Generalized thermoelastic analysis of thin nanobeams with surface effect under thermal shock, free from temperature variation assumptions
摘要
This article presents a theoretical model for the coupled thermoelastic transient dynamics of thin nanobeams due to thermal shock loadings, considering the surface energy effect. A transversely isotropic Euler-Bernoulli nanobeam is analyzed, utilizing the extended Gurtin-Murdoch surface elasticity theory to capture its size-dependent thermoelastic behavior. Variationally consistent equations governing the motion of the nanobeam and the associated boundary conditions are derived from the extended Hamilton’s principle, which include rotary inertia, residual surface stresses, and thermal effects on the surface layers. Unlike most existing thermoelastic models, the model does not make any assumption on the across-thickness and longitudinal variations of temperature. The resulting partial differential equations in spatial coordinates in the Laplace domain are solved using a novel application of the homotopy perturbation method. The inverse transform of the obtained solution is performed numerically through Durbin’s method. The proposed model is validated by comparing it with existing benchmark solutions. A numerical study is conducted to analyze the impact of surface, material, and geometrical parameters on the transient behavior of thermoelastic cantilever nanobeams under axially and transversely applied thermal shock loads. The size-dependent nature of the axial displacement, deflection, and axial stress under thermal shock loading is illustrated for the first time.