TY - JOUR
T1 - Vibration of thick skew plates based on Mindlin shear deformation plate theory
AU - Liew, K. M.
AU - Xiang, Y.
AU - Kitipornchai, S.
AU - Wang, C. M.
PY - 1993/1/1
Y1 - 1993/1/1
N2 - The free flexural vibration of thick skew plates is considered. The total energy functional is derived based on the first order shear deformation plate theory by Mindlin. The newly developed pb-2 Rayleigh-Ritz method is applied to obtain the solution. The method features the versatile pb-2 Ritz functions for approximating the deflection and rotation functions which comprise the product of (1) a two-dimensional polynomial function (p-2) and (2) a basic function (b). The basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset, since it is formed from the product of the boundary equations raised to appropriate powers. Natural frequency parameters for skew Mindlin plates with different combinations of boundary conditions are presented. The solutions, where possible, are verified by comparisons with those available in the open literature. The effect of the Poisson ratio on vibration frequencies of plates with free edges is also investigated.
AB - The free flexural vibration of thick skew plates is considered. The total energy functional is derived based on the first order shear deformation plate theory by Mindlin. The newly developed pb-2 Rayleigh-Ritz method is applied to obtain the solution. The method features the versatile pb-2 Ritz functions for approximating the deflection and rotation functions which comprise the product of (1) a two-dimensional polynomial function (p-2) and (2) a basic function (b). The basic function is the key to ensure the automatic satisfaction of the geometric boundary conditions at the outset, since it is formed from the product of the boundary equations raised to appropriate powers. Natural frequency parameters for skew Mindlin plates with different combinations of boundary conditions are presented. The solutions, where possible, are verified by comparisons with those available in the open literature. The effect of the Poisson ratio on vibration frequencies of plates with free edges is also investigated.
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U2 - 10.1006/jsvi.1993.1361
DO - 10.1006/jsvi.1993.1361
M3 - 21_Publication in refereed journal
VL - 168
SP - 39
EP - 69
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
SN - 0022-460X
IS - 1
ER -