Investigations On The Generalized Thermoelastic Coupling Problems Based On Memory-dependent Derivative

Based on the successful application in many engineering and scientific fields,the calculus of fractional order is getting more and more attention.Scholars proposed a novel MemoryDependent Derivative(MDD)by improving the caputo fractional differential definition,which has a specific physical meaning that reflects the current state of the system is influenced by the past situation.Inspired by this,scholars further modified the classical heat conduction equation by using the memory-dependent derivative,and obtained the new memory-dependent generalized thermoelastic theory.Compared with the existing generalized thermoelastic theory,MDD increases a time delay factor control parameter.For different cases,by selecting different kernel functions(fractional order parameters has been integrated into the kernel function)and time delay factor combination to get more likely as a result,thus provide more possibility to get more real mechanical behavior of materials.The application scope of generalized thermoelastic theory is mainly for the time microscale but the spatial dimension is still macro.With the continuous development of micronano materials and applications,as the research object of the spatial scale also belongs to the micro-nano scale will present size effect,therefore,it is a hot topic to introduce the material size effect theory into the generalized thermoelastic theory.Some scholars put forward that considering the nonlocal theory by Eringen and establish at the new nonlocal generalized thermoelastic theory which can describe both the time and space are microscale,thus for micronano scale structure in the extreme hot environment to provide theoretical basis for the safety analysis.In present work,based on the memory-depend generalized thermoelastic theory and by means of Laplace transform method,a finite thermoelastic rod fixed at both ends and subjected to a moving heat source and a bilayer structure consisting of a hollow spheroid embedded in an infinite body under transient thermal shock are studied.The contents includes:(1)Based on the MDD model and taking into account the nonlocal elastic relationship,we examine time-delay factor effect on thermoelastic response with/without normalized conditions,and consider nonlocal factor influence on the responses of the rob.(2)Considering the memory-dependent generalized thermoelasticity and interface conditions between the two layers of material and comparing the results with the L-S theory,we verify the effectiveness of the predicted results of the new model.And then we discuss the different ratio of related parameters on the response of the bilayer structure.