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Preface | |
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List of Symbols | |
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Introduction | |
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Objectives of the study of structural dynamics | |
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Importance of vibration analysis | |
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Nature of exciting forces | |
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Mathematical modeling of dynamic systems | |
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Systems of units | |
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Organization of the text | |
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Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems | |
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Introduction | |
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Inertia forces | |
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Resultants of inertia forces on a rigid body | |
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Spring forces | |
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Damping forces | |
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Principle of virtual displacement | |
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Formulation of the equations of motion | |
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Modeling of multi-degree-of-freedom discrete parameter system | |
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Effect of gravity load | |
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Axial force effect | |
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Effect of support motion | |
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Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems | |
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Introduction | |
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Principal forces in multi-degree-of-freedom dynamic system | |
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Formulation of the equations of motion | |
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Transformation of coordinates | |
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Finite element method | |
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Finite element formulation of the flexural vibrations of a beam | |
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Static condensation of stiffness matrix | |
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Application of the Ritz method to discrete systems | |
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Principles of Analytical Mechanics | |
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Introduction | |
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Generalized coordinates | |
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Constraints | |
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Virtual work | |
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Generalized forces | |
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Conservative forces and potential energy | |
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Work function | |
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Lagrangian multipliers | |
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Virtual work equation for dynamical systems | |
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Hamilton's equation | |
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Lagrange's equation | |
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Constraint conditions and lagrangian multipliers | |
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Lagrange's equations for discrete multi-degree-of-freedom systems | |
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Rayleigh's dissipation function | |
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Free Vibration Response: Single-Degree-of-Freedom System | |
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Introduction | |
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Undamped free vibration | |
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Free vibrations with viscous damping | |
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Damped free vibration with hysteretic damping | |
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Damped free vibration with Coulomb damping | |
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Forced Harmonic Vibrations: Single-Degree-of-Freedom System | |
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Introduction | |
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Procedures for the solution of the forced vibration equation | |
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Undamped harmonic vibration | |
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Resonant response of an undamped system | |
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Damped harmonic vibration | |
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Complex frequency response | |
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Resonant response of a damped system | |
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Rotating unbalanced force | |
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Transmitted motion due to support movement | |
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Transmissibility and vibration isolation | |
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Vibration measuring instruments | |
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Energy dissipated in viscous damping | |
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Hysteretic damping | |
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Complex stiffness | |
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Coulomb damping | |
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Measurement of damping | |
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Response to General Dynamic Loading and Transient Response | |
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Introduction | |
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Response to an impulsive force | |
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Response to general dynamic loading | |
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REsponse to a step function load | |
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Response to a ramp function load | |
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Response to a step function load with rise time | |
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Response to shock loading | |
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Response to ground motion | |
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Analysis of response by the phase plane diagram | |
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Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods | |
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Introduction | |
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Conservation of energy | |
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Application of Rayleigh method to multi-degree-of-freedom systems | |
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Improved Rayleigh method | |
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Selection of an appropriate vibration shape | |
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Systems with distributed mass and stiffness: Analysis of internal forces | |
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Numerical evaluation of Duhamel's integral | |
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Direct integration of the equations of motion | |
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Integration based on piece-wise linear representation of the excitation | |
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Derivation of general formulae | |
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Constant-acceleration method | |
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Newmark's [beta] method | |
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Wilson-[theta] method | |
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Methods based on difference expressions | |
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Errors involved in numerical integration | |
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Stability of the integration method | |
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Selection of a numerical integration method | |
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Selection of time step | |
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Analysis of nonlinear response | |
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Errors involved in numerical integration of nonlinear systems | |
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Analysis of Response in the Frequency Domain | |
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Transform methods of analysis | |
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Fourier series representation of a periodic function | |
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Response to a periodically applied load | |
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Exponential form of fourier series | |
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Complex frequency response function | |
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Fourier integral representation of a nonperiodic load | |
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Response to a nonperiodic load | |
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Convolution integral and convolution theorem | |
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Discrete Fourier transform | |
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Discrete convolution and discrete convolution theorem | |
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Comparison of continuous and discrete Fourier transforms | |
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Application of discrete inverse transform | |
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Comparison between continuous and discrete convolution | |
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Discrete convolution of an infinite- and a finite-duration waveform | |
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Corrective response superposition methods | |
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Exponential window method | |
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The fast Fourier transform | |
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Theoretical background to fast Fourier transform | |
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Computing speed of FFT convolution | |
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Free-Vibration Response: Multi-Degree-of-Freedom Systems | |
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Introduction | |
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Standard eigenvalue problem | |
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Linearized eigenvalue problem and its properties | |
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Expansion theorem | |
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Rayleigh quotient | |
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Solution of the undamped free-vibration problem | |
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Mode superposition analysis of free-vibration response | |
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Solution of the damped free-vibration problem | |
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Additional orthogonality conditions | |
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Damping orthogonality | |
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Numerical Solution of the Eigenproblem | |
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Introduction | |
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Properties of standard eigenvalues and eigenvectors | |
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Transformation of a linearized eigenvalue problem to the standard form | |
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Transformation methods | |
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Iteration methods | |
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Determinant search method | |
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Numerical solution of complex eigenvalue problem | |
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Semi-definite or unrestrained systems | |
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Selection of a method for the determination of eigenvalues | |
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Forced Dynamic Response: Multi-Degree-of-Freedom Systems | |
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Introduction | |
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Normal coordinate transformation | |
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Summary of mode superposition method | |
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Complex frequency response | |
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Vibration absorbers | |
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Effect of support excitation | |
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Forced vibration of unrestrained system | |
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Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods | |
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Introduction | |
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Rayleigh-Ritz method | |
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Application of Ritz method to forced vibration response | |
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Direct integration of the equations of motion | |
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Analysis in the frequency domain | |
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Analysis of nonlinear response | |
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Formulation of the Equations of Motion: Continuous Systems | |
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Introduction | |
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Transverse vibrations of a beam | |
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Transverse vibrations of a beam: variational formulation | |
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Effect of damping resistance on transverse vibrations of a beam | |
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Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam | |
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Axial vibrations of a bar | |
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Torsional vibrations of a bar | |
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Transverse vibrations of a string | |
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Transverse vibrations of a shear beam | |
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Transverse vibrations of a beam excited by support motion | |
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Effect of axial force on transverse vibrations of a beam | |
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Continuous Systems: Free Vibration Response | |
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Introduction | |
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Eigenvalue problem for the transverse vibrations of a beam | |
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General eigenvalue problem for a continuous system | |
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Expansion theorem | |
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Frequencies and mode shapes for lateral vibrations of a beam | |
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Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations | |
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Frequencies and mode shapes for the axial vibrations of a bar | |
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Frequencies and mode shapes for the transverse vibration of a string | |
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Boundary conditions containing the eigenvalue | |
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Free-vibration response of a continuous system | |
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Undamped free transverse vibrations of a beam | |
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Damped free transverse vibrations of a beam | |
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Continuous Systems: Forced-Vibration Response | |
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Introduction | |
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Normal coordinate transformation: general case of an undamped system | |
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Forced lateral vibration of a beam | |
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Transverse vibrations of a beam under traveling load | |
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Forced axial vibrations of a uniform bar | |
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Normal coordinate transformation, damped case | |
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Wave Propagation Analysis | |
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Introduction | |
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The phenomenon of wave propagation | |
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Harmonic waves | |
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One-dimensional wave equation and its solution | |
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Propagation of waves in systems of finite extent | |
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Reflection and refraction of waves at a discontinuity in the system properties | |
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Characteristics of the wave equation | |
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Wave dispersion | |
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Answers to Selected Problems | |
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Index | |