Applied Structural and Mechanical Vibrations: Theory and Methods, Second Edition, 2nd Edition (Hardback) book cover

Applied Structural and Mechanical Vibrations

Theory and Methods, Second Edition

By Paolo L. Gatti

© 2014 – CRC Press

668 pages | 107 B/W Illus.

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About the Book

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.


"… this book is a good reference book to have on the shelf to refresh your memory about some aspects of vibrations or to ?nd 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

Table of Contents

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




About the Author

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.

Subject Categories

BISAC Subject Codes/Headings:
ARCHITECTURE / Methods & Materials