Dynamics of StructuresThis book covers structural dynamics from a theoretical and algorithmic approach. It covers systems with both single and multiple degreesoffreedom. Numerous case studies are given to provide the reader with a deeper insight into the practicalities of the area, and the solutions to these case studies are given in terms of realtime and frequency in both geometric and modal spaces. Emphasis is also given to the subject of seismic loading. The text is based on many lectures on the subject of structural dynamics given at numerous institutions and thus will be an accessible and practical aid to students of the subject. Key features:

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Contents
Forced Response to Harmonic Loading  
Measurement of Damping  
Forced Response to Periodic Loading  
Response to Arbitrary Loading in the Time  
ULTlDEGREES OF FREEDOM SYSTEMS  
Finite Element Method  
Free Response of Conservative Systems  
Modal Superposition Response to Earthquake  
Properties of Eigenvalues and Eigenvectors  
Direct Time Integration of Linear Systems  
Numerical Methods for Eigenproblems  
Direct Time Integration of Linear Systems  
Direct Time Integration of Nonlinear Systems  
Generalized Elementary Systems  
Response to Earthquake Excitation  
Complex Numbers  
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Common terms and phrases
acceleration method amplitude angular frequency applied assume axial axis beam element boundary conditions coefficients columns components Compute consider constant coordinates corresponding damping ratio deformed shape determine displacement function displacement response dissipated Duhamel integral dynamic loading earthquake eigenvectors elastic forces equal to zero equation of motion equilibrium evaluated example excitation expressed finite element finite element method flexural Fourier series Fourier transform given by equation global graph harmonic loading Hence illustrated in Figure images increment inertia forces initial conditions internal force interpolation functions iteration linear loading function mass matrix maximum displacement modal mode shapes natural frequency Newmark nodes nonlinear number of DOFs numerical integration Nyquist plot obtained oscillator Rayleigh method Rayleigh quotient response spectra rotation SDOF system shear shown in Figure solution spectrum static steadystate response step stiffness matrix structure system subjected tn+1 truss element undamped unit displacement vector velocity virtual displacement written