OVERVIEW

This course is an introduction to Vibrations and Structural Dynamics. The goals of the course are to provide working level engineers who may not have received a thorough background in this important subject 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.

These goals will be achieved by focusing on the characterization of the dynamic characteristics of structures and the prediction of response of structures to dynamic environments. Subjects examined will be free and forced vibration of single and multi-degree-of-freedom systems, Fourier decomposition of excitation forces, modal testing, component loads analysis, and random vibration analysis. We will concentrate on the essential concepts within these topics to enable widely applicable understanding, but specific examples focused on turbomachinery and launch vehicles will be included as well. A variety of software tools, physical demonstrations, and optional assignments will also keep the class active and interesting. As this is “rocket science”, a rigorous explanation of the topics is necessary, i.e., there will be a lot of equations. Course notes are included, but the students will be asked to fill in selective blanks.

• Preliminary Background, Motivation, Math and Units
  
  
• Single Degree-of-Freedom (SDOF) Systems
• Modeling & Free Vibration
• Equation of Motion
• Solution Methods
• Example Problem
• Damped Free Response
• Damping Categories & Solutions
• Measurement of Damping
• Typical Damping Values & Example Problem
  
  
• Forced Response of SDOF Systems
• Response to Harmonic Excitation (Frequency Response)
• Support Excitation, Transmissibility
• Response to Arbitrary Transient Excitation
• Fourier Analysis
• Application in Rocket Engine Turbomachinery
• Dynamic Response in Time Domain
• Shock Response Spectra
  
  
• Structural Systems
• Continuous Model
• Effective Mass
• MDOF Systems
• Equations of Motion
• Modal Analysis
• Finite Element Method
• Forced Response of MDOF Systems
• Transient vs. Frequency Response
• Generalized Coordinates/Modal Superposition
• Harmonic Excitation Solution
• Transient Excitation Solution
• Launch Vehicle (Coupled Loads) Analysis
• Flow Diagram of Coupled Loads
• Component Mode Synthesis
  
  
• Other Topics
• Vibration & Modal Testing
• Random Vibration (Mile’s Equation)

INSTRUCTOR


Dr. Andrew M. Brown, Ph. D, is a recently retired Aerospace Engineer from the NASA-Marshall Space Flight Center/Propulsion Structures & Dynamic Analysis Branch. He joined MSFC in 1986, and has worked mainly on rocket engine dynamics and loads research, development, and production analysis. He has authored or co-authored 11 journal papers and 30 conference papers covering topics ranging from probabilistic design and loads combination methods to techniques for calculating turbine blade forced response in the presence of asymmetric flow. Last year he published a textbook on Structural Dynamics of Rocket Engines and was granted a patent on a turbine blade modification to reduce resonant response. Dr. Brown received a BS in Mechanical Engineering from Duke University and a Masters and Ph.D. in ME from Georgia Tech, and is an Associate Fellow of the American Institute of Astronautics and Aeronautics.

CLASSROOM HOURS / CEUs: 16 classroom hours / 1.6 CEU/PDH