Many vibrating mechanical and structural systems consist of a host structure to which a number of continuous attachments are mounted. In this paper, an efficient method is proposed for determining the eigenfrequencies of an arbitrarily supported Euler–Bernoulli beam with multiple in-span helical spring-mass systems, where the mass of the helical spring is considered. For modeling purposes, each helical spring can be modeled as an axially vibrating elastic rod. The traditional approach of using the eigenfunctions of the beam and rod in the assumed modes method often leads to an intolerably slow convergence rate. To expedite convergence, a spatially linear-varying function that corresponds to the static deformed shape of a rod is included in the series expansion for the rod. The proposed approach is systematic to apply, easy to code, computationally efficient, and can be easily modified to accommodate various beam boundary conditions. Numerical experiments show that with the addition of a spatially linear-varying function, the proposed scheme converges very quickly with the exact solution.
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December 2008
Research Papers
Eigenfrequencies of an Arbitrarily Supported Beam Carrying Multiple In-Span Elastic Rod-Mass Systems
Philip D. Cha,
Philip D. Cha
Professor
Department of Engineering,
e-mail: philip̱cha@hmc.edu
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711
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Michael Chan,
Michael Chan
Student
Department of Engineering,
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711
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Gregory Nielsen
Gregory Nielsen
Student
Department of Engineering,
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711
Search for other works by this author on:
Philip D. Cha
Professor
Department of Engineering,
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711e-mail: philip̱cha@hmc.edu
Michael Chan
Student
Department of Engineering,
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711
Gregory Nielsen
Student
Department of Engineering,
Harvey Mudd College
, 301 Platt Boulevard, Claremont, CA 91711J. Vib. Acoust. Dec 2008, 130(6): 061008 (9 pages)
Published Online: October 22, 2008
Article history
Received:
September 20, 2007
Revised:
June 9, 2008
Published:
October 22, 2008
Citation
Cha, P. D., Chan, M., and Nielsen, G. (October 22, 2008). "Eigenfrequencies of an Arbitrarily Supported Beam Carrying Multiple In-Span Elastic Rod-Mass Systems." ASME. J. Vib. Acoust. December 2008; 130(6): 061008. https://doi.org/10.1115/1.2980384
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