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Introduction | |

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Why Another Book about Mechanical Vibrations? | |

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A Short Overview of Theory | |

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Single Degree of Freedom (sdof) Systems | |

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Damped Vibrations | |

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Multi-Degrees of Freedom (mdof) Dynamic Systems | |

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Modal Analysis | |

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Modal Effective Mass | |

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Response Analysis | |

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Transient Response Analysis | |

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Random Vibrations | |

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Shock-Response Spectrum | |

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Acoustic Loads, Structural Responses | |

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Statistical Energy Analy sis | |

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Inertia-Relief | |

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Mode Acceleration Method | |

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Residual Vectors | |

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Dynamic Model Reduction | |

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Component Model Synthesis | |

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Load Transformation Matrices | |

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Problems | |

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Problem 1 | |

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Single Degree of Freedom System | |

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Introduction | |

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Undamped Sdof System | |

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Solution of an Sdof System with Initial Conditions | |

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Solution of an Sdof System with Applied Forces | |

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Damped Vibration and the Damping Ratio | |

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Solution of the Sdof System in the Time Domain | |

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Solution of the Damped Sdof System with Applied Forces | |

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Solution in the Frequency Domain | |

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State Space Representation of the Sdof System | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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Problem 5 | |

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Problem 6 | |

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Problem 7 | |

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Problem 8 | |

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Damping Models | |

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Introduction | |

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Damped Vibration50 | |

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Linear Damping | |

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Viscous Damping | |

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Structural Damping | |

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Loss Factor | |

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Amplification Factor | |

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Modal Viscous Damping | |

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Modal Structural Damping | |

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Discussion of Modal Damping | |

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Method of Determining Damping from Measurements | |

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The Half-Power Point Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Multi-Degrees of Freedom Linear Dynamic Systems | |

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Introduction | |

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Derivation of the Equations of Motion | |

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Undamped Equations of Motion with Newton's Law | |

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Undamped Equations of Motion using Energies | |

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Undamped Equations of Motion using Lagrange's Equations | |

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Damped Equations of Motion using Lagrange's Equations | |

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Finite Element Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Modal Analysis | |

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Introduction | |

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Undamped Linear Dynamic Systems | |

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Natural Frequencies and Mode Shapes | |

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Orthogonality Relations of Modes | |

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Rigid-Body Modes | |

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Left Eigenvectors | |

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Damped Linear Dynamic Systems | |

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The State Vector | |

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Eigenvalue Problem | |

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Eigenvectors | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Natural Frequencies, an Approximation | |

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Introduction | |

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Static Displacement Method | |

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Ray leigh's Quotient | |

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Dunkerley's Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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Problem 5 | |

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Modal Effective Mass | |

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Introduction | |

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Enforced Acceleration | |

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Modal Effective Masses of an Mdof System | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Response Analysis | |

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Introduction | |

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Forces and Enforced Acceleration | |

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Relative Motions | |

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Absolute Motions | |

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Large-Mass Approach | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Transient-Response Analysis | |

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Introduction | |

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Numerical Time Integration | |

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Discrete Solution Convolution Integral | |

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Explicit Time-Integration MethopP155 | |

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Implicit Time-Integration Methods | |

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Stability | |

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Explicit Time-Integration | |

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Central Difference Method | |

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Runge-Kutta Formulae for First-Order Differential Equations | |

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Runge-Kutta-Nystrom Method for S-O Differential Equations | |

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Implicit Time Integration | |

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Houbolt Method | |

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Wilson theta Method | |

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Newmark-beta Method | |

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The Hughes, Hilber and Taylor (HHT) alpha-Method | |

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The Wood, Bossak and Zienkiewicz (WBZ) alpha-Method | |

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The Generalised-alpha Algorithm | |

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Piecewise Linear Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Shock-Response Spectrum | |

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Introduction | |

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Enforced Acceleration | |

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Numerical Calculation of the SRS, the Piecewise Exact Method | |

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Response Analysis in Combination with Shock-Response Spectra | |

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Matching Shock Spectra with Synthesised Time Histories | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Random Vibration of Linear Dynamic Systems | |

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Introduction | |

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Random Process | |

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Power-Spectral Density | |

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Deterministic Linear Dynamic System | |

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Force-Loaded Sdof System | |

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Enforced Acceleration | |

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Multi-Inputs and Single Output (MISO) | |

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Deterministic Mdof Linear Dynamic System | |

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Random Forces | |

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Random Base Excitation | |

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Random Stresses and Forces | |

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Analysis of Narrow-Band Processes | |

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Crossings | |

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Fatigue Damage due to Random Excitation | |

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Some Practical Aspects | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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Problem 5 | |

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Low-Frequency Acoustic Loads, Structural Responses | |

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Introduction | |

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Acoustic Loads | |

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Equations of Motion | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Statistical Energy Analysis | |

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Introduction | |

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Some Basics about Averaged Quantities | |

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Two Coupled Oscillators | |

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Multimode Subsystems | |

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SEA Parameters | |

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Subsystem Modal Densities | |

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Source Power Input | |

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Subsystem Energies | |

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Damping Loss Factor | |

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Coupling Loss Factor | |

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Stresses and Strains | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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Problem 5 | |

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Problem 6 | |

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Problem 7 | |

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Problem 8 | |

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Free-free Dynamic Systems, Inertia Relief | |

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Introduction | |

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Relative Motion | |

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Relative Forces | |

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Flexibility Matrix | |

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Problems | |

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Problem 1 | |

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Mode Acceleration Method | |

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Introduction | |

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Decomposition of Flexibility and Mass Matrix | |

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Decomposition of the Flexibility Matrix | |

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Decomposition of the Mass Matrix | |

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Convergence Properties of Reconstructed Matrices | |

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Mode Acceleration Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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Problem 5 | |

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Introduction | |

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Residual Vectors | |

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Dickens Method | |

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Rose Method | |

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Problems | |

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Problem 1 | |

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Dynamic Model Reduction Methods | |

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Introduction | |

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Static Condensation Method | |

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Improved Calculation of Eliminated Dofs | |

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Dynamic Reduction | |

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Improved Reduced System (IRS) | |

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Craig-Bampton Reduced Models | |

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Generalised Dynamic Reduction | |

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System Equivalent Reduction Expansion Process (SEREP) | |

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Ritz Vectors | |

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Conclusion | |

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Introduction | |

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The Unified CMS Method | |

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Modal Truncation | |

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General Synthesis of Two Components | |

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General Example | |

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Special CMS Methods | |

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Craig-Bampton Fixed-Interface Method | |

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Free-Interface Method | |

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General-Purpose CMS Method | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Load Transformation Matrices | |

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Introduction | |

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Reduced Model with Boundary Conditions | |

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Reduced Free-Free Dynamic Model | |

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Continuous Dynamic Systems | |

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Problems | |

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Problem 1 | |

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Problem 2 | |

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Problem 3 | |

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Problem 4 | |

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References | |

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Author Index | |

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Subject Index | |