Effect of non-locality in the vibration of a micro-scale beam under two-temperature memory responses

Abstract

ABSTRACT The vibration of elastic micro-beam is of major significance due to wide applications of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Accordingly, the size-dependent thermoelastic model has been developed to deal with higher-order simple material to adopt both size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free-energy. This survey demonstrates the effect of ultra-short-pulsed laser heating in the problem of coupled thermoelastic vibration of a microscale resonator, in which, the non-local heat transport equation is drafted in an integral form of a common derivative on a slipping interval by incorporating the three-phase-lag memory-dependent heat transfer in the context of two-temperature theory. Laplace transform and finite sinusoidal Fourier transform techniques have been employed to determine the lateral vibration of the beam and the scaled thermal moment within the beam. According to the graphical representations corresponding to the numerical results, conclusions about the new theory is constructed. Specific attention is paid to study the effect of thermal non-local parameter, energy absorption depth, memory-dependent derivative, the two-temperature parameter and delay time also.