## Principles and Techniques of VibrationsThisbook will be of interest to mechanical engineers, aerospace engineers, and engineering science and mechanics faculty. The main objective of the book is to present a mathematically rigorous approach to vibrations, one that not only permits efficient formulations and solutions to problems, but also enhances understanding of the physics of the problem. The book takes a very broad view approach to the subject so that the similarity of dynamic characteristics of vibrating systems will be understood. |

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### Contents

Principles of Newtonian and Analytical Dynamics | 50 |

SingleDegreeofFreedom Systems | 103 |

MultiDegreeofFreedom Systems | 140 |

Copyright | |

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### Common terms and phrases

admissible functions algorithm axes boundary conditions boundary-value problem coefficients column comparison functions complex component computed considering Eq constant constraint convergence coordinates defined denote Derive the response differential eigenvalue problem differential equation discrete-time displacement eigenfunctions eigensolutions eigenvalue problem eigenvectors equations of motion equilibrium points Example excitation finite element method first-order forces given by Eq Hamilton's principle Hence Householder's method Inserting Eqs interpolation functions Introducing Eq inverse inverse iteration Jacobi method kinetic energy Lagrange's equations Laplace transformation linear combination mass matrices membrane modal modes Moreover natural frequencies obtain orthogonal orthonormal parameters polynomials positive definite potential energy Rayleigh-Ritz method Rayleigh's quotient real symmetric matrix represents rigid-body rotation satisfy self-adjoint shown in Fig simply solution of Eq solve the eigenvalue spring stiffness and mass stiffness matrix substructure symmetric matrix system of Problem theorem transition matrix tridiagonal vector velocity vibration write zero