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Deformation of modified couple stress thermoelastic diffusion in a thick circular plate due to heat sources

Kumar R., Devi S.

Computational Methods in Science and Technology

2019

Vol. 25, No. 4

167--176

The aim of this study is to present a mathematical model for predicting the results for displacements, stress components, temperature change and chemical potential with considering independently a particular type of heat source. The general solution for the two-dimensional problem of a thick circular plate with heat sources in modified couple stress thermoelastic diffusion has been obtained in the context of one and two relaxation times. Laplace and Hankel transforms technique is applied to obtain the solutions of the governing equations. Resulting quantities are obtained in the transformed domain. The numerical inversion technique has been used to obtain the solutions in the physical domain. Effects of time on the resulting quantities are shown graphically.

Natural vibrations of thick circular plate based on the modified Mindlin theory

Senjanovic I., Hadzic N., Vladimir N., Cho D.-S.

Archives of Mechanics

2014

Vol. 66, nr 6

389--409

Outline of the modified Mindlin theory is presented in which the Mindlin mathematical model with three differential equations of motion for total deflection and rotations is decomposed into a single equation for pure bending vibrations with transverse shear and rotary inertia effects and two differential equations for in-plane shear vibrations. The governing equations are transformed from orthogonal to polar coordinate system for the purpose of circular plate vibration analysis. The fourth order differential equation of flexural vibrations is split further into two second order equations of Bessel type. Also, the in-plane shear differential equations are transformed to Bessel equation by introducing displacement potential functions. The exact values of natural frequencies are listed and compared with FEM results.