J. Jaap Wijker

Random Vibrations in Spacecraft Structures Design (eBook, PDF)

Theory and Applications

• Format: PDF

Produktbeschreibung

This book treats the random mechanical and acoustical vibrations of deterministic and statistical dynamic systems, in the low and high frequency range. The following topics are discussed in great detail:

Vibrations of deterministic linear mechanical dynamic systems exposed to mechanical random loads and or enforced motion (acceleration); Vibrations of deterministic linear mechanical dynamic systems exposed to random acoustic loads (sound pressures; Random vibration of statistically defined mechanical systems and loads using Statistical Energy Analysis (SEA); Non-linear structures excited to random (white noise) mechanical loads analyzed by using the Fokker-Planck-Kolgomorov (FPK) equation.

The theory of random vibration is strongly related to the design of spacecraft structures and is illustrated with simple and more difficult worked examples; each section ends with posed problems; usually answers are provided.

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Produktdetails

• Verlag: Springer Netherlands
• Seitenzahl: 516
• Erscheinungstermin: 19. August 2009
• Englisch
• ISBN-13: 9789048127283
• Artikelnr.: 37412402

Inhaltsangabe

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

Rezensionen

From the reviews: "This text provides an excellent introduction to the wide range of topics required in vibration and acoustic engineering. ... It allows the working engineer to get good in depth coverage of the features without the excessive details other texts have. I recommend this book for the practicing engineer as well as students, it meets its purpose of providing the theory as well as practical applications for mechanical and acoustics vibrations of dynamic systems and how that applies to spacecraft design engineering." (Timothy J. Copeland, Noise Control Engineering Journal, Vol. 58 (5), September-October, 2010)