Structural Dynamics

CE57300

Credit Hours:

3

Learning Objective:

By the end of the course, you will be able to:

  1. Model dynamic systems and describe how they respond to various loadings.
  2. Determine the dynamic characteristics of a variety of linear structural systems.
  3. Obtain and solve the equations of motion for a dynamic system modeled as a linear system.

 

Description:

Analysis of structural members and systems subject to dynamic loads such as wind and earthquake loads; basic theory for single-degree-of-freedom and multi-degree-of-freedom analytical models of civil engineering structures; free vibration, harmonic and transient excitation, foundation motion, response spectrum, frequency domain analysis, Lagrange's equation, modal analysis, lumped parameter methods, computer methods.

Spring 2025 Syllabus

 

Topics Covered:

Week Topic
1

Equation of Motion; Free Body Diagrams; Free Vibration Response

Response to Harmonic Loading

Matlab Common Commands (Refresher)

2

Half-power Bandwidth Method; Response to Periodic Loading

Frequency Response Function; Impulse Response Function; Step Response; Ramp Response; Finite Ramp Response

Rectangular Pulse; Response Spectra; Intro to State Space

3

Frequency Domain Analysis; Fourier Transform

Matlab Introduction to Simulation

4

Practice Exam 

Exam I (in class)

Numerical Solution of the EOM

5

Response Spectra; Design Sprctra

Generalized SDOF Systems; Boundary Conditions

MDOF Systems; Equations of Motion

6

Hamilton's Principle, Lagrange's Equation

Free Vibration Response

Eigenvalue problem

7

Orthogonality of Modes, Modal matrix

Practice Exam

Exam II (in class)

8

Modal Coordinates

Damping in MDOF Systems, Mode Superpostions

9

Frequency Domain Analysis

Vibration Absorber

Modal Participation Factors, Stat Space Form

10

Assumed Modes Methon

Practice Exam

Matlab/Simulink Implementation

11

Exam III (in class)

Lagrange's Equations for Distributed Systems

Matrix Methods for Dynamic Modeling

12

Model Reduction Methods

Experimental Modal Analysis

Response Spectrum Analysis

13

Mathematical Models of Continuous Systems

Boundary Conditions; Torsional Systems

Hamilton's Principle for Continuous Systmes

14

Continuous Systems

Practice Exam

15

Exam IV

16

Base Isolation

Project Presentations

Prerequisites:

Able to solve differential equations.

Understanding of matrix operations and eigensolutions.

 

Applied / Theory:

40/60

 

Web Address:

https://purdue.brightspace.com

 

Exams:

Will use online proctoring.

 

Textbooks:

Structural Dynamics: Theory and Computation by Paz, Mario, Kim, and Young Hoon (2019). 6th edition (any edition can be used, but must check problems and units)

 

Computer Requirements:

Use of MATLAB/SIMULINK will be expected to complete the computer simulations assigned as part of certain homework assignments. Any version of MATLAB/SIMULINK will be suitable for these simulations. OCTAVE is allowed, although help cannot be guaranteed; MATHCAD is not acceptable for this course. You can access MATLAB through the Purdue University MATLAB Portal.