June 24, 2007
June 24, 2007
June 27, 2007
12.1364.1 - 12.1364.13
Teaching of Dynamic Systems with Integrated Analytical and Numerical Techniques
Jiang Zhou, Paul Corder, and Kendrick Aumg Department of Mechanical Engineering Lamar University, Beaumont, TX 77710, USA
Mastering ordinary differential equations is very important and essential to being successful in this course of Dynamics Systems. In order to help the students further explore these new concepts and overcome some of the issues related to these deficiencies in material recall, integrated analytical and numerical techniques are adopted in teaching. One problem can be solved by various different approaches. Analytically, the method of undetermined coefficients and the Laplace transform method are used. Numerically, the transfer function method and the block diagram method in Simulink; LTI models, and symbolic toolbox in Matlab, etc, are used. Numerical approaches, especially with the transfer function method in Simulink, visualize the physics and results behind the seemingly daunting equations. By showing the application of different techniques to the same problem, students are inspired to learn the resulting similarities and differences. The MATLAB graphical user interfaces were developed for second order dynamic systems for both free vibration and forced vibration. The visual interface presents results in a way that students can immediately identify the effects of changing system parameters. Both time response and frequency response are clearly shown in the interface. In the course, a research related project is assigned to identify the dynamic response of a portable telecommunication device. In this project, students are required to use both analytical and numerical approaches to show the insight of the material selection affects the reliability of the portable telecommunication devices.
A course in system dynamics that deals with mathematical modeling and response analysis of dynamic systems is required in most mechanical and many other engineering curricula. The analysis and design methods in the course cover a wide variety of different systems, such as mechanical, electrical, pneumatic, hydraulic, and thermal systems. Although systems are in various fields, mathematically they all can be simplified and represented by ordinary differential equations. Mastering ordinary differential equations (ODEs) is very important and essential to being successful in this course.
In teaching a Dynamic Systems course, basic concepts of solutions of first and second order differential equations and Laplace transforms are expected to be firmly planted in the students’ skill sets. However, the reality is that the students simply do not remember much of former material since these courses were taken a year, or even years earlier. Moreover, new terminology
Zhou, J., & Corder, P., & Aung, K. (2007, June), Teaching Of Dynamic Systems With Integrated Analytical And Numerical Techniques Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. https://peer.asee.org/2865
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