# Comparative analysis of fractional thermoelastic vibrations of a nonlocal nanobeam exposed to travelling and static thermal loads

## TL;DR

This paper studies how thermal loads affect vibrations in nanobeams using a new model that accounts for size-dependent and memory effects.

## Contribution

The novel contribution is the use of the Moore-Gibson Thompson model with fractional thermoelasticity to analyze nonlocal nanobeam vibrations under thermal loads.

## Key findings

- Fractional order and nonlocal parameters significantly influence the amplitude and stability of thermoelastic vibrations.
- The MGT model provides more stable and finite characteristics of thermal waves compared to GN-II, GN-III, LS, and CL models.
- Dynamic thermal loads with velocity and time-dependent ramp-type profiles affect nanobeam behavior differently based on model parameters.

## Abstract

Present innovative investigation comprises a new approach to analyse the fractional order vibration behaviour of thermo-mechanical waves in a non-localized Nano scale beam affected from a travelling thermal load with constant velocity and ramp type thermal load dependent on time within the framework of nonlocal theory of elasticity. Recently developed Moore-Gibson Thompson (MGT) heat transport model coupled with fractional order thermo-elasticity is utilized to evaluate the analytical results of significant physical fields—temperature, lateral deflection, displacement, cross-sectional elastic moment and thermal stress. Inclusion of the theories of nonlocal elasticity and factional order thermoelasticity in thermal conduction model enables it to capture the size-dependent effects and memory effects in heat conduction at the Nano scale. Laplace transform algorithm is facilitated to determine the closed-form solutions. Depth analysis of graphical results characterizes and analyses the impacts of the important quantities such as fractional order parameter, velocity of the dynamic load, time relaxation quantity and non-local parameter on the field variables. Quantitative results reveal that fractional order quantity and nonlocal effect prominently affect the amplitude, frequency and stability of thermo-elastic vibrations. Significance of MGT heat conduction model is observed by comparing the computational outcomes to the results obtained under previous established heat transfer models – GreenNaghdi- II (GN-II), GreenNaghdi - III (GN-III), Lord and Shulman (LS model) and classical theory (CL). Results determined under MGT model express more finite and stable characteristics of thermo-elastic waves inside the beam compared to the other theories of heat transfer. This study emphasises the significance of applied research in revealing the important properties of Nano scale structures that are observed to be especially advantageous in industry and mechanical engineering.