June 18, 2006
June 18, 2006
June 21, 2006
11.588.1 - 11.588.18
Enhancing student understanding of mechanics using simulation software
The wide availability of commercial codes, such as MAPLE®, has made it possible to significantly enhance the teaching of undergraduate courses in mechanics. New problems, usually non-linear, can be introduced which previously could not be treated because of the lack of analytic solutions. By means of numerical solutions to these problems, students can get a feel for finite difference approaches and, perhaps more importantly, their physical understanding can be enhanced and new phenomena explored. The following examples are presented with the underlying equations cast, as much as possible, into non-dimensional form: (i) a finite difference scheme, (ii) a non-linear pendulum subjected to various initial conditions, showing how the period depends on the amplitude, (iii) a non-linear softening spring showing the existence of instabilities, (iv) the stability of an inverted pendulum restrained by a spiral spring, illustrating the existence of multiple equilibrium states and their stability and (v) a numerical simulation of a sweep test (forced motion of a single-degree-of-freedom system in which the forcing frequency varies with time), showing that if the sweep rate is too fast, no resonances will be observed.
The use of software as a teaching aid in undergraduate mechanical engineering courses has been discussed by several authors. A common type used is mathematics software which allows for a wide range of applications from basic to advanced engineering courses. MATLAB®, MATHCAD® and MAPLE®  are some common examples.
In a previous paper one of the authors (Mazzei) discussed his experiences on using commercially available simulation software for dynamics teaching and improving learning. This was done using MSC ADAMS® for rigid body dynamics. Feedback from students showed that simulations can help visualize and understanding of mechanical systems dynamic behavior.
There are numerous papers on the use of software in engineering undergraduate courses. For example in reference Gharghouri discusses his experiences on using MAPLE® for teaching a numerical analysis course. An approach to calculate eigenvalues and eigenvectors for a mechanical vibrations course is given and possible advantages of using the software instead of programming languages is discussed. It was concluded that the use of the software greatly enhanced the delivery of the numerical analysis course.
Another example of a positive use of MAPLE® as a teaching aid can be found in reference where Gerber discusses how the software aided in teaching circuits and systems.
In this paper several examples developed utilizing MAPLE® are presented. The goal is to improve student understanding of mechanical vibrations and dynamics by investigating non- linear physical phenomena and resonance with the aid of the software.
Scott, R., & Mazzei, A. (2006, June), Enhancing Student Understanding Of Mechanics Using Simulation Software Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--264
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