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Three-dimensional free vibration analysis of functionally graded material plate resting on Pasternak foundation

English Abstract

A three-dimensional approach to analyze the free vibration of rectangular FGM plates resting on Pasternak foundation is developed based on the linear, small strain, three-dimensional elasticity theory using Ritz method. The three displacement components are expanded by a triplicate series of Chebyshev polynomials multiplying appropriate boundary functions. The nature frequency parameters can be obtained by solving the governing matrix which established by the Ritz procedure. The elastic foundation are modeled as Pasternak foundation with two parameters which considering the Winkler foundation stiffness and the shearing layer stiffness. The convergence study shows a fast convergence rate. A few terms can give reasonable frequencies of the first few modes, and the convergence rate is independent of the volume fraction. The comparisons with other theories and approaches also show good agreements. A detailed parametric study is performed. The natural frequency parameters decrease with the increase of thickness-side ratios , volume fraction indices , and increase with the increase of aspect ratios . For the free vibration of rectangular FGM plates resting on Paternak foundations, the vertical displacement of the plate increases with the increase of the foundation stiffness, and the displacement of the top surface of the plate is always larger than that of the bottom surface. The difference in displacements indicates stretching and compressing of the thickness during vibration. It also should be noticed that there may exist cross points between different frequencies in the figures of the frequency parameters with respect to the varying thickness-side ratios. It is indicated that flexural vibration mode may turn into shear vibration mode by the increasing of the thickness-side ratio. The three-dimensional plate theory can give a physical insight of displacements along the thickness direction of the plate, thickness shear modes can be shown directly as well as flexural modes. These are not obtained by two-dimensional plate theories

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Fang, Yi Zhi


Faculty of Science and Technology


Department of Civil and Environmental Engineering




Vibration -- Mathematical models

Functionally gradient materials

Plates (Engineering) -- Vibration -- Mathematical models


Iu, Vai Pan

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1/F Zone C
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