Applied Structural and Mechanical Vibrations Theory and Methods, Second Edition

The second edition of Applied Structural and Mechanical Vibrations: Theory and Methods continues the first edition’s dual focus on the mathematical theory and the practical aspects of engineering vibrations measurement and analysis. This book emphasises the physical concepts, brings together theory and practice, and includes a number of worked-out examples of varying difficulty and an extensive list of references. What’s New in the Second Edition: Adds new material on response spectra Includes revised chapters on modal analysis and on probability and statistics Introduces new material on stochastic processes and random vibrations The book explores the theory and methods of engineering vibrations. By also addressing the measurement and analysis of vibrations in real-world applications, it provides and explains the fundamental concepts that form the common background of disciplines such as structural dynamics, mechanical, aerospace, automotive, earthquake, and civil engineering. Applied Structural and Mechanical Vibrations: Theory and Methods presents the material in order of increasing complexity. It introduces the simplest physical systems capable of vibratory motion in the fundamental chapters, and then moves on to a detailed study of the free and forced vibration response of more complex systems. It also explains some of the most important approximate methods and experimental techniques used to model and analyze these systems. With respect to the first edition, all the material has been revised and updated, making it a superb reference for advanced students and professionals working in the field.

Review of some fundamentals Introduction The role of modelling (linear and nonlinear, discrete and continuous systems, deterministic and random data) Some definitions and methods Springs, dampers and masses Summary and comments Mathematical preliminaries Introduction Fourier series and Fourier transform Laplace transform Dirac delta and related topics The notion of Hilbert space Analytical mechanics: An overview Introduction Systems of material particles The principle of virtual work and d’Alembert’s principle: Lagrange’s and Hamilton’s equations Lagrange’s equations: Fundamental properties, some generalisations and complements Hamilton’s principle Small-amplitude oscillations Single degree of freedom systems Introduction Harmonic oscillator I: Free vibration Harmonic oscillator II: Forced vibration Damping in real systems, equivalent viscous damping Summary and comments More SDOF systems: Shock response, transient response and some approximate methods Introduction Time domain: Impulse response function and Duhamel integral Frequency and Laplace domains: Frequency response function and transfer function Generalised SDOF systems Rayleigh (energy) method and improved Rayleigh method Summary and comments Multiple degrees of freedom (MDOF) systems Introduction A simple undamped -DOF system: Free vibration Undamped n-DOF systems: Free vibration Eigenvalues and eigenvectors sensitivity analysis A few considerations on the structure and properties of the matrices M, K and C Unrestrained systems: Rigid-body modes Damped systems: Proportional and nonproportional damping Generalised and complex eigenvalue problems: Reduction to standard form Summary and comments More MDOF systems: Forced vibration and response analysis Introduction Mode superposition Harmonic excitation: Proportional viscous damping Time-domain and frequency-domain response Systems with rigid-body modes The case of nonproportional viscous damping MDOF systems with hysteretic damping A few remarks on other solution strategies: Laplace transform and direct integration Frequency response functions of a -DOF system Summary and comments Continuous systems Introduction The flexible string in transverse motion Free vibration of a finite string: Standing waves and normal modes Axial and torsional vibrations of rods Flexural (bending) vibrations of beams A two-dimensional continuous system: The flexible membrane The differential eigenvalue problem Bending vibrations of thin plates Forced vibration and response analysis: The modal approach Some final considerations: Alternative form of FRFs and the introduction of damping Summary and comments MDOF and continuous systems: Approximate methods Introduction The rayleigh quotient The Rayleigh–Ritz method Summary and comments Experimental modal analysis Introduction Experimental modal analysis: Overview of the fundamentals Modal testing procedures A few selected topics in experimental modal analysis Summary and comments Probability and statistics: Preliminaries to random vibrations Introduction On the concept of probability Probability: Axiomatic formulation and some results Random variables and distribution functions Random vectors More on conditional probability Convergences and the law of large numbers A few remarks on probability and statistics Stochastic processes and random vibrations Introduction The concept of random process Basic calculus of random processes Spectral representation of random processes Response of linear systems to random excitation Stationary narrowband processes: A few selected topics Summary and comments Appendices References Index

Paolo L. Gatti graduated in nuclear physics from the State University of Milano (Italy) and worked for 12 years for a private engineering company, where he became head of the vibration testing and data acquisition department. Since 2000, he has worked as an independent consultant in mechanical and structural vibrations, acoustics, and statistical analyses of experimental data. In these fields of activity, he is also an accredited technical consultant for the Court of Justice of Milan. He is also the author of Probability Theory and Mathematical Statistics for Engineers, published by Spon Press (Taylor & Francis Group) in 2005.