New Orleans, Louisiana
June 26, 2016
June 26, 2016
August 28, 2016
Computers in Education
Today’s students are quite accustomed to availing themselves of the latest in computer innovations and technology to aid in learning and the attainment of student outcomes. For example, use of tablets and cellphones in the classroom to take notes, collaborate on projects and to search the web for information is commonplace. Likewise, advancements in computer software and tools afford in-depth simulations of both mechanical and thermal systems. MATHEMATICA, with its symbolic and visual capabilities, is one such tool that, despite its robustness, has seen little utilization in the classroom environment, yet it is viewed as a tool for those who pursue research in every discipline from economics to engineering. In this paper, the capabilities of MATHEMATICA are explored as a tool to model and visualize the forced mechanical response of viscoelastically-damped, multiple degree of freedoms systems through a Newtonian approach, although the Lagrangian approach is equally applicable. By visualizing as well as solving for the behavior of the system, the ability to understand the behavior of dynamical systems is dramatically increased. This possesses value for both an analyst actually utilizing the model as well as an educator who wishes to demonstrate the behavior of these systems without repeatedly undertaking complicated calculations by encapsulating their behavior in a ready to use package. Proportional damping permits the resulting Eigen-value problem to be diagonalized using a Cholesky Decomposition method. In addition, multiple harmonics can be included as part of the forcing function. Displacement results for each mass permit the generation of graphical output and also provide the needed input for the animated motions of all included masses for two degree of freedom systems. While the ultimate goal is to solve the dynamic response of general nth degree of freedom systems, explicit results are presented for the second, fourth, and tenth order degree of freedom system to demonstrate the efficiency of the software. All results are demonstrated in an interactive, user friendly program developed explicitly for this purpose.
Howe, D. K., & Barton, O. (2016, June), Developing an Interactive Computer Program to Enhance Student Learning of Dynamical Systems Paper presented at 2016 ASEE Annual Conference & Exposition, New Orleans, Louisiana. 10.18260/p.26746
ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2016 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015