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Simulation of Multiple-Degree-of-Freedom Oscillatory Systems Within an Undergraduate Project-based Learning Environment

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Conference

2021 ASEE Virtual Annual Conference Content Access

Location

Virtual Conference

Publication Date

July 26, 2021

Start Date

July 26, 2021

End Date

July 19, 2022

Conference Session

Engineering Physics and Physics Division Technical Session 2

Tagged Division

Engineering Physics and Physics

Page Count

21

Permanent URL

https://peer.asee.org/37716

Download Count

7

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Paper Authors

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Günter Bischof Joanneum University of Applied Sciences

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Günter Bischof is currently an associate professor at Joanneum University of Applied Sciences and teaches engineering and applied mathematics.

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Lukas Eckstein Joanneum University of Applied Sciences

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Lukas Eckstein is currently studying Automotive Engineering at the Joanneum University of Applied Sciences.

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Benjamin Gahleitner Joanneum University of Applied Sciences

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Benjamin Gahleitner is currently studying Automotive Engineering at the Joanneum University of Applied Sciences. Prior to his studies, he attended a HTL, a technical secondary school that specializes on mechanical engineering.

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Mario Gasparic Joanneum University of Applied Sciences

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Mario Gasparic is currently studying Automotive Engineering at the Joanneum University of Applied Sciences. Prior to his studies, he attended a grammar school in Slovenska Bistrica, Slovenia.

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Moritz Reisenberger Joanneum University of Applied Sciences

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Moritz Reisenberger is currently studying Automotive Engineering at the Joanneum University of Applied Sciences.

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Sascha Savoric Joanneum University of Applied Sciences

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Sascha Savoric is currently studying Automotive Engineering at the Joanneum University of Applied Sciences. Prior to his studies, he attended a HTL, a technical secondary school that specializes on Mechatronics and Automatisation.

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Christian J. Steinmann HM&S IT Consulting

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Christian Steinmann is manager of HM&S IT-Consulting and provides services for Automotive SPiCE. Currently, his main occupation is process improvement for embedded software development for an automobile manufacturer. On Fridays, he is teaching computer science and programming courses at Joanneum University of Applied Sciences in Graz, Austria.

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Alexander Tretton

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Alexander Tretton is currently a student at the Joanneum University of Applied Science and started his studies in automotive engeneering in fall 2019.

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Abstract

Coupled oscillations can be found throughout the physical world on both micro and macro levels, from oscillating molecules to lattice vibrations in solids, up to the oscillations of macroscopic mechanical or electrical systems. Despite the fact that the dynamics of such systems is governed by forces originating from a variety of potentials, the harmonic-oscillator potential approximation can be used for almost every system close to equilibrium, which makes it fundamental in many fields of physics. The equations of motion of single harmonic-oscillators as well as of one-dimensional linear elastic multiple-degree-of-freedom systems can be solved analytically, which enables a quantitative study of idealized model systems and, furthermore, some qualitative insight into the behavior of more complex real-life systems. Multi-dimensional multiple-degree-of-freedom systems are, in general, no longer accessible to analytical solutions. A perpendicular spring configuration, for instance, introduces a nonlinearity of the Duffing type and can lead to chaotic behavior. In order to engage our students with the analysis of multiple-degree-of-freedom oscillatory systems, an interdisciplinary undergraduate student research project was initiated, which encompassed the development of computer programs for the simulation and visualization of elastically coupled particles aligned in a straight line, as well as for the simulation of two-dimensional arrays of coupled oscillators. The equation of motion of one-dimensional oscillatory systems was solved numerically and ‒ for small systems ‒ analytically in order to test the quality of the numerical integration. In the case of two-dimensional arrays, the conservation of total energy was used for validation. Three teams of three students each took up the challenge and worked simultaneously and competitively on that project, with the additional complication that the team members had to work in different locations due to the Covid-19 pandemic. The integration of the coupled systems of differential equations was programmed in C#, with a graphical user interface that provides a display of the vibrating systems, graphs of the mass displacements over time, and phase-space diagrams. The dynamic visual output of the program was designed to provide a playful insight into the behavior of multiple-degree-of-freedom lumped-mass systems. In this paper, the theoretical background, the approach to the problem and the outcome of the undergraduate student projects are presented and discussed.

Bischof, G., & Eckstein, L., & Gahleitner, B., & Gasparic, M., & Reisenberger, M., & Savoric, S., & Steinmann, C. J., & Tretton, A. (2021, July), Simulation of Multiple-Degree-of-Freedom Oscillatory Systems Within an Undergraduate Project-based Learning Environment Paper presented at 2021 ASEE Virtual Annual Conference Content Access, Virtual Conference. https://peer.asee.org/37716

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