2nd Edition
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
Biography
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."
—Choice
"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