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Effect of Thermal Environment and Peripheral Loading on Axisymmetric Vibrations of Non-uniform FG Circular Plates via Generalized Differential Quadrature Method

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Abstract

In this article, axisymmetric vibrations of a non-uniform functionally graded circular plate subjected to uniform in-plane peripheral loading and non-linear temperature rise across the thickness have been analyzed on the basis of classical theory of plates. The thickness of the plate is assumed to vary exponentially along the radial direction. The plate material is graded in thickness direction using a power-law model and its mechanical properties are temperature-dependent. Keeping the uniform thermal environment over the top and bottom surfaces, the equations for thermoelastic equilibrium and axisymmetric motion for such a plate model have been derived by Hamilton’s energy principle. Employing generalized differential quadrature method, the frequency equations for clamped and simply supported plates have been obtained and solved numerically using MATLAB. The lowest three roots have been retained as the frequencies for the first three modes of vibration. The influence of various parameters, such as power-law index, in-plane force parameter and temperature difference with varying values of thickness parameter, has been analyzed on the vibration characteristics of the plate. By allowing the frequency to approach zero, the critical buckling loads with varying values of other parameters have been computed. The benchmark results for linear as well as uniform temperature rise have also been computed. The validity of the present technique is verified by comparing the results with the published work.

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Acknowledgments

The financial support provided by MHRD, India (Grant No. MHRD-02-23-200-44) in carrying this research work is gratefully acknowledged by Rahul Saini.

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  1. Department of Mathematics, IIT Roorkee, Roorkee, 247667, India

    Rahul Saini & Roshan Lal

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  1. Rahul Saini
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Correspondence to Rahul Saini.

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Saini, R., Lal, R. Effect of Thermal Environment and Peripheral Loading on Axisymmetric Vibrations of Non-uniform FG Circular Plates via Generalized Differential Quadrature Method. J. Vib. Eng. Technol. 9, 873–886 (2021). https://doi.org/10.1007/s42417-020-00270-x

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