Abstract
The analysis presented here is to study the effect of thermal gradient on the vibration of visco-elastic rectangular plate (having clamped boundary condition on all the four edges) of variable thickness whose thickness varies parabolically in both directions. The effect of linear temperature variation has been considered. A frequency equation of plate has been obtained by Rayleigh-Ritz technique with two terms of deflection function. The assumption of small deflection and linear visco-elastic properties of ‘Kelvin’ type are taken. Deflection and time period corresponding to the first two modes of vibrations for clamped plate have been computed for various combinations of aspect ratio, thermal constants, and taper constants. Numerical computations have been performed for an alloy ‘Duralium’ and the results obtained are depicted graphically.
Highlights
In the course of time, the study of vibration of plates has acquired great importance in the field of research, engineering and space technology
Since new materials and alloys are in great use in the construction of technically designed structures the application of visco-elasticity is the need of the hour
Thermal induced vibrations of plates of variable thickness are very useful for research workers in nuclear and chemical engineering
Summary
In the course of time, the study of vibration of plates has acquired great importance in the field of research, engineering and space technology. A.K. Gupta et al / Thermal effect on vibration of clamped visco-elastic rectangular plate. The effect of thermal gradient on the frequencies of an orthotropic plate of linearly varying thickness has been discussed by Tomar and Gupta [22]. Tomar and Gupta [21] discussed the effect of thermal gradient on frequencies of an orthotropic rectangular plate whose thickness varies in two directions. Gupta and Khanna [8] solved the problem of vibration of visco-elastic rectangular plate with linearly thickness variations in both directions. The aim of present investigation is to study the effect of thermal gradient on the vibration of a clamped visco-elastic rectangular plate whose thickness varies parabolically in both directions, which is an extension of authors’ work [7]. All the material parameters used in numerical calculations have been taken for alloy ‘Duralium’
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