Session: 09-03-01: Applied Mechanics, Dynamic Systems, and Control Engineering

Paper Number: 94574

94574 - Virtual Vibrations Laboratory 

At our institution, vibrations class is a four-credit-hour elective course with no physical laboratory component to it. Class meets twice a week, 100 minutes each time, studying typical topics that are covered in an introductory vibrations course. These topics constitute one degree and two degree of freedom systems under free and forced vibrations. Lacking a physical vibrations lab, yet having the luxury of covering course topics for 200 minutes per week, it was decided to devote some instruction time to reinforce conceptual understanding and validation of vibration topics through a virtual laboratory setting. To attain our objective, it was decided to employ SIMULINK to simulate vibration experiments. Some of these virtual experiments are presented below. Throughout the semester, a total of 400 minutes, which are equivalent to four-class periods, was devoted to teach students how to work with the software and implement the building blocks for each vibration topic in SIMULINK. After every four lectures, 50 minutes or, equivalently, one-half of every fifth lecture period, were devoted to teach students the skills needed to finish their project assignments in SIMULINK environment.

Fortunately, the learning curve for students, because of the user-friendly nature of SIMULINK, was reasonable, if not gentle. Instead of writing a code, students used SIMULINK’s building blocks to implement each experiment on a computer. Also, avoiding rigors of solving governing differential equations by classical methods was something that students liked in using SIMULINK. In fact, working with building blocks in SIMULINK to solve the governing differential equations was a fun activity that they enjoyed.

 

In their project assignments, students simulated response of single degree and two degree of freedom systems to free vibrations, damped free vibrations, harmonic forced vibrations, and transient unit step excitations. Using the scope and power spectral density windows in SIMULINK clear understanding of stable and unstable response of the system for different system parameters and excitations were achieved. Beating phenomenon, together with system resonance to harmonic excitations were realized. Phase diagram together with instability, and stability of the responses were simulated and analyzed. Response of nonlinear systems to different initial conditions in free vibrations was simulated and analyzed as well.
 

In this paper, it is attempted to present the development of some of the virtual experiments named above in the same chronological order. It is hoped that the outcome helps other students of vibration learn the intricate concepts and topics of this course in a rather fun and simple way to understand.

Presenting Author: Ali Mohammadzadeh Grand Valley State University

Presenting Author Biography: Ali R. Mohammadzadeh is associate professor of mechanical engineering at Grand Valley State University's Padnos school of engineering and computing. He earned his PhD in mechanical engineering from the University of Michigan in Ann Arbor. His research interest is in the field of fluid solid interaction

Authors:

Ali Mohammadzadeh Grand Valley State University
Salim Haidar Grand Valley State University