Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness

Abstract

In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as one-dimensional distribution in linear form only. An approximate but quiet convenient frequency equation is derived using Rayleigh-Ritz technique with a two-term deflection function. The frequencies corresponding to the first two modes of vibration of a clamped parallelogram plate have been computed for different values of aspect ratio, thermal gradient, taper constants and skew angle. The results have been presented in tabular forms. The results obtained in this study are reduced to that of unheated parallelogram plates of uniform thickness and have generally been compared with the published one.

In this paper, the effect of thermal gradient on the vibration of parallelogram plate with linearly varying thickness in both direction having clamped boundary conditions on all the four edges is analyzed. Thermal effect on vibration of such plate has been taken as one-dimensional distribution in linear form only. An approximate but quiet convenient frequency equation is derived using Rayleigh-Ritz technique with a two-term deflection function. The frequencies corresponding to the first two modes of vibration of a clamped parallelogram plate have been computed for different values of aspect ratio, thermal gradient, taper constants and skew angle. The results have been presented in tabular forms. The results obtained in this study are reduced to that of unheated parallelogram plates of uniform thickness and have generally been compared with the published one.

Cite this paper

nullA. Gupta, M. Kumar, S. Kumar and A. Khanna, "Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness,"*Applied Mathematics*, Vol. 2 No. 1, 2011, pp. 33-38. doi: 10.4236/am.2011.21004.

nullA. Gupta, M. Kumar, S. Kumar and A. Khanna, "Thermal Effect on Vibration of Parallelogram Plate of Bi-Direction Linearly Varying Thickness,"

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