The book "Theory of Vibration with Applications" by William T. Thomson, Fourth Edition, is a comprehensive resource on the theory and applications of vibration. The author, a Professor Emeritus at the University of California, Santa Barbara, has updated the content to include new chapters and expanded material, particularly focusing on computational methods and the finite element method. Key topics covered include: - ** Oscillatory Motion**: Harmonic and periodic motion, vibration terminology. - **Free Vibration**: Vibration models, equations of motion, energy methods, Rayleigh method, virtual work, damped free vibration, logarithmic decrement, Coulomb damping. - **Harmonically Excited Vibration**: Forced harmonic vibration, rotating unbalance, rotor unbalance, whirling of rotating shafts, support motion, vibration isolation, equivalent viscous damping, structural damping, sharpness of resonance, vibration-measuring instruments. - **Transient Vibration**: Impulse excitation, arbitrary excitation, Laplace transform formulation, pulse excitation and rise time, shock response spectrum, shock isolation, finite difference numerical computation, Runge-Kutta method. - **Systems with Two or More Degrees of Freedom**: Normal mode analysis, initial conditions, coordinate coupling, forced harmonic vibration, digital computation. - **Properties of Vibrating Systems**: Flexibility and stiffness influence coefficients, reciprocity theorem, stiffness matrix of beam elements, static condensation for pinned joints, orthogonality of eigenvectors, modal matrix, decoupling forced vibration equations, modal damping in forced vibration, normal mode summation, equal roots, unrestrained (degenerate) systems. - **Lagrange's Equation**: Generalized coordinates, virtual work, kinetic and potential energy, generalized force. - **Computational Methods**: Root solving, Gauss elimination, matrix iteration, convergence of iteration procedures, dynamic matrix, transformation of coordinates, systems with discrete mass matrix, Cholesky decomposition, Jacobi diagonalization, computer program notes. - **Vibration of Continuous Systems**: Vibrating string, longitudinal vibration of rods, torsional vibration of rods, vibration of suspension bridges, Euler equation for beams, effect of rotary inertia and shear deformation, system with repeated identical sections. - **Introduction to the Finite Element Method**: Element stiffness and mass, transformation of coordinates, element stiffness and mass in global coordinates, vibrations involving beam elements, spring constraints on structures, generalized force for distributed load, generalized force proportional to displacement. - **Mode-Summation Procedures for Continuous Systems**: Mode-summation method, beam orthogonality, normal modes of constrained structures, mode-acceleration method, component-mode synthesis. - **Classical Methods**: Rayleigh method, Dunkerley's equation, Rayleigh-Ritz method, Holzer method, digital computer program for the torsional system, Myklestad's method for beams, coupled flexure-torsion vibration, transfer matrices, systems with damping, geared system, branched systems, transfer matrices forThe book "Theory of Vibration with Applications" by William T. Thomson, Fourth Edition, is a comprehensive resource on the theory and applications of vibration. The author, a Professor Emeritus at the University of California, Santa Barbara, has updated the content to include new chapters and expanded material, particularly focusing on computational methods and the finite element method. Key topics covered include: - ** Oscillatory Motion**: Harmonic and periodic motion, vibration terminology. - **Free Vibration**: Vibration models, equations of motion, energy methods, Rayleigh method, virtual work, damped free vibration, logarithmic decrement, Coulomb damping. - **Harmonically Excited Vibration**: Forced harmonic vibration, rotating unbalance, rotor unbalance, whirling of rotating shafts, support motion, vibration isolation, equivalent viscous damping, structural damping, sharpness of resonance, vibration-measuring instruments. - **Transient Vibration**: Impulse excitation, arbitrary excitation, Laplace transform formulation, pulse excitation and rise time, shock response spectrum, shock isolation, finite difference numerical computation, Runge-Kutta method. - **Systems with Two or More Degrees of Freedom**: Normal mode analysis, initial conditions, coordinate coupling, forced harmonic vibration, digital computation. - **Properties of Vibrating Systems**: Flexibility and stiffness influence coefficients, reciprocity theorem, stiffness matrix of beam elements, static condensation for pinned joints, orthogonality of eigenvectors, modal matrix, decoupling forced vibration equations, modal damping in forced vibration, normal mode summation, equal roots, unrestrained (degenerate) systems. - **Lagrange's Equation**: Generalized coordinates, virtual work, kinetic and potential energy, generalized force. - **Computational Methods**: Root solving, Gauss elimination, matrix iteration, convergence of iteration procedures, dynamic matrix, transformation of coordinates, systems with discrete mass matrix, Cholesky decomposition, Jacobi diagonalization, computer program notes. - **Vibration of Continuous Systems**: Vibrating string, longitudinal vibration of rods, torsional vibration of rods, vibration of suspension bridges, Euler equation for beams, effect of rotary inertia and shear deformation, system with repeated identical sections. - **Introduction to the Finite Element Method**: Element stiffness and mass, transformation of coordinates, element stiffness and mass in global coordinates, vibrations involving beam elements, spring constraints on structures, generalized force for distributed load, generalized force proportional to displacement. - **Mode-Summation Procedures for Continuous Systems**: Mode-summation method, beam orthogonality, normal modes of constrained structures, mode-acceleration method, component-mode synthesis. - **Classical Methods**: Rayleigh method, Dunkerley's equation, Rayleigh-Ritz method, Holzer method, digital computer program for the torsional system, Myklestad's method for beams, coupled flexure-torsion vibration, transfer matrices, systems with damping, geared system, branched systems, transfer matrices for