TY  - BOOK
AU  - Humar,J.L
TI  - Dynamics of structures
SN  - 9780415620864
AV  - TA654 .H79 2012
PY  - 2012///]
CY  - Boca Raton, FL
PB  - CRC Press - Taylor and Francis Croup
KW  - Structural dynamics
N1  - "A Balkema Book."; Includes bibliographical references and index; Contents;  	Preface	;  	Preface to Second Edition	;  	List of symbols	; 1.	Introduction	; 1.1.	Objectives of the study of structural dynamics	; 1.2.	Importance of vibration analysis	; 1.3.	Nature of exciting forces	; 1.3.1.	Dynamic forces caused by rotating machinery	; 1.3.2.	Wind loads	; 1.3.3.	Blast loads	; 1.3.4.	Dynamic forces caused by earthquakes	; 1.3.5.	Periodic and nonperiodic loads	; 1.3.6.	Deterministic and nondeterministic loads	; 1.4.	Mathematical modeling of dynamic systems	; 1.5.	Systems of units	; 1.6.	Organization of the text	;  	PART 1	; 2.	Formulation of the equations of motion: Single-degree-of-freedom systems	; 2.1.	Introduction	; 2.2.	Inertia forces	; 2.3.	Resultants of inertia forces on a rigid body	; 2.4.	Spring forces	; 2.5.	Damping forces	; 2.6.	Principle of virtual displacement	; 2.7.	Formulation of the equations of motion	; 2.7.1.	Systems with localized mass and localized stiffness	; 2.7.2.	Systems with localized mass but distributed stiffness	; 2.7.3.	Systems with distributed mass but localized stiffness	; 2.7.4.	Systems with distributed stiffness and distributed mass	; 2.8.	Modeling of multi-degree-of-freedom discrete parameter system	; 2.9.	Effect of gravity load	; 2.10.	Axial force effect	; 2.11.	Effect of support motion	;  	Selected readings	;  	Problems	; 3.	Formulation of the equations of motion: Multi-degree-of-freedom systems	; 3.1.	Introduction	; 3.2.	Principal forces in multi-degree-of-freedom dynamic system	; 3.2.1.	Inertia forces	; 3.2.2.	Forces arising due to elasticity	; 3.2.3.	Damping forces	; 3.2.4.	Axial force effects	; 3.3.	Formulation of the equations of motion	; 3.3.1.	Systems with localized mass and localized stiffness	; 3.3.2.	Systems with localized mass but distributed stiffness	; 3.3.3.	Systems with distributed mass but localized stiffness	; 3.3.4.	Systems with distributed mass and distributed stiffness	; 3.4.	Transformation of coordinates	; 3.5.	Static condensation of stiffness matrix	; 3.6.	Application of Ritz method to discrete systems	;  	Selected readings	;  	Problems	; 4.	Principles of analytical mechanics	; 4.1.	Introduction	; 4.2.	Generalized coordinates	; 4.3.	Constraints	; 4.4.	Virtual work	; 4.5.	Generalized forces	; 4.6.	Conservative forces and potential energy	; 4.7.	Work function	; 4.8.	Lagrangian multipliers	; 4.9.	Virtual work equation for dynamical systems	; 4.10.	Hamilton's equation	; 4.11.	Lagrange's equation	; 4.12.	Constraint conditions and Lagrangian multipliers	; 4.13.	Lagrange's equations for multi-degree-of-freedom systems	; 4.14.	Rayleigh's dissipation function	;  	Selected readings	;  	Problems	;  	PART 2	; 5.	Free vibration response: Single-degree-of-freedom system	; 5.1.	Introduction	; 5.2.	Undamped free vibration	; 5.2.1.	Phase plane diagram	; 5.3.	Free vibrations with viscous damping	; 5.3.1.	Critically damped system	; 5.3.2.	Overdamped system	; 5.3.3.	Underdamped system	; 5.3.4.	Phase plane diagram	; 5.3.5.	Logarithmic decrement	; 5.4.	Damped free vibration with hysteretic damping	; 5.5.	Damped free vibration with coulomb damping	; 5.5.1.	Phase plane representation of vibrations under Coulomb damping	;  	Selected readings	;  	Problems	; 6.	Forced harmonic vibrations: Single-degree-of-freedom system	; 6.1.	Introduction	; 6.2.	Procedures for the solution of the forced vibration equation	; 6.3.	Undamped harmonic vibration	; 6.4.	Resonant response of an undamped system	; 6.5.	Damped harmonic vibration	; 6.6.	Complex frequency response	; 6.7.	Resonant response of a damped system	; 6.8.	Rotating unbalanced force	; 6.9.	Transmitted motion due to support movement	; 6.10.	Transmissibility and vibration isolation	; 6.11.	Vibration measuring instruments	; 6.11.1.	Measurement of support acceleration	; 6.11.2.	Measurement of support displacement	; 6.12.	Energy dissipated in viscous damping	; 6.13.	Hysteretic damping	; 6.14.	Complex stiffness	; 6.15.	Coulomb damping	; 6.16.	Measurement of damping	; 6.16.1.	Free vibration decay	; 6.16.2.	Forced-vibration response	;  	Selected readings	;  	Problems	; 7.	Response to general dynamic loading and transient response	; 7.1.	Introduction	; 7.2.	Response to an Impulsive Force	; 7.3.	Response to general dynamic loading	; 7.4.	Response to a step function load	; 7.5.	Response to a ramp function load	; 7.6.	Response to a step function load with rise time	; 7.7.	Response to shock loading	; 7.7.1.	Rectangular pulse	; 7.7.2.	Triangular pulse	; 7.7.3.	Sinusoidal pulse	; 7.7.4.	Effect of viscous damping	; 7.7.5.	Approximate response analysis for short-duration pulses	; 7.8.	Response to ground motion	; 7.8.1.	Response to a short-duration ground motion pulse	; 7.9.	Analysis of response by the phase plane diagram	;  	Selected readings	;  	Problems	; 8.	Analysis of single-degree-of-freedom systems: Approximate and numerical methods	; 8.1.	Introduction	; 8.2.	Conservation of energy	; 8.3.	Application of Rayleigh method to multi-degree-of-freedom systems	; 8.3.1.	Flexural vibrations of a beam	; 8.4.	Improved Rayleigh method	; 8.5.	Selection of an appropriate vibration shape	; 8.6.	Systems with distributed mass and stiffness: analysis of internal forces	; 8.7.	Numerical evaluation of Duhamel's integral	; 8.7.1.	Rectangular summation	; 8.7.2.	Trapezoidal method	; 8.7.3.	Simpson's method	; 8.8.	Direct integration of the equations of motion	; 8.9.	Integration based on piece-wise linear representation of the excitation	; 8.10.	Derivation of general formulas	; 8.11.	Constant-acceleration method	; 8.12.	Newmark's β method	; 8.12.1.	Average acceleration method	; 8.12.2.	Linear acceleration method	; 8.13.	Wilson-method	; 8.14.	Methods based on difference expressions	; 8.14.1.	Central difference method	; 8.14.2.	Houbolt's method	; 8.15.	Errors involved in numerical integration	; 8.16.	Stability of the integration method	; 8.16.1.	Newmark's β method	; 8.16.2.	Wilson-method	; 8.16.3.	Central difference method	; 8.16.4.	Houbolt's method	; 8.17.	Selection of a numerical integration method	; 8.18.	Selection of time step	;  	Selected readings	;  	Problems	; 9.	Analysis of response in the frequency domain	; 9.1.	Transform methods of analysis	; 9.2.	Fourier series representation of a periodic function	; 9.3.	Response to a periodically applied load	; 9.4.	Exponential form of Fourier series	; 9.5.	Complex frequency response function	; 9.6.	Fourier integral representation of a nonperiodic load	; 9.7.	Response to a nonperiodic load	; 9.8.	Convolution integral and convolution theorem	; 9.9.	Discrete Fourier transform	; 9.10.	Discrete convolution and discrete convolution theorem	; 9.11.	Comparison of continuous and discrete fourier transforms	; 9.12.	Application of discrete inverse transform	; 9.13.	Comparison between continuous and discrete convolution	; 9.14.	Discrete convolution of an infinite- and a finite-duration waveform	; 9.15.	Corrective response superposition methods	; 9.15.1.	Corrective transient response based on initial conditions	; 9.15.2.	Corrective periodic response based on initial conditions	; 9.15.3.	Corrective responses obtained from a pair of force pulses	; 9.16.	Exponential window method	; 9.17.	The fast Fourier transform	; 9.18.	Theoretical background to fast Fourier transform	; 9.19.	Computing speed of FFT convolution	;  	Selected readings	;  	Problems	;  	PART 3	; 10.	Free vibration response: Multi-degree-of-freedom system	; 10.1.	Introduction	; 10.2.	Standard eigenvalue problem	; 10.3.	Linearized eigenvalue problem and its properties	; 10.4.	Expansion theorem	; 10.5.	Rayleigh quotient	; 10.6.	Solution of the undamped free vibration problem	; 10.7.	Mode superposition analysis of free-vibration response	; 10.8.	Solution of the damped free-vibration problem	; 10.9.	Additional orthogonality conditions	; 10.10.	Damping orthogonality	;  	Selected readings	;  	Problems	; 11.	Numerical solution of the eigenproblem	; 11.1.	Introduction	; 11.2.	Properties of standard eigenvalues and eigenvectors	; 11.3.	Transformation of a linearized eigenvalue;  problem to the standard form	; 11.4.	Transformation methods	; 11.4.1.	Jacobi diagonalization	; 11.4.2.	Householder's transformation	; 11.4.3.	QR transformation	; 11.5.	Iteration methods	; 11.5.1.	Vector iteration	; 11.5.2.	Inverse vector iteration	; 11.5.3.	Vector iteration with shifts	; 11.5.4.	Subspace iteration	; 11.5.5.	Lanczos iteration	; 11.6.	Determinant search method	; 11.7.	Numerical solution of complex eigenvalue problem	; 11.7.1.	Eigenvalue problem and the orthogonality relationship	; 11.7.2.	Matrix iteration for determining the complex eigenvalues	; 11.8.	Semidefinite or unrestrained systems	; 11.8.1.	Characteristics of an unrestrained system	; 11.8.2.	Eigenvalue solution of a semidefinite system	; 11.9.	Selection of a method for the determination of eigenvalues	;  	Selected readings	;  	Problems	; 12.	Forced dynamic response: Multi-degree-of-freedom systems	; 12.1.	Introduction	; 12.2.	Normal coordinate transformation	; 12.3.	Summary of mode superposition method	; 12.4.	Complex frequency response	; 12.5.	Vibration absorbers	; 12.6.	Effect of support excitation	; 12.7.	Forced vibration of unrestrained system	;  	Selected readings	;  	Problems	; 13.	Analysis of multi-degree-of-freedom systems: Approximate and numerical methods	; 13.1.	Introduction	; 13.2.	Rayleigh-Ritz method	; 13.3.	Application of Ritz method to forced vibration response	; 13.3.1.	Mode superposition method	; 13.3.2.	Mode acceleration method	; 13.3.3.	Static condensation and Guyan's reduction	; 13.3.4.	Load-dependent Ritz vectors	; 13.3.5.	Application of lanczos vectors in the transformation of the equations of motion	; 13.4.	Direct integration of the equations of motion	; 13.4.1.	Explicit integration schemes	; 13.4.2.	Implicit integration schemes	; 13.4.3.	Mixed methods in direct integration	; 13.5.	Analysis in the frequency domain	; 13.5.1.	Frequency analysis of systems with classical mode shapes	; 13.5.2.	Frequency analysis of systems without classical mode shapes	;  	Selected readings	;  	Problems	;  	PART 4	; 14.	Formulation of the equations of motion: Continuous systems	; 14.1.	Introduction	; 14.2.	Transverse vibrations of a beam	; 14.3.	Transverse vibrations of a beam: variational formulation	; 14.4.	Effect of damping resistance on transverse vibrations of a beam	; 14.5.	Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam	; 14.6.	Axial vibrations of a bar	; 14.7.	Torsional vibrations of a bar	; 14.8.	Transverse vibrations of a string	; 14.9.	Transverse vibrations of a shear beam	; 14.10.	Transverse vibrations of a beam excited by support motion	; 14.11.	Effect of axial force on transverse vibrations of a beam	;  	Selected readings	;  	Problems	; 15.	Continuous systems: Free vibration response	; 15.1.	Introduction	; 15.2.	Eigenvalue problem for the transverse vibrations of a beam	; 15.3.	General eigenvalue problem for a continuous system	; 15.3.1.	Definition of the eigenvalue problem	; 15.3.2.	Self-adjointness of operators in the eigenvalue problem	; 15.3.3.	Orthogonality of eigenfunctions	; 15.3.4.	Positive and positive definite operators	; 15.4.	Expansion theorem	; 15.5.	Frequencies and mode shapes for lateral vibrations of a beam	; 15.5.1.	Simply supported beam	; 15.5.2.	Uniform cantilever beam	; 15.5.3.	Uniform beam clamped at both ends	; 15.5.4.	Uniform beam with both ends free	; 15.6.	Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations	; 15.7.	Frequencies and mode shapes for the axial vibrations of a bar	; 15.7.1.	Axial vibrations of a clamped-free bar	; 15.7.2.	Axial vibrations of a free-free bar	; 15.8.	Frequencies and mode shapes for the transverse vibration of a string	; 15.8.1.	Vibrations of a string tied at both ends	; 15.9.	Boundary conditions containing the eigenvalue	; 15.10.	Free-vibration response of a continuous system	; 15.11.	Undamped free transverse vibrations of a beam	; 15.12.	Damped free transverse vibrations of a beam	;  	Selected readings	;  	Problems	; 16.	Continuous systems: Forced-vibration response	; 16.1.	Introduction	; 16.2.	Normal coordinate transformation: general case of an undamped system	; 16.3.	Forced lateral vibration of a beam	; 16.4.	Transverse vibrations of a beam under traveling load	; 16.5.	Forced axial vibrations of a uniform bar	; 16.6.	Normal coordinate transformation, damped case	;  	Selected readings	;  	Problems	; 17.	Wave propagation analysis	; 17.1.	Introduction	; 17.2.	The Phenomenon of wave propagation	; 17.3.	Harmonic waves	; 17.4.	One dimensional wave equation and its solution	; 17.5.	Propagation of waves in systems of finite extent	; 17.6.	Reflection and refraction of waves at a discontinuity in the system properties	; 17.7.	Characteristics of the wave equation	; 17.8.	Wave dispersion	;  	Selected readings	;  	Problems	;  	PART 5	; 18.	Finite element method	; 18.1.	Introduction	; 18.2.	Formulation of the finite element equations	; 18.3.	Selection of shape functions	; 18.4.	Advantages of the finite element method	; 18.5.	Element Shapes	; 18.5.1.	One-dimensional elements	; 18.5.2.	Two-dimensional elements	; 18.6.	One-dimensional bar element	; 18.7.	Flexural vibrations of a beam	; 18.7.1.	Stiffness matrix of a beam element	; 18.7.2.	Mass matrix of a beam element	; 18.7.3.	Nodal applied force vector for a beam element	; 18.7.4.	Geometric stiffness matrix for a beam element	; 18.7.5.	Simultaneous axial and lateral vibrations	; 18.8.	Stress-strain relationships for a continuum	; 18.8.1.	Plane stress	; 18.8.2.	Plane strain	; 18.9.	Triangular element in plane stress and plane strain	; 18.10.	Natural coordinates	; 18.10.1.	Natural coordinate formulation for a uniaxial bar element	; 18.10.2.	Natural coordinate formulation for a constant strain triangle	; 18.10.3.	Natural coordinate formulation for a linear strain triangle	;  	Selected readings	;  	Problems	; 19.	Component mode synthesis	; 19.1.	Introduction	; 19.2.	Fixed interface methods	; 19.2.1.	Fixed interface normal modes	; 19.2.2.	Constraint modes	; 19.2.3.	Transformation of coordinates	; 19.2.4.	Illustrative example	; 19.3.	Free interface method	; 19.3.1.	Free interface normal modes	; 19.3.2.	Attachment modes	; 19.3.3.	Inertia relief attachment modes	; 19.3.4.	Residual flexibility attachment modes	; 19.3.5.	Transformation of coordinates	; 19.3.6.	Illustrative example	; 19.4.	Hybrid method	; 19.4.1.	Experimental determination of modal parameters	; 19.4.2.	Experimental determination of the static constraint modes	; 19.4.3.	Component modes and transformation of component matrices	; 19.4.4.	Illustrative example	;  	Selected readings	;  	Problems	; 20.	Analysis of nonlinear response	; 20.1.	Introduction	; 20.2.	Single-degree-of freedom system	; 20.2.1.	Central difference method	; 20.2.2.	Newmark's β Method	; 20.3.	Errors involved in numerical integration of nonlinear systems	; 20.4.	Multiple degree-of-freedom system	; 20.4.1.	Explicit integration	; 20.4.2.	Implicit integration	; 20.4.3.	Iterations within a time step	;  	Selected readings	;  	Problems	;  	Answers to selected problems	;  	Index
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