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Damped Beams: A Versatile Matlab Script For The Animation Of A Variety Of Beam Vibration Problems

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2009 Annual Conference & Exposition


Austin, Texas

Publication Date

June 14, 2009

Start Date

June 14, 2009

End Date

June 17, 2009



Conference Session

Teaching Dynamics

Tagged Division


Page Count


Page Numbers

14.400.1 - 14.400.11



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Paper Authors


Raymond Jacquot University of Wyoming

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Ray Jacquot, Ph.D., P.E., received his BSME and MSME degrees at the University of Wyoming in 1960 and 1962 respectively. He was an NSF Science Faculty Fellow at Purdue University where he received the Ph.D. in 1969. He joined the Electrical Engineering faculty of the University of Wyoming in 1969. He is a member of ASEE, IEEE and ASME and has been active in ASEE for over three decades serving as Rocky Mountain Section Chair and PIC IV Chair. His professional interests are in modeling, control, simulation and animation of dynamic systems. He is currently Professor Emeritus of Electrical and Computer Engineering. E-mail:

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Jeffrey Anderson University of Wyoming

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Jeffrey Anderson earned his Ph.D. in Electrical and Computer Engineering at the University of Wyoming with a research emphasis in image processing. He received his BS and ME from the University of Utah in 1989 and 1992 respectively. He has worked on a closed-loop controller for mechanical ventilation of patients with adult respiratory distress syndrome. Additionally he has worked on a servo lung simulator with a related control method that was awarded a U.S. Patent. He is a member of IEEE and ASEE. He is currently an Assistant Academic Professional Lecturer in both the Electrical and Computer Engineering and the Mechanical Engineering Departments at the University of Wyoming. Email:

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David Walrath University of Wyoming

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David Walrath, Ph.D., P.E., earned his BSME and MSME degrees from the University of Wyoming in 1974 and 1975. He received his Ph.D. in Mechanical and Aerospace Engineering from the University of Delaware in 1986. He is currently a Professor of Mechanical Engineering at the University of Wyoming. His interests include solid mechanics and materials modeling and testing with emphasis on the study and use of fiber-reinforced composite materials. E-mail

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract

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 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. 10.18260/1-2--4615

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: © 2009 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