Vibration Mechanics, 1991 Linear Discrete Systems

Objectives This book is used to teach vibratory mechanics to undergraduate engineers at the Swiss Federal Institute of Technology of Lausanne. It is a basic course, at the level of the first university degree, necessary for the proper comprehension of the following disciplines. Vibrations of continuous linear systems (beams, plates) random vibration of linear systems vibrations of non-linear systems dynamics of structures experimental methods, rheological models, etc. Effective teaching methods have been given the highest priority. Thus the book covers basic theories of vibratory mechanics in an ap­ propriately rigorous and complete way, and is illustrated by nume­ rous applied examples. In addition to university students, it is suitable for industrial engineers who want to strengthen or complete their training. It has been written so that someone working alone should find it easy to read. pescription The subject of the book is the vibrations of linear mechanical sys­ tems having only a finite number of degrees of freedom (ie discrete linear systems). These can be divided into the following two catego­ ries : -X- systems of solids which are considered to be rigid, and which are acted upon by elastic forces and by linear resist.ive forces (viscous damping forces). deformable continuous systems which have been made discrete. In other words, systems which are replaced (approximately) by systems having only a limited number of degrees of freedom, using digital or experimental methods.

1 Introduction.- 1.1 Brief history.- 1.2 Disruptive or useful vibrations.- 2 The Linear Elementary Oscillator of Mechanics.- 2.1 Definitions and notation.- 2.2 Equation of motion and vibratory states.- 2.3 Modified forms of the equation of motion.- 3 The Free State of the Elementary Oscillator.- 3.1 Conservative free state · Harmonic oscillator.- 3.2 Conservation of energy.- 3.3 Examples of conservative oscillators.- 3.4 Dissipative free state.- 3.5 Energy of the dissipative oscillator.- 3.6 Phase plane graph.- 3.7 Examples of dissipative oscillators.- 4 Harmonic Steady State.- 4.1 Amplitude and phase as a function of frequency.- 4.2 Graph of rotating vectors.- 4.3 Use of complex numbers · Frequency response.- 4.4 Power consumed in the steady state.- 4.5 Natural and resonant angular frequencies.- 4.6 The Nyquist graph.- 4.7 Examples of harmonic steady states.- 5 Periodic Steady State.- 5.1 Fourier series · Excitation and response spectra.- 5.2 Complex form of the Fourier series.- 5.3 Examples of periodic steady states.- 6 Forced State.- 6.1 Laplace transform.- 6.2 General solution of the forced state.- 6.3 Response to an impulse and to a unit step force.- 6.4 Responses to an impulse and to a unit step elastic displacement.- 6.5 Fourier transformation.- 6.6 Examples of forced states.- 7 Electrical Analogues.- 7.1 Generalities.- 7.2 Force-current analogy.- 7.3 Extension to systems with several degrees of freedom · Circuits of forces.- 8 Systems with Two Degrees of Freedom.- 8.1 Generalities · Concept of coupling.- 8.2 Free state and natural modes of the conservative system.- 8.3 Study of elastic coupling.- 8.4 Examples of oscillators with two degrees of freedom.- 9 The Frahm Damper.- 9.1 Definition and differential equations of the system.- 9.2 Harmonic steadystate.- 9.3 Limiting cases of the damping.- 9.4 Optimization of the Frahm damper.- 9.5 Examples of applications.- 9.6 The Lanchester damper.- 10 The Concept of the Generalized Oscillator.- 10.1 Definition and energetic forms of the generalized oscillator.- 10.2 Differentiation of a symmetrical quadratic form · Equations of Lagrange.- 10.3 Examination of particular cases.- 11 Free State of the Conservative Generalized Oscillator.- 11.1 Introduction.- 11.2 Solution of the system by linear combination of specific solutions.- 11.3 Solution of the system by change of coordinates.- 11.4 Response to an initial excitation.- 11.5 Rayleigh quotient.- 11.6 Examples of conservative generalized oscillators.- 12 Free State of the Dissipative Generalized Oscillator.- 12.1 Limits of classical modal analysis.- 12.2 Dissipative free state with real modes.- 12.3 Response to an initial excitation in the case of real modes.- 12.4 General case.- 12.5 Hamiltonian equations for the system.- 12.6 Solution of the differential system.- 12.7 Response to an initial excitation in the general case.- 12.8 Direct search for specific solutions.- 12.9 Another form of the characteristic equation.- 13 Example of Visualization of Complex Natural Modes.- 13.1 Description of the system.- 13.2 Energetic form · Differential equation.- 13.3 Isolation of a mode.- 13.4 Numerical examples.- 13.5 Summary and comments.- 14 Forced State of the Generalized Oscillator.- 14.1 Introduction.- 14.2 Dissipative systems with real modes.- 14.3 Dissipative systems in the general case.- 14.4 Introduction to experimental modal analysis.- Symbol List.

About the French edition:'The book is well written, uses clear standard notation, and is very well produced. One strength of the book is that for each section, several well-chosen practical examples are treated in detail. . . . this book rates as one of the best written in French.'Journal of Applied Mechanics, Vol. 57, 1990