Non-homogeneity effect on the vibration of the rectangular visco-elastic plate subjected to the linear temperature effect with quadratic thickness variation in both directions

Sudhanshu  Aggarwal

doi:10.14311/AP.2024.64.0297

Authors

Sudhanshu Aggarwal National Post Graduate College Barhalganj, Department of Mathematics, Gorakhpur-273402, Uttar Pradesh, India https://orcid.org/0000-0001-6324-1539

DOI:

https://doi.org/10.14311/AP.2024.64.0297

Keywords:

Rayleigh-Ritz technique, taper constants, clamped plate, differential equation, thermal constant

Abstract

The present work investigates the effect of non-homogeneity on the vibration of a rectangular visco-elastic plate. The plate is subjected to linear temperature variation in the x-direction with quadratic thickness variation in both directions. The quadratic variation has been considered in the material density of the plate only along the x-axis, and it is assumed that non-homogeneity transpires because of this variation. The governing differential equation is solved using the Rayleigh-Ritz technique. All four edges of the plate should be clamped to drive the frequency equation. Deflection and time period have been evaluated for several combinations of values of the thermal constant, constant of nonhomogeneity, taper constants, and length-to-width ratio (aspect ratio) for the first two vibration
modes of the clamped plate. The results presented are compared with those found in the literature.

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