0
RESEARCH PAPERS

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

Abstract

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
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In