SPRING
2008		 ME492 Advanced Topics in Structural Mechanics
DYNAMICS OF STRUCTURES
COURSE TOPICS 
Chopra: 
(chapters)
Other(s)
I. SDF Systems: Equations of Motion and Problem Statement
    
1. Simple structures
2. Single-Degree-of-Freedom sytem
3. Force-displacement relation
4. Damping force
5. Equation of motion: external force
6. Mass-spring-damper system
7. Equation of motion: earthquake excitation
8. Problem statement and element forces
9. Combining static and dynamic responses
10. Methods of solution of the differential equations
1
pp. 3-34
  
II. SDF Systems: Free Vibrations
    
1. Undamped free vibrations
2. Viscously damped free vibrations
3. Coulomb-damped free vibrations
2
pp. 39-61

III. SDF Systems: Response to Harmonic and Periodic Excitations
    
1. Harmonic vibrations of undamped systems
2. Harmonic vibrations with viscous damping
3. Response to vibration generator
4. Natural frequency and damping from harmonic tests
5. Energy dissipated in viscous damping
3
pp. 65-90.
pp. 99-103
 
IV. SDF Systems: Response to Arbitrary and Step Excitations
    
1. Response to unit impulse
2. Response to arbitrary force
3. Step force
4. Ramp or linearly increasing force
5. Step force with finite rise time
4
pp. 125-135

V. SDF Systems: Numerical Evaluation of Dynamic Response
    
1. Time-stepping methods
2. Interpolation of excitation
3. Central difference methods
4. Newmark's methods
5. Stability and computational error
6. Analysis of nonlinear response
 5
pp. 165-193
VI. SDF Systems: Earthquake Response of Linear Systems

1. Earthquake excitation
2. Equation of motion
3. response quantities
4. Response history
5. Response spectrum concept
6. Deformation, pseudo-velocity, and pseudo-acceleration response spectra
7. Peak structural response from the response spectrum
8. Response spectrum characteristics
9. Elastic design spectrum
10. Comparison of design and response spectra
11. Distinction betweendesign and response spectra
12. Velocity and acceleration response spectra
6
pp. 197-245
  
VII. SDF Systems: Earthquake Response of Inelastic Systems
    
1. Force-deformation relations
2. Normalized yield strength, yield strength reduction factor, and ductility factor
3. Equation of motion and controlling parameters
4. Effects of yielding
5. Response spectrum for yield deformation and yield strength
7. Yield strength and deformation from the response spectrum
8. Relative effects of yielding and damping
9. Dissipated energy
10. Energy dissipation devices
11. Inelastic design spectrum
12. Application of the design spectrum
13. Comparison of design and response spectra
7
pp. 257-302

VIII. SDF Systems: Generalized SDF Systems

1. Generalized SDF systems
2. Systems with distributed mass and elasticity
3. Natural vibration frequency by Rayleigh's method
  8
pp. 305-307
309-321
328-332

IX. MDF Systems: Equations of Motion, Problem Statement, and Solution Methods

1. Simple system: two-story shear building
2. General approach for linear systems
3. Static condensation
4. Planar or symmetric-plan systems: ground motion
5. Multiple support excitation
6. Inelastic systems
7. Problem statement
8. Element force
9. Methods for solving the equations of motion: overview
9
pp. 345-375
384-391
  
X. MDF Systems: Free Vibrations

1. Systems without damping
2. Natural vibration frequencies and modes
3. Modal and spectral matrices
4. Orthogonality of modes
5. Interpretation of modal orthogonality
6. Normalization of modes
7. Modal expansion of displacements
8. Solution of free vibration equations: undamped systems
9. Free vibration of systems with damping
10. Solution of free vibration equations: classically damped systems
11. Solution methods for the eigenvalue problem
12. Rayleigh quotient
13. Inverse vector iteration method
10
pp. 401-435

XI. MDF Systems: Damping in Structures

1. Example of vibration properties
2. Estimating modal damping ratios
3. Damping matrix
4. Classical damping matrix
11
pp. 447-458
  
XII. MDF Systems: Dynamic Analysis and Response of Linear Systems

1. Analysis of two-dof systems without damping
2. Vibration absorber or tuned mass damper
3. Modal equations for undamped systems
4. Modal equations for damped systems
5. Displacement response
6. Element forces
7. Modal analysis: summary
12
pp. 467-482
  
XIII. MDF Systems: Earthquake Analysis of Linear Systems

1. Modal analysis
2. Multistory buildings with symmetric plan
3. Peak response from earthquake response spectrum
4. Multistory buildings with symmetric plan
13
pp. 507-532
555-572
  
XIV. Systems with Distributed Mass and Elasticity

1. Equation of undamped motion: applied forces
2. Equation of undamped motion: support excitation
3. Natural vibration frequencies and modes
4. Modal orthogonality
5. Modal analysis of forced dynamic response
6. Earthquake response history analysis
7. Earthquake response spectrum analysis
8. Difficulty in analyzing practical systems
  16
pp. 629-658

XV. Finite Elements in Structural Dynamics

1. Rayleigh-Ritz method
2. Finite Element method
3. Mass and damping matrices
4. Natural frequencies and modes
5. Response history: modal methods
6. Response history: direct integration methods
7. Explicit direct integration
8. Implicit direct integration
9. Direct integration: stability and accuracy analysis

 		17
pp. 661-684
 		Cook: Ch11 - pp 373-426

Renato Perucchio
 updated 16 January 2008
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