Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution

Abstract

In the present paper, free vibration analysis of bi-directional functionally graded circular plates subjected to two-dimensional temperature variation has been presented on the basis of first-order shear deformation theory. The mechanical properties of the plate material are assumed to be temperature-dependent and graded in thickness as well as radial direction. Using the thermal boundary conditions of the plate, the exact solution of two-dimensional heat conduction equation has been obtained by separation of variables technique. The thermoelastic equilibrium equations and equations of motion for such plate have been derived from an energy-based Hamilton’s principle. The generalized differential quadrature method has been applied to compute the numerical values for thermally induced displacements and natural frequencies. MATLAB has been used to obtain these values for clamped and simply supported plates. The influence of thermal environment together with various plate parameters such as power-law index, heterogeneity parameter and density parameter on the natural frequencies has been investigated for the first three modes. The results obtained herein for some special cases are in good agreement with those obtained by other numerical methods. Three-dimensional mode shapes for specified plates have been illustrated.

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Acknowledgements

The authors wish to express their sincere thanks to the learned reviewers for their constructive comments and valuable suggestions in improving the paper. The financial support provided by Ministry of Human Resource Development, India, Grant No. MHRD-02-23-200-44 is gratefully acknowledged by Rahul Saini, to carrying this research work which is a part of his Ph.D. work at Indian Institute of Technology Roorkee, Roorkee, India.

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Saini, R., Lal, R. Axisymmetric vibrations of temperature-dependent functionally graded moderately thick circular plates with two-dimensional material and temperature distribution. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-01056-1

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Keywords

  • Vibration
  • Bi-directional functionally graded plates
  • Two-dimensional temperature variation
  • Temperature-dependent mechanical properties
  • Generalized differential quadrature method