Vibrational analysis of viscous thin beams stressed by laser mechanical load using a heat transfer model with a fractional Atangana-Baleanu operator

Abstract

This article investigates the thermoelastic responses of an initially stressed viscoelastic microbeam considering the Kelvin–Voigt scheme. For this purpose, fractional heat conduction models with phase lags and Euler–Bernoulli beam theory are used to derive the governing system equations. In the formulation, for the first time, the fractional Atangana-Baleanu (AB) operator without singulars and non-localized kernels is introduced. The microbeam is thermally loaded and exposed to a heat source moving along its axis in the form of a laser pulse. The system of equations is solved using the usual Laplace transform approach, and the resulting expressions for beam deflection, displacement, temperature change, and associated thermal stress are presented. The findings are graphed and the impacts of the fractional order parameter, viscosity factor, applied, and laser pulse length are investigated. The results show that the presence of the Atangana-Baleanu fractional operator and the viscosity coefficients leads to a decrease in the propagation of mechanical and thermal waves compared to the classical case.