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Developing an Interactive Computer Program to Enhance Student Learning of Dynamical Systems

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2016 ASEE Annual Conference & Exposition


New Orleans, Louisiana

Publication Date

June 26, 2016

Start Date

June 26, 2016

End Date

August 28, 2016





Conference Session

Modeling and Simulation

Tagged Division

Computers in Education

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Paper Authors


Daniel K. Howe George Mason University

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Daniel Howe is a Junior in Mechanical Engineering at George Mason University. A native of Fairfax, VA, he enrolled in the major in January 2015. In addition to the curriculum, he researches the mechanics of dynamic systems as a research assistant to the Department Chair, Oscar Barton, Jr., PhD, PE. In particular, his researches focuses on the computer modeling of vibrations in dynamic systems. Mr. Howe also provides academic support as a tutor for mathematics, science, and engineering in the Volgeneau School of Engineering, and is the Secretary of the George Mason University Chapter of the American Society of Mechanical Engineers.

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Oscar Barton Jr. George Mason University

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Oscar Barton, Jr., Ph.D, P.E. is a Professor of Mechanical Engineering at George Mason University A native of Washington, D.C., Professor Barton received his B.S in Mechanical Engineering from Tuskegee (Institute) University, his M.S in Mechanical Engineering and Ph.D degree in Applied Mechanics from Howard University. Dr. Barton joined the faculty of Mechanical Engineering Department at George Mason University fall 2014, after completing a 22 year career at the U.S. Naval Academy. His research focuses on the development of approximate closed form solutions for linear self-adjoint systems, those that govern the responses of composite structures, and the analysis of dynamic systems. More recently, He has mentored numerous midshipmen through independent research projects and has directed two Trident Scholars, the Naval Academy's flagship research program. He has published over 50 journal and conference articles on these topics.

Dr. Barton is actively involved in curriculum development and program assessment. He chairs ASME Committee on Engineering Accreditation. He serves a Commissioner for Engineering Accreditation Commission of ABET, Inc. and was a program evaluator for 6 six years prior to joining the commission. Dr. Barton holds a professional engineering license in the State Maryland. He is a member of the Board of Education, ASME.

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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

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