Free Vibration Studies on Stress-Free Three-Dimensional Elastic Solids

[+] Author and Article Information
K. M. Liew, K. C. Hung, M. K. Lim

Dynamics and Vibration Centre, School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 2263

J. Appl. Mech 62(1), 159-165 (Mar 01, 1995) (7 pages) doi:10.1115/1.2895897 History: Received February 04, 1993; Revised December 07, 1993; Online October 30, 2007


A comprehensive investigation on free vibration of three-dimensional elastic solids of rectangular planform is reported. The continuum is considered to be free from normal and in-plane stresses on the facets. Functions representing the spatial displacement fields of the continuum in a complete Cartesian coordinate system are expressed in terms of sets of orthogonal polynomial functions in the x, y, and z directions. The energy functional derived based on the three-dimensional elasticity theory is minimized to arrive at the governing eigenvalue equation. In this paper, the vibration of stress-free elastic solids in the forms of short columns, thick plates, and solid cubes are studied. Frequency parameters and the first known three-dimensional deformed mode shapes have been generated for these stress-free elastic solids.

Copyright © 1995 by The American Society of Mechanical Engineers
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