June 14, 2009
June 14, 2009
June 17, 2009
14.400.1 - 14.400.11
DampedBeams: A Versitile MATLAB Script for Animation of a Variety of Beam Vibration Problems
The authors report development of a single piece of software that animates responses of an elastic beam with external viscous damping and four different sets of support conditions. The motion can be unforced, stimulated by initial deflection, or when externally forced by several combinations of temporal and spatial forms for the forcing function. Several examples are presented.
Beams are fundamental building blocks of structures and machine assemblies, hence understanding of their lateral vibration is key to understanding the dynamics of those systems. Free and forced vibration of beams may be analyzed by employing eigenfunction expansions and solving the problem in normal coordinates which are the time dependent coefficients of the generalized Fourier expansion in the eigenfunctions.1,2 The purpose of this paper is to create an awareness of this and other available software for the animation of beam vibration. The software reported here is designed to animate both free and forced vibration of beams with a variety of boundary conditions and forcing functions, and is intended for a second course in vibrations.
There is a considerable body of literature dealing with the visualization of partial differential equation solutions. A detailed bibliography on visualization of partial differential solutions is available at http://www.eng.uwyo.edu/classes/matlabanimate. Reports of animation to enhance understanding of vibration principles have been in the papers of Gramoll and his colleagues, including axial vibration of an elastic bar.3,4 The first report of animation employing MATLAB handle graphics was by Watkins et al.5 Animation of the beam lateral vibration using MATLAB was first reported in 2001.6 An alternative to writing scripts in MATLAB or some other programming language is to use a commercial finite element program as reported by Barker.7 The application of the handle graphics to animate a wide variety of partial differential equation problems is illustrated in reference.8
MATLAB is perhaps the most widely used general-purpose scientific and engineering software package used in engineering education and engineering practice. It is thus appropriate to develop software for the purpose given here in that computing environment. The reasons to choose MATLAB over other numeric and symbolic computing environments are MATLAB is a compact computing environment with simple syntax and array computing; It incorporates powerful 2-D and 3-D graphics; It is portable and readily available; There exist intrinsic robust ODE solution routines available for initial value problems, A student edition is available; Authors have positive past experiences with other applications.
Jacquot, R., & Anderson, J., & Walrath, D. (2009, June), Damped Beams: A Versatile Matlab Script For The Animation Of A Variety Of Beam Vibration Problems Paper presented at 2009 Annual Conference & Exposition, Austin, Texas. https://peer.asee.org/4615
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