Implementation of Legendre wavelet method for the size dependent bending analysis of nano beam resonator under nonlocal strain gradient theory

The bending analysis due to thermoelastic loading in nanoscale materials is primarily determined by the physical aspect of the material and the modeling of structures. This paper examines the prediction of bending characteristics of the Euler-Bernoulli beam using Moore-Gibson-Thompson (MGT) thermoelasticity theory in conjunction with nonlocal strain gradient theory (NSGT). The coupled equations for dimensionless deflection and temperature change with ramp-type heating boundary conditions are formulated and solved using the Laplace transform method and the wavelet approximation method. The stiffness softening and hardening effects due to nonlocal and length-scale parameters are assessed, and their discrepancies are discussed. Findings further reveal that the impact of the thermal relaxation parameter on deflection and temperature is negligible. Moreover, the different aspect ratios of the beam's structure depict the prominently behavior of structural simulations in bending.

Automated summary

This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.