TY - JOUR
T1 - Free vibration studies on stress-free three-dimensional elastic solids
AU - Liew, K. M.
AU - Hung, K. C.
AU - Lim, M. K.
PY - 1995/3
Y1 - 1995/3
N2 - 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.
AB - 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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M3 - 21_Publication in refereed journal
VL - 62
SP - 159
EP - 165
JO - Journal of Applied Mechanics, Transactions ASME
JF - Journal of Applied Mechanics, Transactions ASME
SN - 0021-8936
IS - 1
ER -