Free vibration analysis of two-dimensional non-homogeneous rectangular plates of variable thickness
The free transverse vibrations of two-dimensional non-homogeneous rectangular plates of variable thickness have been analysedbased on Kirchhoff plate theory. The non-homogeneity of the plate material is assumed to vary along both the axial directions of the plate and arise due to the arbitrary variations in the Young’s modulus and density of the plate material with the in-plane coordinates. The thickness of the plate is varying bidirectionally and taken as the Cartesian product of linear variations along the two concurrent edges of the plate. The governing differential equation of motion for such a plate model has been derived using Hamilton’s energy principle. The resulting equation has been reduced to an eigenvalue problem using two-dimensional generalized differential quadraturemethod for four different boundary conditions. The effect of various parameters such as thickness parameters, non-homogeneity parameters, density parameters, and aspect ratio on the frequencies has been investigated for all the four plates. For a specified plate,three-dimensional mode shapes have been presented. To validate the numerical results comparison has been carried out.”
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