RANDOM VIBRATIONS

About the Course

Engineers are more frequently designing, analyzing, and testing their systems for random vibrations. This is because modern structural and electro-mechanical systems are often exposed to vibration environments that are random in nature. Some example environments are acoustic noise, turbulent flow, rough pavement, wind, ocean waves, and earthquakes. Random vibrations are also artificially generated as an environmental stress screening technique and for modal analysis/system identification.

Yet, most practicing engineers have not had the opportunity for formal education in this field. This course is designed for practicing engineers and managers, who may be involved in random vibration design, analysis, and/or test, and who want to bridge that educational gap. This course will also be of interest to those already familiar with one aspect of random vibrations and are interested in broadening their horizons, e.g., from analysis to testing.

In this course, the fundamentals of random vibrations theory are explained, including the definition and explanation of special terms. Practical aspects of design, analysis, and testing are presented, including design for metal fatigue, signal analysis, test control, and specification of random vibration environments.

A bachelors degree in engineering, or equivalent, is presumed.

Course Format

Each approximately one hour-long lecture is followed by a short problem designed to reinforce the concepts presented. There is ample class time for discussion of the fundamental concepts. Questions are encouraged. Limited discussions on more advanced topics and techniques are included for the more advanced student.

The instructors are also available for discussion about specific situations or problems students may have at work.

Class hours are 8:00 am to 5:00 pm, Monday through Thursday, with a one hour lunch break. 

Course Materials

 Each participant will receive:

 o Course Notes: A copy of all transparencies, problems and solutions

o Educational Software: A simple signal analysis program (for PCs), that exercises estimation algorithms developed in the course

Preparation

Although it is not a prerequisite, it is recommended that you review the fundamentals of probability and statistics from an undergraduate text.

You may also wish to review the documentation you may have for testing equipment, analysis software, etc..

Bring a calculator to work in-class problems.

If you wish to discuss a specific problem, bring what you need to address it.

Course Outline 

Random Variables:  single random variables; correlated random variables; common probability distributions

Random Processes:  auto-correlation; stationary processes

Fourier Transforms:  Fourier series and transforms; delta functions

Spectral Density:  spectral analysis; Wiener's theorem; spectral and cross-spectral density; coherence

Statistics of Stationary Processes:  level crossings; peaks

Vibration of Single-Degree-of-Freedom Systems: free and forced vibration; transfer functions; response to arbitrary loadings

Random Vibration of SDOF Systems: spectral density of response; response to white noise

 Multi-Degree-of-Freedom Systems: modal analysis; response to random loads; modal combination

Design for Random Vibration Extreme Loads: three-sigma criteria; first passage of extreme loads

Design for Random Vibration Fatigue Stresses: material models of metal fatigue; fatigue stress analysis; probabilistic fatigue analysis

Statistical Parameter Estimation: properties of estimators; confidence intervals; sampling distributions

Time-Domain Estimation: ensemble and temporal averages; non- stationary processes; shock response spectra

Discrete Fourier Transform: DFT; aliasing, leakage, data windows; fast Fourier transform (FFT)

Frequency-Domain Estimation: spectral density estimates; real-time estimates; transfer function estimates; random vibration test control

Educational Software

Special Topics: e.g., nonlinear random vibration; probabilistic design

Guest Lectures: From time to time, specialists from industry are invited to participate and present specialized instruction.