Fractional order and memory-dependent analysis to the dynamic response of a bi-layered structure due to laser pulse heating

Abstract

Ultrashort laser technology has been widely used in micro-machining due to its high power, precision of operation, low cost, high control and extremely short duration. This motivates us to investigate the transient response of a bi-layered structure subjected to a non-Gaussian laser beam on its bounding surface in the context of the time-fractional derivative based on generalized thermoelastic theories. Comparison studies between the fractional order and the memory-dependent derivative models are performed and the thermal contact resistance at the interface is also considered. The coupled governing equations involving with thermal relaxation time, fractional order parameter, time delay and kernel function, which can be chosen freely according to specific problems, are solved by using Laplace transform technique together with its numerical inversion. During the analysis, the first layer is selected as the copper material and the material characteristic parameters of the second layer such as the thermal conductivity, mass density and specific heat capacity are given by ratios to those of the first layer. The influences of the material characteristic parameters on the heat conduction and the structural responses are emphatically discussed, and the non-dimensional temperature, displacement as well as stress at different values of fractional order parameter, time delay factor, kernel function and thermal contact resistance are obtained and illustrated graphically. Finally, based on the obtained results, the bi-layered structure heated by a non-Gaussian laser beam may be reasonably designed in engineering.