Preface
Notations
Chapter 1 MECHANICAL SYSTEMS WITH ONE DEGREE OF FREEDOM
1.1 A simple mass-spring system
1.2 Free vibrations
1.3 Transient vibrations
1.4 Forced harmonic vibrations
1.5 Fourier series
1.6 Complex notation
Problems
Chapter 2 FREQUENCY DOMAIN
2.1 Introduction
2.2 Frequency response
2.3 Correlation functions
2.4 Spectral density
2.5 Examples of spectral density
2.6 Coherence
2.7 Time averages of power and energy
2.8 Frequency response and point mobility functions
2.9 Loss factor
2.10 Response of a 1-DOF system, a summary
Problems
Chapter 3 WAVES IN SOLIDS
3.1 Stresses and strains
3.2 Losses in solids
3.3 Transverse waves
3.4 Longitudinal waves
3.5 Torsional waves
3.6 Waves on a string
3.7 Bending or flexural waves-beams
3.8 Waves on strings and beams-a comparison
3.9 Flexural waves-plates
3.10 Orthotropic plates
3.11 Energy flow
Problems
Chapter 4 INTERACTION BETWEEN LONGITUDINAL AND TRANSVERSE WAVES
4.1 Generalised wave equation
4.2 Intensity
4.3 Coupling between longitudinal and transverse waves
4.4 Bending of thick beamsplates
4.5 Quasi longitudinal waves in thick plates
4.6 Rayleigh waves
4.7 Sandwich plates-general
4.8 Bending of sandwich plates
4.9 Equations governing bending of sandwich plates
4.10 Wavenumbers of sandwich plates
4.11 Bending stiffness of sandwich plates
4.12 Bending of I-beams
Problems
Chapter 5 WAVE ATTENUATION DUE TO LOSSES AND TRANSMISSION ACROSS JUNCTIONS
5.1 Excitation and propagation of L-waves
5.2 Excitation and propagation of F-waves
5.3 Point excited infinite plate
5.4 Spatial Fourier transforms
5.5 Added damping
5.6 Losses in sandwich plates
5.7 Coupling between flexural and inplane waves
5.8 Transmission of F-waves across junctions, diffuse incidence
5.9 Transmission of F-waves across junctions, normal incidence
5.10 Atenuation due to change of cross section
5.11 Some other methods to increase attenuation
5.12 Velocity level differences and transmission losses
5.13 Measurements on junctions between beams
Problems
Chapter 6 LONGITUDINAL VIBRATIONS OF FINITE BEAMS
6.1 Free longitudinal vibrations in finite beams
6.2 Forced longitudinal vibrations in finite beams
6.3 The mode summation technique
6.4 Kinetic energy of vibrating beam
6.5 Mobilities
6.6 Mass mounted on a rod
6.7 Transfer matrices
Problems
Chapter 7 FLEXURAL VIBRATIONS OF FINITE BEAMS
7.1 Free flexural vibrations of beams
7.2 Orthogonality and norm of eigenfunctions
7.3 Forced excitation of F-waves
7.4 Mode summation and modal parameters
7.5 Point mobility and power
7.6 Transfer matrices for bending of beams
7.7 Infinite periodic structures
7.8 Forced vibration of periodic structures
7.9 Finite composite beam
Problems
Chapter 8 FLEXURAL VIBRATIONS OF FINITE PLATES
8.1 Free vibrations of simply supported plates
8.2 Forced response of a simply supported plate
8.3 Forced excitation of a rectangular plate with two opposite sides simply supported
8.4 Power and energy
8.5 Mobility of plates
8.6 The Rayleigh-Ritz method
8.7 Application of the Rayleigh-Ritz method
8.8 Non flat plates
8.9 The effect of an added mass or mass-spring system on plate vibrations
8.10 Small disturbances
8.11 Plates mounted on resilient layers
8.12 Vibration of orthotropic plates
8.13 Circular and homogeneous plates
8.14 Bending of plates in tension
Problems
References
Index
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