2nd Edition

Applied Structural and Mechanical Vibrations Theory and Methods, Second Edition

By Paolo L. Gatti Copyright 2014
    668 Pages 107 B/W Illustrations
    by CRC Press

    668 Pages 107 B/W Illustrations
    by CRC Press

    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


    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


    Fourier series and Fourier transform

    Laplace transform

    Dirac delta and related topics

    The notion of Hilbert space

    Analytical mechanics: An overview


    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


    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


    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


    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


    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


    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


    The rayleigh quotient

    The Rayleigh–Ritz method

    Summary and comments

    Experimental modal analysis


    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


    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


    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





    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.

    "… this book is a good reference book to have on the shelf to refresh your memory about some aspects of vibrations or to find a reference to deepen your understanding. It is also a good book for people – like physicists or electrical engineers – who have a technical background but not in this area of mechanical engineering."
    —Noise Control Engineering Journal

    "The book is very well written and could be considered as quite different from earlier books on the topic, and can be recommended for graduate research level students as well as practicing engineers."
    Journal of Structural Engineering

    "An excellent addition to the literature. Upper-division undergraduates through professionals."

    "This reviewer recommends this book strongly for use in universities libraries and laboratories involved in vibration measurements."
    —Applied Mechanics Reviews

    "The book is well written and structured, and is a good reference book"
    —The Structural Engineer

    "This book provides students, researchers and engineers with a concise and comprehensive introduction to mechanical and structural vibrations. It gives methods for solving problems in this field of area but opens doors to experimental vibration analysis and random vibrations. …This book provides a background in techniques and methods and sounds guidelines and understanding of theoretical concepts in vibration analysis."
    —Christian Cremona, Sétra/CTOA, France