Fundamentals of Structural Dynamics

This course is intended to be an introductory course in Vibrations and Structural Dynamics.  The goals of the course will be to provide students with the ability to characterize the dynamic characteristics of structures, and enable the prediction of response of structures to dynamic environments.  Subjects examined in the course will be free and forced vibration of single degree-of-freedom systems, forced response of multi-DOF systems, modal testing, and component loads analysis.  The course will concentrate on the essential concepts within these topics to enable widely-applicable understanding, but we’ll include examples of applications focused on rocket engines and launch vehicles as well. 

Learning Objectives:
• Goals 
o Characterization of the dynamic characteristics of structures 
o prediction of response of structures to dynamic environment
• Subjects 
o free and forced vibration of single degree-of-freedom systems
o forced response of multi-DOF systems (transient, frequency, random)
o modal testing 
o component loads analysis  

This is an introductory course for engineers new to or outside of the field.  Most engineering schools do not require a course in vibrations, so many working engineers do not have an understanding of natural frequencies, mode shapes, and loads analysis, topics that are constantly under consideration in the design of aerospace hardware.  This course will provide them with the understanding necessary to work with dynamics experts as well as tools enabling them to make basic calculations on their own.  In addition, it will provide a foundation for new engineers who wish to enter this discipline.

Course Information

Type of Course: Instructor-Led Short Course
Course Length: 2-3 days
AIAA CEU's available: Yes 


Preliminary Background, Motivation, Math and Units

SDOF Systems

  1. Modeling & Free Vibration
    1. Equation of Motion
    2. Solution Methods
    3. Example Problem
  2. Damped Free Response
    1. Damping Categories & Solutions
    2. Measurement of Damping 
    3. Typical Damping Values & Example Problem 

Forced Response of SDOF Systems

  1. Response to Harmonic Excitation (Frequency Response)
  2. Support Excitation, Transmissibility
  3. Response to Arbitrary Transient Excitation
    1. Fourier Analysis
  4. Application in Rocket Engine Turbomachinery
  5. Dynamic Response in Time Domain
    1. Shock Response Spectra

Structural Systems

  1. Continuous Model
    1. Effective Mass
  2. MDOF Systems
    1. Equations of Motion
    2. Modal Analysis
    3. Finite Element Method
  3. Forced Response of MDOF Systems
    1. Transient vs. Frequency Response
    2. Generalized Coordinates/Modal Superposition
    3. Harmonic Excitation Solution
    4. Transient Excitation Solution
  4. Launch Vehicle (Coupled Loads) Analysis
    1. Flow Diagram of Coupled Loads
    2. Component Mode Synthesis

Other Topics

  1. Vibration & Modal Testing
  2. Random Vibration (Mile’s Equation)


Dr. Andrew Brown

Dr. Brown has worked for 25 years in the Structural Dynamics discipline at NASA Marshall Space Flight Center.  He received a BSME from Duke and a Masters and Ph.D. from Georgia Tech.  He has worked extensively in the areas of probabilistic structural analysis, inverse loads determination, analysis of mistuned bladed-disks, and rocket engine systems loads.  Currently he is leading structural dynamic analysis for the development of the J2X upper-stage rocket engine. 


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