## Random Vibrations: Analysis of Structural and Mechanical SystemsThe topic of Introduction to Random Vibrations is the behavior of structural and mechanical systems when they are subjected to unpredictable, or random, vibrations. These vibrations may arise from natural phenomena such as earthquakes or wind, or from human-controlled causes such as the stresses placed on aircraft at takeoff and landing. Study and mastery of this topic enables engineers to design and maintain structures capable of withstanding random vibrations, thereby protecting human life. Introduction to Random Vibrations will lead readers in a user-friendly fashion to a thorough understanding of vibrations of linear and nonlinear systems that undergo stochastic random excitation. Provides over 150 worked out example problems and, along with over 225 exercises, illustrates concepts with true-to-life engineering design problems Offers intuitive explanations of concepts within a context of mathematical rigor and relatively advanced analysis techniques. Essential for self-study by practicing engineers, and for instruction in the classroom. |

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### Contents

body | 1 |

Chapter 2 Fundamentals of Probability and Random Variables | 11 |

Chapter 3 Expected Values of Random Variables | 59 |

Chapter 4 Analysis of Stochastic Processes | 103 |

Chapter 5 Time Domain Linear Vibration Analysis | 167 |

Chapter 6 Frequency Domain Analysis | 219 |

Chapter 7 Frequency Bandwidth and Amplitude | 261 |

Chapter 8 Matrix Analysis of Linear Systems | 307 |

Chapter 10 Introduction to Nonlinear Stochastic Vibration | 415 |

Chapter 11 Failure Analysis | 487 |

Chapter 12 Effect of Parameter Uncertainty | 557 |

back matter | 613 |

Appendix B Fourier Analysis | 617 |

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### Common terms and phrases

amplitude analysis autocorrelation function autocovariance function coefficients components conditional probability conditional probability density consider covariant stationary cumulative distribution function damping defined delta-correlated process denote derivative differential equation Dirac delta function equation of motion evaluate Example expected value Find finite Fokker-Planck equation Fourier transform frequency Gaussian process given gives impulse response impulse response function initial conditions integral linear system matrix mean and variance mean value mean-squared mean-zero method moments narrowband process nonlinear nonstationary Note obtain particular peak perturbation possible values probability density function probability distribution problem random variable Rayleigh approximation relationship response variance scalar SDF system second-moment situation spectral density state-space stationary process stationary response stochastic process uncertain parameters vector white noise zero ζω µ µ σ σ τ τ ω ω ω ωω