Aerospace and Mechanical Engineering
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AEM 5441: Structural Dynamics

Catalog Description



AEM 4441

Structural Dynamics

3 Credits


Catalog Description1:


Frequency and time domain analysis of multi-degree of freedom mechanical systems. Natural frequencies and normal modes of vibration. Free and forced vibrations of strings, rods, shafts and beams; Introduction to finite elements in structural dynamics. Design project.


Course Web Address2:




Prerequisites by Topic1,2:


1.      A knowledge of systems (AEM 4301)

2.      A knowledge of deformable body mechanics (AEM 3031)




Leonard Meirovitch, Elements of Vibration, Analysis, McGraw Hill.


Format of Course1,2:


3 lectures per week


Computer Usage1,2:




Course Objectives1,2:


Learn how to model discrete single-degree and multiple-degree vibratory systems and calculate the free and forced response of these systems. Learn to model continuous vibratory systems vibration of strings, axial vibration of rods, torsional vibration of shafts, and transverse vibrations of slender beams. Calculate the mode shapes and frequencies for the free response of continuous vibratory systems and use modal methods to calculate the forced response of these systems. Learn to use finite element methods for the analysis of the vibrations of structures. Apply the methods learned to a realistic engineering vibration problem and write a report on the results.


Course Outcomes1,2:


Students who successfully complete the course will demonstrate the following outcomes by exams, homework and an engineering report


1.      An ability to apply knowledge of mathematics, science, and engineering by developing the equations of motion for vibratory systems and solving for the free and forced response.

2.      Ability to identify, formulate and solve engineering problems. This will be accomplished by having students model, analyze and modify a vibratory structure order to achieve specified requirements.

3.      Understanding professional and ethical responsibilities. This will be accomplished by emphasizing the importance of understanding how structural vibrations may affect safety and reliability of engineering systems.

4.      An ability to communicate effectively will be accomplished by having students prepare a written report on their design/analysis project.

5.      An ability to use the techniques, skill and modern engineering tools necessary for engineering practice will be accomplished by giving students realistic problems which will require MatLab for solutions.

6.      An understanding of space structures by discussing vibration problems unique to large flexible structures


Relationship of course to program objectives:


This course supports all five of the AEM program objectives.


Relationship of course to program outcomes:


This course achieves the following outcomes:


1.      Apply mathematics

2.      System design

3.      Identify engineering problems

4.      Communication skills

5.      Engineering tools

6.      Structures

7.      Space structures



Course Outline1,2:


(Hrs, approx.)



Free vibration of single degree of freedom linear systems


Forced response of single degree of freedom linear systems


Forced response of single degree of freedom linear systems


Free response of two degree of freedom linear systems


Forced response of two degree of freedom linear systems


Response of multi-degree of freedom systems


Matrix methods for multi-degree of freedom systems


Equations of motion for string, axially motion of rods and torsional vibrations of shafts


Separation of variable solutions for strings, shafts, and rods


Free transverse vibrations of slender beams


Solution of forced vibration problems by modal expansions


Finite element methods for vibration problems


Finite element methods


Outcome Measurement1,2:


Outcomes are measured with homework, exams, and a design project.


Student Survey Questions:


This course improved my ability to do the following:

1. Apply knowledge of math, science and engineering

2. Identify, formulate and solve engineering problems

3. Understand professional and ethical responsibilities

4. Communicate effectively

5. Use tools of modern engineering

6. Understand space structures

Please answer the following questions regarding the course:

7. The textbook was clearly written and appropriate for the course

8. The homework helped me to understand the concepts presented in the course

9. The tests were appropriate in length and content

10. The level of work required in this course was appropriate for the credit given

11. The design/analysis project helped me to understand how the course material is applied to a realistic vibrations problem.

In this course I acquired the following:

12. An improved understanding of structural vibrations

13. An understanding of the unique vibrational problems associated with large space structures.

14. An ability to use finite-element methods to analyze structural vibrations



Last modified:






1. Include on web syllabus

2. Include on syllabus handed out to students.



Last Modified: 2007-07-24 at 10:04:42 -- this is in International Standard Date and Time Notation