## Dynamics of structures |

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### Contents

Overview of Structural Dynamics | 1 |

Formulation of the Equation of Motion | 17 |

FreeVibration Response | 41 |

Copyright | |

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acceleration amplitude analysis approximation assumed shape autocorrelation function axial force beam column components computed considered constant coordinates corresponding damping matrix damping ratio defined deflection degrees of freedom derived Dirac delta function displacement displacement vector distribution Duhamel integral dynamic response earthquake earthquake-response effective energy ensemble equations of motion equilibrium equivalent evaluated example expressed in terms factor FIGURE first-mode flexural Fourier free vibrations free-vibration gaussian girder given by Eq ground motion harmonic increment inertia forces influence coefficients input integral iteration linear mass matrix MDOF method modal mode shapes nodal nonlinear normal noted obtained orthogonality power spectral density Prob probability density function procedure process x(t properties random process random variables relationship represents result rotational SDOF system shear shown in Fig solution spectral density function static stationary stationary process statistically independent stiffness coefficients stiffness matrix Substituting Eq transformation undamped uniform values vector velocity wave zero