2.3.5 Evaluation of PSD; 2.3.6 Digital Simulation of Random Process; Problems; 2.4 Deterministic Linear Dynamic Systems; 2.4.1 Force Loaded SDOF System; 2.4.2 SDOF with Enforced Acceleration; 2.4.3 Multi-inputs and Single Output(MISO); 2.4.4 Unit Load Random Vibration Responses; Problems; 2.5 Deterministic MDOF Linear Dynamic Systems; 2.5.1 Random Forces; 2.5.2 MDOF system loaded by random enforced acceleration; 2.5.3 Random Forces and Stresses; Problems; 2.6 Complex Modal Analysis, Lyapunov's Equation; 2.6.1 State-Space Equation; 2.6.2 Enforced Acceleration; 2.6.3 Derivation Miles' Equation; 2.6.4 Power transfer between two oscillators; 2.6.5 Augmented State-Space Equation under Non-White Excitation; Problems; 2.7 Limit Load Factors; 2.7.1 Introduction; 2.7.2 Equations of Motion 2 SDOF System; 2.7.3 Frequency Transfer Function; 2.7.4 Random Responses; 2.7.5 Feedback Factor; 2.7.6 Limit Load Factors; 2.8 Force-Limit Prediction Methods; 2.8.1 Introduction; 2.8.2 Simple Coupled Two SDOF System; 2.8.3 Complex coupled two SDOF system; 2.8.4 Semi-Empirical Method; Problems; 2.9 Analysis of Narrow{band Processes; 2.9.1 Crossings; 2.9.2 Peaks; 2.9.3 Fatigue Damage due to Random Loads; Problems; 2.10 Wide-Band Fatigue Damage; Problems; 2.11 Practical Aspects Enforced Acceleration; Problems; 2.12 3-Sigma Strength Verification; 2.12.1 Strength Verification; 2.12.2 Estimation of Payload Random Vibration Load Factors for Structure Design; 2.12.3 Random Vibration Input Reduction; 2.12.4 Acceleration Response Curve; 2.12.5 Random Response Spectrum; 2.12.6 Relating Random to Sinusoidal Vibration; 2.12.7 Method for Calculating rms Von Mises Stress; Problems; 2.12.8 Random Vibration Component Test Specification; 2.13 Random Responses Analysis in the Time Domain; 2.13.1 introduction; 2.13.2 Simulation of the Random Time Series; Problems; Part II Acoustic Random Vibration; 3 Low Frequency Acoustic Loads; 3.1 Introduction; 3.2 Acoustic Loads; Problems; 3.3 Response Analysis; Problems; 3.4 Modal Damping; 3.5 Simpli ??ed Acoustic Response Analysis; 3.5.1 Introduction; 3.5.2 Acoustic loads transformed into mechanical random vibrations; 3.5.3 The Stress in an Acoustically Loaded Panel; 3.5.4 Acoustic and Random Vibration Test Tailoring; Problems; 3.6 Fluid Structure Interaction; 3.6.1 Introduction; 3.6.2 Wave Equation; 3.6.3 Pressure Structure Interaction; 3.6.4 Structural Responses; Part III Statistical Energy Analysis; 4 Statistical Energy Analysis; 4.1 Introduction; 4.2 Some Basics about Averaged Quantities; 4.3 Two Coupled Oscillators; 4.4 Multimode Systems; 4.5 SEA Parameters; 4.5.1 Dissipation Loss Factor; 4.5.2 Coupling Loss Factor; 4.5.3 Modal densities; 4.5.4 Subsystem Energies; 4.5.5 Source Power inputs; 4.5.6 Stresses and Strains ; 4.6 Applications; 4.6.1 Panel in an Acoustic Field; 4.6.2 Sandwich Panels; 4.7 Test-Based SEA Equations; 4.8 SEA Strategy; Problems; Part IV Fokker-Planck-Kolgomorov Method or Diffusion Equation Method; 5 Fokker-Planck-Kolmogorov Method or Diffusion Equation Method; 5.1 Introduction; 5.2 Probability Theory; 5.3 Markoff Process; 5.4 Smoluchowki or Chapman-Kolmogorov Equation; 5.5 Derivation Fokker-Planck-Kolmogorov Equation; 5.5.1 Calculation of FPK Equation coefficients; 5.5.2 Exact Stationary Response Solutions of Nonlinear Dynamic Systems; 5.6 Ito-Stratonovich Dilemma in Stochastic Processes; 5.7 Behavior of Linear Systems with Random Parametric Excitation; 5.7.1 Moments and Autocorrelation; 5.8 Generation FPK Equation for MDOF systems Problems; 5.9 Numerical solution of the FPK equation; 5.9.1 Solution of the FPK equation by the Finite Element Method; 5.9.2 General Finite Element Approach Problems ; 5.9.3 Solution of the FPK equation by the Finite Difference Method Problems; 5.10 Applications; 5.10.1 Vibrating Thin plates exposed to Acoustic Loads; 5.10.2 Stochastic Analysis of Two Dimensional Nonlinear Panels with Structural Damping under Random Pressures ; A Simulation of the Random Time Series; Problems; B Tables of Integrals; B.1 Approximations of Inverse Transform of the Standard Normal; B.2 Integrals of Probability Density Functions; C Some Fourier Transforms; Problems; D Modal Effective Mass; Problems; E Thevenin's and Norton's Theorems for Equivalent Linear Mechanical System; Problems; F Lyapunov Equation; G Correlation Coefficients; H Approximations for the Joint Acceptance and Acoustic Response Analysis; H.1 Theory; Problems; I Simplification of Conductance; J Modal Density of Composite Sandwich Panels; J.1 Equation of motion; J.2 Modal Density; K Wave Propagation and Group Velocity; L Finite Difference Approximations for Various Orders; L.1 Introduction; L.2 Second Order Approximation; L.3 Fourth Order Approximation; L.4 Sixth Order Approximation; L.5 Eighth Order Approximation; L.5.1 Tenth Order Approximation; L.5.2 Stability; Problems; M The Galerkin Method; Problems; N Wiener Process, Stochastic Integrals, Stochastic Differential Equations; N.1 Wiener Process; N.2 It^o versus Stratonovich; N.3 Stochastic Integrals; N.3.1 Correlation Function; Problems; O Glossary; References; Index