Effects of nonlocal thermoelasticity on nanoscale beams based on couple stress theory

A modified nonlocal Bernoulli-Euler model was established in this paper to analyze thermoelastic interactions in isotropic nanobeams subjected to ramp-type heating, depending on the modified couple stress and generalized thermoelasticity theories. To solve this problem, the thermoelasticity theory with one thermal relaxation time (Lord-Shulman [LS]) is proposed. Due to the modified couple stress, the analytical expressions for deflection, temperature, flexure moment, and displacement in the nanobeam were obtained by using the Laplace transform technique. In addition, comparisons were shown in graphs to estimate the effects of the various parameters such as the couple stress, and the ramping time parameter on all the fields studied under consideration. Also, the numerical results are provided to demonstrate the small-scale impact on the resonator of the nanobeams.