Engineering Vibrations

A thorough study of the oscillatory and transient motion of mechanical and structural systems, Engineering Vibrations, Second Edition presents vibrations from a unified point of view, and builds on the first edition with additional chapters and sections that contain more advanced, graduate-level topics. Using numerous examples and case studies to reinforce concepts, the author reviews basic principles, incorporates advanced abstract concepts from first principles, and weaves together physical interpretation and fundamental principles with applied problem solving. For each class of system, the text explores the fundamental dynamics and studies free and forced vibrations. This revised version combines the physical and mathematical facets of vibration, and emphasizes the connecting ideas, concepts, and techniques. What’s New in the Second Edition: Includes a section on the forced response of structurally damped one-dimensional continua Adds three new chapters: Dynamics of Two-Dimensional Continua, Free Vibration of Two-Dimensional Continua, and Forced Vibration of Two-Dimensional Continua Addresses the linear and geometrically nonlinear characterization of three-dimensional deformation for mathematically two-dimensional structures, and the dynamics and vibration of various types of structures within this class Covers deformation, dynamics, and vibration of membranes, of Kirchhoff plates, of von Karman plates, and of Mindlin plates Details a full development for the characterization of deformation and motion for mathematically two-dimensional continua Discusses the free and forced vibration of two-dimensional continua and the steady state response of two-dimensional continua with structural damping Engineering Vibrations, Second Edition offers a systematic and unified treatment of mechanical and structural vibrations, and provides you with a complete overview of vibration theory and analysis.

PRELIMINARIES Degrees of Freedom Equivalent Systems Springs Connected in Parallel and in Series A Brief Review of Complex Numbers A Review of Elementary Dynamics Concluding Remarks Bibliography Problems FREE VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS Free Vibration of Undamped Systems Free Vibration of Systems with Viscous Damping Coulomb (Dry Friction) Damping Concluding Remarks Bibliography Problems FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS – 1: PERIODIC EXCITATION Standard Form of the Equation of Motion Superposition Harmonic Forcing Structural Damping Selected Applications Response to General Periodic Loading Concluding Remarks Bibliography Problems FORCED VIBRATION OF SINGLE DEGREE OF FREEDOM SYSTEMS – 2: NONPERIODIC EXCITATION Two Generalized Functions Impulse Response Response to Arbitrary Excitation Response to Step Loading Response to Ramp Loading Transient Response by Superposition Shock Spectra Concluding Remarks Bibliography Problems OPERATIONAL METHODS The Laplace Transform Free Vibrations Forced Vibrations Concluding Remarks Bibliography Problems DYNAMICS OF MULTI-DEGREE OF FREEDOM SYSTEMS Newtonian Mechanics of Discrete Systems Lagrange’s Equations Symmetry of the System Matrices Concluding Remarks Bibliography Problems FREE VIBRATION OF MULTI-DEGREE OF FREEDOM SYSTEMS The General Free Vibration Problem and Its Solution Unrestrained Systems Properties of Modal Vectors Systems with Viscous Damping Evaluation of Amplitudes and Phase Angles Concluding Remarks Bibliography Problems FORCED VIBRATION OF MULTI-DEGREE OF FREEDOM SYSTEMS Introduction Modal Coordinates General Motion in Terms of the Natural Modes Decomposition of the Forced Vibration Problem Solution of Forced Vibration Problems Mode Isolation Rayleigh Damping Systems with General Viscous Damping Concluding Remarks Bibliography Problems DYNAMICS OF ONE-DIMENSIONAL CONTINUA Mathematical Description of 1-D Continua Characterization of Local Deformation Longitudinal Motion of Elastic Rods Torsional Motion of Elastic Rods Transverse Motion of Strings and Cables Transverse Motion of Elastic Beams Geometrically Nonlinear Beam Theory Translating 1-D Continua Concluding Remarks Bibliography Problems FREE VIBRATION OF ONE-DIMENSIONAL CONTINUA The General Free Vibration Problem Free Vibration of Uniform Second Order Systems Free Vibration of Euler-Bernoulli Beams Free Vibration of Euler-Bernoulli Beam-Columns Free Vibration of Rayleigh Beams Free Vibration of Timoshenko Beams Normalization of the Modal Functions Orthogonality of the Modal Functions Evaluation of Amplitudes and Phase Angles Concluding Remarks Bibliography Problems FORCED VIBRATION OF ONE-DIMENSIONAL CONTINUA Modal Expansion Decomposition of the Forced Vibration Problem Solution of Forced Vibration Problems Steady State Response of One-Dimensional Continua with Structural Damping Concluding Remarks Bibliography Problems DYNAMICS OF TWO-DIMENSIONAL CONTINUA Characterization of Local Deformation Membranes Elastic Plates Concluding Remarks Bibliography Problems FREE VIBRATION OF TWO-DIMENSIONAL CONTINUA The Scalar Product and Orthogonality The General Free Vibration Problem Free Vibration of Ideal Membranes Free Vibration of Kirchhoff Plates Free Vibration of Uniformly Stretched von Karman Plates Free Vibration of Mindlin Plates Normalization of the Modal Functions Orthogonality of the Modal Functions Evaluation of Amplitudes and Phase Angles Concluding Remarks Bibliography Problems FORCED VIBRATION OF TWO-DIMENSIONAL CONTINUA Mathematical Representation of Point Loads for Two-Dimensional Continua Forced Vibration of Systems with One Dependent Variable Forced Vibration of Systems with Multiple Dependent Variables: Mindlin Plates Steady State Response of Two-Dimensional Continua with Structural Damping Concluding Remarks Bibliography Problems INDEX

William J. Bottega is Professor of Mechanical and Aerospace Engineering at Rutgers University, where he has been since 1984. He received his Ph.D. in applied mechanics from Yale University, his M.S. in theoretical and applied mechanics from Cornell University, and his B.E. from the City College of New York. He also spent several years in R&D at General Dynamics where he worked on vibration and sound-structure interaction problems. In addition, Dr. Bottega is the author of numerous archival publications on various areas of theoretical and applied mechanics.