1 Foundations of Dynamics1.1 Kinematics of particles
1.2 Kinetics of particles
1.3 Power, work, and energy
1.4 Conservation of energy
1.5 Dynamics of rigid bodies
1.6 Example
1.7 The Euler{Lagrange equations
1.8 Summary
2 Numerical Solution of Ordinary Di_erential Equations
2.1 Why numerical methods?
2.2 Practical implementation
2.3 Analysis of a first order equation 2.4 Analysis of second order di_erential equations
2.4.1 The central di_erence method
2.4.2 The generalized trapezoidal rule
2.4.3 Newmark's method
2.5 Performance of the methods
2.6 Summary
3 Single-Degree-of-Freedom Systems
3.1 The SDOF oscillator
3.2 Undamped free vibration
3.3 Damped free vibration
3.4 Forced vibration 3.4.1 Suddenly applied constant load
3.4.2 Sinusoidal load
3.4.3 General periodic loading
3.5 Earthquake ground motion 3.6 Nonlinear response
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3.7 Integrating the equation of motion
3.8 Example
4 Systems with Multiple Degrees of Freedom
4.1 The 2{DOF system as a warm-up problem
4.2 The shear building 4.3 Free vibration of the NDOF system
4.3.1 Orthogonality of the eigenvectors
4.3.2 Initial conditions
4.4 Structural damping 4.4.1 Modal damping
4.4.2 Rayleigh damping
4.4.3 Caughey damping
4.4.4 Non-classical damping 4.5 Damped forced vibration of the NDOF system
4.6 Resonance in NDOF systems
4.7 Numerical integration of the NDOF equations
5 Nonlinear Response of NDOF Systems
5.1 A point of departure
5.2 The shear building, revisited
5.3 The principle of virtual work 5.4 Nonlinear dynamic computations
5.5 Assembly of equations
5.6 Adding damping to the equations of motion
5.7 The structure of the NDOF code 5.8 Implementation
6 Earthquake Response of NDOF Systems
6.1 Special case of the elastic system
6.2 Modal recombination
6.3 Response spectrum methods
6.4 Implementation
6.5 Example
7 Special Methods for Large Systems
7.1 Ritz projection onto a smaller subspace
7.2 Static correction method
7.3 Summary 8 Dynamic Analysis of Truss Structures
8.1 What is a truss?
8.2 Element kinematics
8.3 Element and nodal static equilibrium
8.4 The principle of virtual work
8.5 Constitutive models for axial force
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8.6 Solving the static equations of equilibrium
8.7 Dynamic analysis of truss structures
8.8 Distributed element mass
8.9 Earthquake response of truss structures
8.10 Implementation
8.11 Example
9 Axial Wave Propagation
9.1 The axial bar problem
9.2 Motion without applied loading
9.3 Classical solution by separation of variables
9.4 Modal analysis with applied loads
9.5 The Ritz method and _nite element analysis
9.5.1 Dynamic principle of virtual work
9.5.2 Finite element functions
9.5.3 A slightly di_erent formulation
9.5.4 Boundary conditions 9.5.5 Higher order interpolation
9.5.6 Initial conditions
9.6 Axial bar dynamics code
10 Dynamics of Planar Beams: Theory 10.1 Beam kinematics
10.1.1 Motion of a beam cross section
10.1.2 Strain{displacement relationships
10.1.3 Normal and shear strain
10.2 Beam kinetics
10.3 Constitutive equations
10.4 Equations of motion
10.4.1 Balance of linear momentum
10.4.2 Balance of angular momentum
10.5 Summary of beam equations
10.6 Linear beam theory
10.6.1 Linearized kinematics
