Non-linear Thermoelastic Analysis of an Anisotropic Rectangular Plate

TL;DR

This paper presents a comprehensive non-linear thermoelastic analysis of a rotating anisotropic rectangular plate under electromagnetic influence, employing fractional calculus and eigenvalue methods for analytical solutions.

Contribution

It introduces a fractional order energy model within the Green-Naghdi framework for the first time in analyzing such plates, providing a novel analytical solution approach.

Findings

Analytical closed-form solutions derived for the governing equations.

Graphical results showing stress variations across the plate.

Insights into the effects of electromagnetic fields and rotation on thermoelastic behavior.

Abstract

Three-dimensional thermoelastic analysis in presence of electro magnetic field is investigated of a rectangular plate. In the context of Green-Naghdi model-II, fractional order energy equation is adopted for a rotating anisotropic rectangular plate which is subjected to simply supported and isothermal on its four lateral edges. Normal mode analysis is adopted to the governing equations to formulate a Vector-matrix differential equation. The analytical closed form solution of the Vector-matrix differential equation is obtained for the physical parameters using eigen value approach methodology. Numerical results are represented graphically with a sinusoidal spatial variations of the stress applied on the top surface of the plate.