## Elastokinetics: an introduction to the dynamics of elastic systems |

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### Contents

OF FREEDOM SYSTEM free vibrations | 7 |

some general observations | 25 |

DISCRETE SYSTEMS generalized coordinates | 35 |

Copyright | |

18 other sections not shown

### Common terms and phrases

amplitude approximate arbitrary assume base vectors boundary conditions called Chapter classical plate theory coefficient conclude consider constant corresponding curvilinear coordinates damping defined denote derive dimensionless disc dispersion relation displacement field eigenfunctions eigenvalues energy flux equations of motion Euler-Bernoulli beam Exercise expression Figure follows forced motion problem free vibration function given group velocity Hamilton's principle harmonic homogeneous boundary conditions inertia initial conditions integral isotropic iterated structure Lagrange's equations Lagrangian Lagrangian coordinates Laplace transforms linear load mass mechanical system medium mode shape natural frequencies normal coordinates normal mode obtain orthogonal oscillator particle phase velocity plane potential energy Reismann respectively result satisfy scalar second order tensor shear shown in Fig simply supported solution static strain energy strain tensor stress equations substitution surface theorem traveling waves unbounded values vanish wave motion wave number yields zero