Non-local Fractional Thermoviscoelastic Bending Analysis of Non-simple Nanobeam Under Ramp-Type Heating

Abstract

In this paper, a novel non-local thermoviscoelasticity model incorporates non-Fourier effects within a fractional calculus framework. It focuses on the thermal impact on a non-simple nanobeam subjected to ramp-type heat loading. The study investigates the thermoelastic behavior of a viscoelastic nanoscale rectangular beam based on the non-local Euler-Bernoulli beam theory (EBBT) under thermal heating conditions. This paper uses integral transformation methods to derive closed-form solutions for temperature, bending moments, deflection, and thermal stress. These solutions are initially formulated in the Laplace domain and then converted into the time domain using the Gaver-Stehfest algorithm. Numerical results for silicon nitride are analyzed and graphically visualized with Mathematica software. The study examines the effects of relaxation time, ramping time parameters, and fractional order parameters across various fields, comparing the findings with previously published literature. This research highlights the complex interplay between thermal and mechanical responses in nanobeams and provides new insights into the behavior of viscoelastic materials under non-local and fractional thermoelastic conditions.