Fundamentals of Structural Dynamics

Front Cover
Fundamentals of Structural Dynamics
Copyright Page
Contents
About the authors
Preface
1 Overview of structural dynamics
	1.1 Objective of structural dynamic analysis
	1.2 Characteristics of structural dynamics
	1.3 Classification of vibrations
	1.4 Vibration problems in engineering
	1.5 Procedures of dynamic response analysis of structures
		1.5.1 Description of system configuration
		1.5.2 Analysis of excitation
		1.5.3 Mechanism of vibration energy dissipation
		1.5.4 Equation of motion of a system
		1.5.5 Solution of equation of motion
		1.5.6 Vibration tests
	Problems
	References
2 Formulation of equations of motion of systems
	2.1 System constraints
	2.2 Representation of system configuration
	2.3 Real displacements, possible displacements, and virtual displacements
	2.4 Generalized force
	2.5 Conservative force and potential energy
	2.6 Direct equilibrium method
	2.7 Principle of virtual displacements
	2.8 Lagrange’s equation
	2.9 Hamilton’s principle
	2.10 Principle of total potential energy with a stationary value in elastic system dynamics
		2.10.1 Principle of virtual work and principle of total potential energy with a stationary value in statics
		2.10.2 Derivation of the principle of total potential energy with a stationary value in elastic system dynamics
	2.11 The “set-in-right-position” rule for assembling system matrices and method of computer implementation in Matlab
		2.11.1 The “set-in-right-position” rule for assembling system matrices
		2.11.2 Method of computer implementation in Matlab for assembling system matrices
	References
	Problems
3 Analysis of dynamic response of SDOF systems
	3.1 Analysis of free vibrations
		3.1.1 Undamped free vibrations
		3.1.2 Damped free vibrations
		3.1.3 Stability of motion
	3.2 Response of SDOF systems to harmonic loads
	3.3 Vibration caused by base motion and vibration isolation
		3.3.1 Vibration caused by base motion
		3.3.2 Vibration isolation
	3.4 Introduction to damping theory
		3.4.1 Viscous-damping theory
			3.4.1.1 Viscous-damping-force model
			3.4.1.2 Problems of viscous damping
			3.4.1.3 Equivalent viscous damping
		3.4.2 Hysteretic-damping theory
		3.4.3 Frictional damping theory
	3.5 Evaluation of viscous-damping ratio
		3.5.1 Free-vibration decay method
		3.5.2 Resonant amplification method
		3.5.3 Half-power (band-width) method
		3.5.4 Resonance energy loss per cycle method
	3.6 Response of SDOF systems to periodic loads
	3.7 Response of SDOF systems to impulsive loads
		3.7.1 Sine-wave impulsive load
		3.7.2 Rectangular impulsive load
		3.7.3 Triangular impulsive load
		3.7.4 Response ratios to different types of impulsive loads
		3.7.5 Response spectra (shock spectra)
		3.7.6 Approximate analysis of response to impulsive loads
	3.8 Time-domain analysis of dynamic response to arbitrary dynamic loads
	3.9 Frequency-domain analysis of dynamic response to arbitrary dynamic loads
		3.9.1 Express the system response to periodic loads in complex form
		3.9.2 Fourier integral method
	References
	Problems
4 Analysis of dynamic response of MDOF systems: mode superposition method
	4.1 Analysis of dynamic properties of multidegree-of-freedom systems
		4.1.1 Natural frequencies, mode shapes, and principal vibration
		4.1.2 Orthogonality of mode shapes
		4.1.3 Repeated frequency case
	4.2 Coupling characteristics and uncoupling procedure of equations of MDOF systems
		4.2.1 Coupling characteristics of equations of MDOF systems
		4.2.2 Uncoupling procedure of equations of MDOF systems
	4.3 Analysis of free vibration response of undamped systems
	4.4 Response of undamped systems to arbitrary dynamic loads
	4.5 Response of damped systems to arbitrary dynamic loads
	References
	Problems
5 Analysis of dynamic response of continuous systems: straight beam
	5.1 Differential equations of motion of undamped straight beam
	5.2 Modal expansion of displacement and orthogonality of mode shapes of straight beam
	5.3 Free vibration analysis of undamped straight beam
	5.4 Forced vibration analysis of undamped straight beam
	5.5 Forced vibration analysis of damped straight beam
	References
	Problems
6 Approximate evaluation of natural frequencies and mode shapes
	6.1 Rayleigh energy method
	6.2 Rayleigh–Ritz method
	6.3 Matrix iteration method
		6.3.1 Iteration procedure for fundamental frequency and mode
		6.3.2 Iteration procedure for higher frequencies and modes
	6.4 Subspace iteration method
	6.5 Reduction of degrees of freedom in dynamic analysis
		6.5.1 Preliminary comments
		6.5.2 Kinematic constraints method
		6.5.3 Static condensation method
		6.5.4 Rayleigh–Ritz method
	References
	Problems
7 Step-by-step integration method
	7.1 Basic idea of step-by-step integration method
	7.2 Linear acceleration method
	7.3 Wilson-θ method
	7.4 Newmark method
	7.5 Stability and accuracy of step-by-step integration method
	Problems
	References
Index
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