Free vibration studies on stress-free three-dimensional elastic solids

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)159-165
Journal / PublicationJournal of Applied Mechanics, Transactions ASME
Issue number1
Publication statusPublished - Mar 1995
Externally publishedYes


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.

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