Natural Frequencies and Mode Shapes of Beams Carrying a Two Degree-of-Freedom Spring-Mass System

[+] Author and Article Information
Ming Une Jen, E. B. Magrab

Department of Mechanical Engineering, College of Engineering, University of Maryland, College Park, MD 20742

J. Vib. Acoust 115(2), 202-209 (Apr 01, 1993) (8 pages) doi:10.1115/1.2930331 History: Received December 01, 1991; Revised March 01, 1992; Online June 17, 2008


An exact solution for the natural frequencies and mode shapes for a beam elastically constrained at its ends and to which a rigid mass is elastically mounted is obtained. The attached mass can both translate and rotate. The general solution is obtained using the Laplace transform with respect to the spatial variable and yields the exact solutions to several previously published simpler configurations that were obtained using approximate methods. Numerous numerical results are presented for the natural frequency coefficients that extend previously reported results and that show the transition between various limiting cases. In addition, values are presented for the lowest two natural frequency coefficients for a beam that is clamped at both ends and is carrying a two dof spring-mass system. Representative mode shapes at selected values of the system’s parameters are also given.

Copyright © 1993 by The American Society of Mechanical Engineers
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