## Introduction to Finite Element Vibration AnalysisThis is an introduction to the mathematical basis of finite element analysis as applied to vibrating systems. Finite element analysis is a technique that is very important in modeling the response of structures to dynamic loads. Although this book assumes no previous knowledge of finite element methods, those who do have knowledge will still find the book to be useful. It can be utilised by aeronautical, civil, mechanical, and structural engineers as well as naval architects. This second edition includes information on the many developments that have taken place over the last twenty years. Existing chapters have been expanded where necessary, and three new chapters have been included that discuss the vibration of shells and multi-layered elements and provide an introduction to the hierarchical finite element method. |

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### Contents

1 | |

19 | |

Introduction to the Finite Element Displacement Method | 45 |

Inplane Vibration of Plates | 119 |

Vibration of Solids | 148 |

Flexural Vibration of Plates | 192 |

Vibration of Stiffened Plates and Folded Plate Structures | 248 |

Vibration of Shells | 266 |

Analysis of Free Vibration | 316 |

Forced Response I | 357 |

Forced Response II | 413 |

Computer Analysis Techniques | 449 |

Equations of Motion of MultiDegree | 467 |

Answers to Problems | 473 |

479 | |

497 | |

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### Common terms and phrases

accuracy analysis analytical solution antisymmetric applied assumed beam element bending boundary conditions calculated cantilever Chapter coefﬁcients constant cross-section damping deﬁned deformation degrees of freedom density derived diagonal displacement functions eigenvalues eigenvectors energy expressions equation of motion equivalent nodal forces evaluated Example ﬁnite element ﬁrst ﬁxed free vibration freedom system Geometry given by equation gives global axes idealisation inertia and stiffness inertia matrix integration points kinetic energy linear load membrane mesh method middle surface modal mode shapes natural frequencies node points number of degrees obtained plane polynomial power spectral density quadratic rectangular element response Section shear strain shell element shown in Figure solving stiffness matrix strain energy stress structure Sturm sequence sub-triangle Substituting equation symmetric Table technique thickness tion transformation triangle triangular element values vectors virtual displacements zero