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Session 1620

An Integrated Vibrations and System Simulation Course

George M. Swisher, Corinne M. Darvennes Tennessee Technological University

Abstract

This paper describes a junior-level, three-credit-hour, one-semester, required course in Mechanical Engineering (ME) at Tennessee Technological University. The authors have integrated the analytical (classical) study of vibrating systems with extensive use of digital simulation of the differential equations of motion. This course is a result of combining a traditional three-credit hour, one-quarter vibrations course with a one-hour, one-quarter digital system simulation course. Simulation, employing a sophisticated computation system, lends reality to the solution process and matches the procedures used by practicing engineers in that ME speciality.

I. Introduction

On the quarter system, the ME faculty taught a classical vibrations course emphasizing one and two degrees of freedom systems and their mathematical solutions. A follow-on, one-credit hour digital simulation laboratory (requiring the vibrations class as a pre-requisite) emphasized the numerical solutions of differential equations using such higher-level programs as SL-1 (developed by Xerox in the late 1960’s), CSMP (developed by IBM in the late 1960’s), ACSL1, and now MATLAB®2; this evolution followed the introduction of each new package designed to solve differential equations. In 1989, during the university transition to the semester system, the faculty combined these two courses into the course described in this paper. MATLAB on a VAX mainframe system was started in 1992 with the migration to the PC version in 1996. The current prerequisites for the combined course are beginning courses in computer programming (FORTRAN or C), engineering dynamics, and ordinary differential equations. System simulation is accomplished using MATLAB’s ordinary differential equation (ODE) solvers, primarily ODE23 and ODE45, in a just-in-time, balanced presentation mode. In the current curriculum, this is the ME students’ introduction to MATLAB and also serves as the foundation for its later use in other ME courses.

II. Course Content

The major student outcomes of the course are that the student must be able to a) derive the system differential equations for single (one) and multiple degree-of-freedom vibrating systems {sdf and mdf systems}; b) solve for the analytical solutions for single degree-of-freedom systems for free and forced responses; c) solve analytically for the natural frequencies and mode shapes for multiple degree-of-freedom systems, with primary emphasis on two degree-of-freedom systems; d) demonstrate a fundamental capability of using MATLAB to manipulate matrices and solve coupled ordinary differential equations; e) design a simple vibration absorber system; f) utilize MATLAB’s differential equation solvers to solve for time-domain free and forced responses of one and two degree-of-freedom systems; and e) use MATLAB’s eigenvalue/eigenvector matrix functions to solve for the natural frequencies and mode shapes for

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Swisher, G. M., & Darvennes, C. (1999, June), An Integrated Vibrations And System Simulation Course Paper presented at 1999 Annual Conference, Charlotte, North Carolina. 10.18260/1-2--7752