Effect of thermal gradient on vibration of non-homogeneous visco-elastic elliptic plate of variable thickness |
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Authors: | A K Gupta Lalit Kumar |
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Institution: | 1.Department of Mathematics,M.S. College,Saharanpur,India;2.Department of Mathematics,Kisan (P.G.) College,Dist. Ghaziabad,India |
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Abstract: | An analysis and numerical results are presented for free transverse vibrations of non-homogeneous visco-elastic elliptic plate
whose temperature and thickness spatial variations both are parabolic along a line through plate centre. The variation in
density is assumed as parabolic along a line through plate centre, which raise non-homogeneity of the plate materials and
make problem interesting as introducing variation in non-homogeneity of the material mass density reduce the problem practical
importance in comparison to homogenous plate. For visco-elastic, the basic elastic and viscous elements are combined. We have
taken Kelvin model for visco-elasticity that is the combination of the elastic and viscous elements in parallel. Here the
elastic element means the spring and the viscous element means the dashpot. The governing differential equation of motion
has been solved by Galerkin’s technique. Deflection, time period and logarithmic decrement corresponding to the first two
modes of vibrations of a clamped non-homogeneous visco-elastic elliptic plate for various values of taper constant, thermal
constants, non-homogeneity constant and aspect ratio are obtained and shown graphically. |
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Keywords: | |
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