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Mechanical Vibrations : Theory and Application to Structural Dynamics.

By: Material type: TextTextSeries: New York Academy of Sciences SeriesPublisher: Newark : John Wiley & Sons, Incorporated, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (617 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118900185
Subject(s): Genre/Form: Additional physical formats: Print version:: Mechanical VibrationsDDC classification:
  • 624.1/76
LOC classification:
  • TA654 .G45 2015
Online resources:
Contents:
Cover -- TItle Page -- Copyright -- Contents -- Foreword -- Preface -- Introduction -- Suggested Bibliography -- List of main symbols and definitions -- Chapter 1 Analytical Dynamics of Discrete Systems -- Definitions -- 1.1 Principle of virtual work for a particle -- 1.1.1 Nonconstrained particle -- 1.1.2 Constrained particle -- 1.2 Extension to a system of particles -- 1.2.1 Virtual work principle for N particles -- 1.2.2 The kinematic constraints -- 1.2.3 Concept of generalized displacements -- 1.3 Hamilton's principle for conservative systems and Lagrange equations -- 1.3.1 Structure of kinetic energy and classification of inertia forces -- 1.3.2 Energy conservation in a system with scleronomic constraints -- 1.3.3 Classification of generalized forces -- 1.4 Lagrange equations in the general case -- 1.5 Lagrange equations for impulsive loading -- 1.5.1 Impulsive loading of a mass particle -- 1.5.2 Impulsive loading for a system of particles -- 1.6 Dynamics of constrained systems -- 1.7 Exercises -- 1.7.1 Solved exercises -- 1.7.2 Selected exercises -- References -- Chapter 2 Undamped Vibrations of n-Degree-of-Freedom Systems -- Definitions -- 2.1 Linear vibrations about an equilibrium configuration -- 2.1.1 Vibrations about a stable equilibrium position -- 2.1.2 Free vibrations about an equilibrium configuration corresponding to steady motion -- 2.1.3 Vibrations about a neutrally stable equilibrium position -- 2.2 Normal modes of vibration -- 2.2.1 Systems with a stable equilibrium configuration -- 2.2.2 Systems with a neutrally stable equilibrium position -- 2.3 Orthogonality of vibration eigenmodes -- 2.3.1 Orthogonality of elastic modes with distinct frequencies -- 2.3.2 Degeneracy theorem and generalized orthogonality relationships -- 2.3.3 Orthogonality relationships including rigid-body modes.
2.4 Vector and matrix spectral expansions using eigenmodes -- 2.5 Free vibrations induced by nonzero initial conditions -- 2.5.1 Systems with a stable equilibrium position -- 2.5.2 Systems with neutrally stable equilibrium position -- 2.6 Response to applied forces: forced harmonic response -- 2.6.1 Harmonic response, impedance and admittance matrices -- 2.6.2 Mode superposition and spectral expansion of the admittance matrix -- 2.6.3 Statically exact expansion of the admittance matrix -- 2.6.4 Pseudo-resonance and resonance -- 2.6.5 Normal excitation modes -- 2.7 Response to applied forces: response in the time domain -- 2.7.1 Mode superposition and normal equations -- 2.7.2 Impulse response and time integration of the normal equations -- 2.7.3 Step response and time integration of the normal equations -- 2.7.4 Direct integration of the transient response -- 2.8 Modal approximations of dynamic responses -- 2.8.1 Response truncation and mode displacement method -- 2.8.2 Mode acceleration method -- 2.8.3 Mode acceleration and model reduction on selected coordinates -- 2.9 Response to support motion -- 2.9.1 Motion imposed to a subset of degrees of freedom -- 2.9.2 Transformation to normal coordinates -- 2.9.3 Mechanical impedance on supports and its statically exact expansion -- 2.9.4 System submitted to global support acceleration -- 2.9.5 Effective modal masses -- 2.9.6 Method of additional masses -- 2.10 Variational methods for eigenvalue characterization -- 2.10.1 Rayleigh quotient -- 2.10.2 Principle of best approximation to a given eigenvalue -- 2.10.3 Recurrent variational procedure for eigenvalue analysis -- 2.10.4 Eigensolutions of constrained systems: general comparison principle or monotonicity principle -- 2.10.5 Courant's minimax principle to evaluate eigenvalues independently of each other.
2.10.6 Rayleigh's theorem on constraints (eigenvalue bracketing) -- 2.11 Conservative rotating systems -- 2.11.1 Energy conservation in the absence of external force -- 2.11.2 Properties of the eigensolutions of the conservative rotating system -- 2.11.3 State-space form of equations of motion -- 2.11.4 Eigenvalue problem in symmetrical form -- 2.11.5 Orthogonality relationships -- 2.11.6 Response to nonzero initial conditions -- 2.11.7 Response to external excitation -- 2.12 Exercises -- 2.12.1 Solved exercises -- 2.12.2 Selected exercises -- References -- Chapter 3 Damped Vibrations of n-Degree-of-Freedom Systems -- Definitions -- 3.1 Damped oscillations in terms of normal eigensolutions of the undamped system -- 3.1.1 Normal equations for a damped system -- 3.1.2 Modal damping assumption for lightly damped structures -- 3.1.3 Constructing the damping matrix through modal expansion -- 3.2 Forced harmonic response -- 3.2.1 The case of light viscous damping -- 3.2.2 Hysteretic damping -- 3.2.3 Force appropriation testing -- 3.2.4 The characteristic phase lag theory -- 3.3 State-space formulation of damped systems -- 3.3.1 Eigenvalue problem and solution of the homogeneous case -- 3.3.2 General solution for the nonhomogeneous case -- 3.3.3 Harmonic response -- 3.4 Experimental methods of modal identification -- 3.4.1 The least-squares complex exponential method -- 3.4.2 Discrete Fourier transform -- 3.4.3 The rational fraction polynomial method -- 3.4.4 Estimating the modes of the associated undamped system -- 3.4.5 Example: experimental modal analysis of a bellmouth -- 3.5 Exercises -- 3.5.1 Solved exercises -- 3.6 Proposed exercises -- References -- Chapter 4 Continuous Systems -- Definitions -- 4.1 Kinematic description of the dynamic behaviour of continuous systems: Hamilton's principle -- 4.1.1 Definitions.
4.1.2 Strain evaluation: Green's measure -- 4.1.3 Stress-strain relationships -- 4.1.4 Displacement variational principle -- 4.1.5 Derivation of equations of motion -- 4.1.6 The linear case and nonlinear effects -- 4.2 Free vibrations of linear continuous systems and response to external excitation -- 4.2.1 Eigenvalue problem -- 4.2.2 Orthogonality of eigensolutions -- 4.2.3 Response to external excitation: mode superposition (homogeneous spatial boundary conditions) -- 4.2.4 Response to external excitation: mode superposition (nonhomogeneous spatial boundary conditions) -- 4.2.5 Reciprocity principle for harmonic motion -- 4.3 One-dimensional continuous systems -- 4.3.1 The bar in extension -- 4.3.2 Transverse vibrations of a taut string -- 4.3.3 Transverse vibration of beams with no shear deflection -- 4.3.4 Transverse vibration of beams including shear deflection -- 4.3.5 Travelling waves in beams -- 4.4 Bending vibrations of thin plates -- 4.4.1 Kinematic assumptions -- 4.4.2 Strain expressions -- 4.4.3 Stress-strain relationships -- 4.4.4 Definition of curvatures -- 4.4.5 Moment-curvature relationships -- 4.4.6 Frame transformation for bending moments -- 4.4.7 Computation of strain energy -- 4.4.8 Expression of Hamilton's principle -- 4.4.9 Plate equations of motion derived from Hamilton's principle -- 4.4.10 Influence of in-plane initial stresses on plate vibration -- 4.4.11 Free vibrations of the rectangular plate -- 4.4.12 Vibrations of circular plates -- 4.4.13 An application of plate vibration: the ultrasonic wave motor -- 4.5 Wave propagation in a homogeneous elastic medium -- 4.5.1 The Navier equations in linear dynamic analysis -- 4.5.2 Plane elastic waves -- 4.5.3 Surface waves -- 4.6 Solved exercises -- 4.7 Proposed exercises -- References -- Chapter 5 Approximation of Continuous Systems by Displacement Methods -- Definitions.
5.1 The Rayleigh-Ritz method -- 5.1.1 Choice of approximation functions -- 5.1.2 Discretization of the displacement variational principle -- 5.1.3 Computation of eigensolutions by the Rayleigh-Ritz method -- 5.1.4 Computation of the response to external loading by the Rayleigh-Ritz method -- 5.1.5 The case of prestressed structures -- 5.2 Applications of the Rayleigh-Ritz method to continuous systems -- 5.2.1 The clamped-free uniform bar -- 5.2.2 The clamped-free uniform beam -- 5.2.3 The uniform rectangular plate -- 5.3 The finite element method -- 5.3.1 The bar in extension -- 5.3.2 Truss frames -- 5.3.3 Beams in bending without shear deflection -- 5.3.4 Three-dimensional beam element without shear deflection -- 5.3.5 Beams in bending with shear deformation -- 5.4 Exercises -- 5.4.1 Solved exercises -- 5.4.2 Selected exercises -- References -- Chapter 6 Solution Methods for the Eigenvalue Problem -- Definitions -- 6.1 General considerations -- 6.1.1 Classification of solution methods -- 6.1.2 Criteria for selecting the solution method -- 6.1.3 Accuracy of eigensolutions and stopping criteria -- 6.2 Dynamical and symmetric iteration matrices -- 6.3 Computing the determinant: Sturm sequences -- 6.4 Matrix transformation methods -- 6.4.1 Reduction to a diagonal form: Jacobi's method -- 6.4.2 Reduction to a tridiagonal form: Householder's method -- 6.5 Iteration on eigenvectors: the power algorithm -- 6.5.1 Computing the fundamental eigensolution -- 6.5.2 Determining higher modes: orthogonal deflation -- 6.5.3 Inverse iteration form of the power method -- 6.6 Solution methods for a linear set of equations -- 6.6.1 Nonsingular linear systems -- 6.6.2 Singular systems: nullspace, solutions and generalized inverse -- 6.6.3 Singular matrix and nullspace -- 6.6.4 Solution of singular systems -- 6.6.5 A family of generalized inverses.
6.6.6 Solution by generalized inverses and finding the nullspace N.
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Cover -- TItle Page -- Copyright -- Contents -- Foreword -- Preface -- Introduction -- Suggested Bibliography -- List of main symbols and definitions -- Chapter 1 Analytical Dynamics of Discrete Systems -- Definitions -- 1.1 Principle of virtual work for a particle -- 1.1.1 Nonconstrained particle -- 1.1.2 Constrained particle -- 1.2 Extension to a system of particles -- 1.2.1 Virtual work principle for N particles -- 1.2.2 The kinematic constraints -- 1.2.3 Concept of generalized displacements -- 1.3 Hamilton's principle for conservative systems and Lagrange equations -- 1.3.1 Structure of kinetic energy and classification of inertia forces -- 1.3.2 Energy conservation in a system with scleronomic constraints -- 1.3.3 Classification of generalized forces -- 1.4 Lagrange equations in the general case -- 1.5 Lagrange equations for impulsive loading -- 1.5.1 Impulsive loading of a mass particle -- 1.5.2 Impulsive loading for a system of particles -- 1.6 Dynamics of constrained systems -- 1.7 Exercises -- 1.7.1 Solved exercises -- 1.7.2 Selected exercises -- References -- Chapter 2 Undamped Vibrations of n-Degree-of-Freedom Systems -- Definitions -- 2.1 Linear vibrations about an equilibrium configuration -- 2.1.1 Vibrations about a stable equilibrium position -- 2.1.2 Free vibrations about an equilibrium configuration corresponding to steady motion -- 2.1.3 Vibrations about a neutrally stable equilibrium position -- 2.2 Normal modes of vibration -- 2.2.1 Systems with a stable equilibrium configuration -- 2.2.2 Systems with a neutrally stable equilibrium position -- 2.3 Orthogonality of vibration eigenmodes -- 2.3.1 Orthogonality of elastic modes with distinct frequencies -- 2.3.2 Degeneracy theorem and generalized orthogonality relationships -- 2.3.3 Orthogonality relationships including rigid-body modes.

2.4 Vector and matrix spectral expansions using eigenmodes -- 2.5 Free vibrations induced by nonzero initial conditions -- 2.5.1 Systems with a stable equilibrium position -- 2.5.2 Systems with neutrally stable equilibrium position -- 2.6 Response to applied forces: forced harmonic response -- 2.6.1 Harmonic response, impedance and admittance matrices -- 2.6.2 Mode superposition and spectral expansion of the admittance matrix -- 2.6.3 Statically exact expansion of the admittance matrix -- 2.6.4 Pseudo-resonance and resonance -- 2.6.5 Normal excitation modes -- 2.7 Response to applied forces: response in the time domain -- 2.7.1 Mode superposition and normal equations -- 2.7.2 Impulse response and time integration of the normal equations -- 2.7.3 Step response and time integration of the normal equations -- 2.7.4 Direct integration of the transient response -- 2.8 Modal approximations of dynamic responses -- 2.8.1 Response truncation and mode displacement method -- 2.8.2 Mode acceleration method -- 2.8.3 Mode acceleration and model reduction on selected coordinates -- 2.9 Response to support motion -- 2.9.1 Motion imposed to a subset of degrees of freedom -- 2.9.2 Transformation to normal coordinates -- 2.9.3 Mechanical impedance on supports and its statically exact expansion -- 2.9.4 System submitted to global support acceleration -- 2.9.5 Effective modal masses -- 2.9.6 Method of additional masses -- 2.10 Variational methods for eigenvalue characterization -- 2.10.1 Rayleigh quotient -- 2.10.2 Principle of best approximation to a given eigenvalue -- 2.10.3 Recurrent variational procedure for eigenvalue analysis -- 2.10.4 Eigensolutions of constrained systems: general comparison principle or monotonicity principle -- 2.10.5 Courant's minimax principle to evaluate eigenvalues independently of each other.

2.10.6 Rayleigh's theorem on constraints (eigenvalue bracketing) -- 2.11 Conservative rotating systems -- 2.11.1 Energy conservation in the absence of external force -- 2.11.2 Properties of the eigensolutions of the conservative rotating system -- 2.11.3 State-space form of equations of motion -- 2.11.4 Eigenvalue problem in symmetrical form -- 2.11.5 Orthogonality relationships -- 2.11.6 Response to nonzero initial conditions -- 2.11.7 Response to external excitation -- 2.12 Exercises -- 2.12.1 Solved exercises -- 2.12.2 Selected exercises -- References -- Chapter 3 Damped Vibrations of n-Degree-of-Freedom Systems -- Definitions -- 3.1 Damped oscillations in terms of normal eigensolutions of the undamped system -- 3.1.1 Normal equations for a damped system -- 3.1.2 Modal damping assumption for lightly damped structures -- 3.1.3 Constructing the damping matrix through modal expansion -- 3.2 Forced harmonic response -- 3.2.1 The case of light viscous damping -- 3.2.2 Hysteretic damping -- 3.2.3 Force appropriation testing -- 3.2.4 The characteristic phase lag theory -- 3.3 State-space formulation of damped systems -- 3.3.1 Eigenvalue problem and solution of the homogeneous case -- 3.3.2 General solution for the nonhomogeneous case -- 3.3.3 Harmonic response -- 3.4 Experimental methods of modal identification -- 3.4.1 The least-squares complex exponential method -- 3.4.2 Discrete Fourier transform -- 3.4.3 The rational fraction polynomial method -- 3.4.4 Estimating the modes of the associated undamped system -- 3.4.5 Example: experimental modal analysis of a bellmouth -- 3.5 Exercises -- 3.5.1 Solved exercises -- 3.6 Proposed exercises -- References -- Chapter 4 Continuous Systems -- Definitions -- 4.1 Kinematic description of the dynamic behaviour of continuous systems: Hamilton's principle -- 4.1.1 Definitions.

4.1.2 Strain evaluation: Green's measure -- 4.1.3 Stress-strain relationships -- 4.1.4 Displacement variational principle -- 4.1.5 Derivation of equations of motion -- 4.1.6 The linear case and nonlinear effects -- 4.2 Free vibrations of linear continuous systems and response to external excitation -- 4.2.1 Eigenvalue problem -- 4.2.2 Orthogonality of eigensolutions -- 4.2.3 Response to external excitation: mode superposition (homogeneous spatial boundary conditions) -- 4.2.4 Response to external excitation: mode superposition (nonhomogeneous spatial boundary conditions) -- 4.2.5 Reciprocity principle for harmonic motion -- 4.3 One-dimensional continuous systems -- 4.3.1 The bar in extension -- 4.3.2 Transverse vibrations of a taut string -- 4.3.3 Transverse vibration of beams with no shear deflection -- 4.3.4 Transverse vibration of beams including shear deflection -- 4.3.5 Travelling waves in beams -- 4.4 Bending vibrations of thin plates -- 4.4.1 Kinematic assumptions -- 4.4.2 Strain expressions -- 4.4.3 Stress-strain relationships -- 4.4.4 Definition of curvatures -- 4.4.5 Moment-curvature relationships -- 4.4.6 Frame transformation for bending moments -- 4.4.7 Computation of strain energy -- 4.4.8 Expression of Hamilton's principle -- 4.4.9 Plate equations of motion derived from Hamilton's principle -- 4.4.10 Influence of in-plane initial stresses on plate vibration -- 4.4.11 Free vibrations of the rectangular plate -- 4.4.12 Vibrations of circular plates -- 4.4.13 An application of plate vibration: the ultrasonic wave motor -- 4.5 Wave propagation in a homogeneous elastic medium -- 4.5.1 The Navier equations in linear dynamic analysis -- 4.5.2 Plane elastic waves -- 4.5.3 Surface waves -- 4.6 Solved exercises -- 4.7 Proposed exercises -- References -- Chapter 5 Approximation of Continuous Systems by Displacement Methods -- Definitions.

5.1 The Rayleigh-Ritz method -- 5.1.1 Choice of approximation functions -- 5.1.2 Discretization of the displacement variational principle -- 5.1.3 Computation of eigensolutions by the Rayleigh-Ritz method -- 5.1.4 Computation of the response to external loading by the Rayleigh-Ritz method -- 5.1.5 The case of prestressed structures -- 5.2 Applications of the Rayleigh-Ritz method to continuous systems -- 5.2.1 The clamped-free uniform bar -- 5.2.2 The clamped-free uniform beam -- 5.2.3 The uniform rectangular plate -- 5.3 The finite element method -- 5.3.1 The bar in extension -- 5.3.2 Truss frames -- 5.3.3 Beams in bending without shear deflection -- 5.3.4 Three-dimensional beam element without shear deflection -- 5.3.5 Beams in bending with shear deformation -- 5.4 Exercises -- 5.4.1 Solved exercises -- 5.4.2 Selected exercises -- References -- Chapter 6 Solution Methods for the Eigenvalue Problem -- Definitions -- 6.1 General considerations -- 6.1.1 Classification of solution methods -- 6.1.2 Criteria for selecting the solution method -- 6.1.3 Accuracy of eigensolutions and stopping criteria -- 6.2 Dynamical and symmetric iteration matrices -- 6.3 Computing the determinant: Sturm sequences -- 6.4 Matrix transformation methods -- 6.4.1 Reduction to a diagonal form: Jacobi's method -- 6.4.2 Reduction to a tridiagonal form: Householder's method -- 6.5 Iteration on eigenvectors: the power algorithm -- 6.5.1 Computing the fundamental eigensolution -- 6.5.2 Determining higher modes: orthogonal deflation -- 6.5.3 Inverse iteration form of the power method -- 6.6 Solution methods for a linear set of equations -- 6.6.1 Nonsingular linear systems -- 6.6.2 Singular systems: nullspace, solutions and generalized inverse -- 6.6.3 Singular matrix and nullspace -- 6.6.4 Solution of singular systems -- 6.6.5 A family of generalized inverses.

6.6.6 Solution by generalized inverses and finding the nullspace N.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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