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RESEARCH PAPERS: Vibration and Sound

On the Vibration of a Point-Supported Linear Distributed System

[+] Author and Article Information
L. A. Bergman, D. Michael McFarland

Department of Aeronautical and Astronautical Engineering, University of Illinois at Urbana-Champaign, 104 South Mathews Avenue, Urbana, Illinois 61801

J. Vib., Acoust., Stress, and Reliab 110(4), 485-492 (Oct 01, 1988) (8 pages) doi:10.1115/1.3269555 History: Received January 15, 1988; Online November 23, 2009

Abstract

The vibration of a constrained dynamical system, consisting of an Euler-Bernoulli beam with homogeneous boundary conditions, supported in its interior by arbitrarily located pin supports and translational and torsional linear springs, is studied. A generalized differential equation is obtained by the method of separation of variables and is solved in terms of the Green’s function and its derivatives of the unconstrained beam. System natural frequencies and modes are obtained, and the orthogonality relation for the natural modes is derived. A general solution for the forced response is given. Finally, two pertinent problems from the literature are examined, and results obtained are compared with those of a small, dedicated finite element formulation to assess the relative accuracy and efficiency of each.

Copyright © 1988 by ASME
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