Mechanical Vibration

Abstract

Introduction and Background Basic Concepts of Systems and Structures Basic Concepts of Vibration Basic Concepts of Random Vibration Types of System Models Basic Dynamics Units Concluding Summary Single Degree-of-Freedom Vibration: Discrete Models Motivating Examples Mathematical Modeling: Deterministic Undamped Free Vibration Harmonic Forcing with no Damping Concepts Summary Single Degree-of-Freedom Vibration: Discrete Models with Damping Damping Free Vibration with Viscous Damping Free Response with Coulomb Damping Forced Vibration with Viscous Damping Forced Harmonic Vibration Periodic but Not Harmonic Excitation Concepts Summary Single Degree-of-Freedom Vibration: General Loading and Advanced Topics Arbitrary Loading: Laplace Transform Step Loading Impulsive Excitation Arbitrary Loading Introduction to Lagrange.s Equation Notions of Randomness Notions of Control The Inverse Problem A Self-Excited System and its Stability Solution Analysis and Design Techniques A Model of a Bouncing Ball Concepts Summary Single Degree-of-Freedom Vibration: Probabilistic Forces Introduction Example Problems and Motivation Random Variables Mathematical Expectation Useful Probability Densities Two Random Variables Random Processes Random Vibration Concepts Summary Vibration Control Motivation Approaches to Controlling Vibration Feedback Control Performance of Feedback Control Systems Control of Response Sensitivity to Parameter Variations State Variable Models Concepts Summary Variational Principles and Analytical Dynamics Introduction Virtual Work Lagrange.s Equation of Motion Hamilton's Principle Lagrange's Equation with Damping Concepts Summary Multi Degree-of-Freedom Vibration: Introductory Topics Example Problems and Motivation The Concepts of Stiness and Flexibility Derivation of Equations of Motion Undamped Vibration Direct Method: Free Vibration with Damping Modal Analysis Real and Complex Modes Concepts Summary Multi Degree-of-Freedom Vibration: Advanced Topics Overview Unrestrained Systems The Geometry of the Eigenvalue Problem Periodic Structures Inverse Vibration Sloshing of Fluids in Containers Stability of Motion Multivariable Control MDOF Stochastic Response Stochastic Control Rayleigh.s Quotient Monte Carlo Simulation Concepts Summary Continuous Models for Vibration Continuous Limit of a Discrete Formulation Vibration of String Longitudinal (Axial) Vibration of Beams Torsional Vibration of Shafts 10.5 Transverse Vibration of Beams 10.6 Beam Vibration: Special Problems Concepts Summary Continuous Models for Vibration: Advanced Models Vibration of Membranes Vibration of Plates Random Vibration of Continuous Structures Approximate Methods Variables That Do Not Separate Concepts Summary Nonlinear Vibration Examples of Nonlinear Vibration The Phase Plane Perturbation Methods The Mathieu Equation The van der Pol Equation Motion in the Large Nonlinear Control Advanced Topics Concluding Summary Appendices A Mathematical Concepts for Vibration Complex Numbers Matrices Taylor Series and Linearization Ordinary Dierential Equations Laplace Transforms Fourier Series and Transforms Partial Dierential Equations Index

The authors' abstract, as published at the source., 2017 · DOI ↗