The Dynamic Responses Of One-dimensional Nonlocal Generalized Magneto-thermoelastic Problems

To amend the paradox that heat propagates with an infinite speed in media in the classical heat conduction theory,scholars have put forward non-Fourier heat conduction models that describe the heat wave effect,that is,heat propagates in media with a finite speed.Due to thermal induced stress,combining with the classical theory of thermoelasticity,scholars have developed generalized theories of thermoelasticity.Furthermore,to describe the time-dependent effect of heat transportation,scholars have proposed fractional-order generalized thermoelasticity theories.The above theories are suitable for describing the generalized thermoelastic coupling problems with microcosmic time scale while with macroscopic spatial scale.With the rise of high-tech devices accompanied with the trend of miniaturization,the mechanical responses of the device show a strong size correlation,that is,nonlocal effects.In order to describe the dynamic response of the thermo-elastic coupling problems at both microcosmic time and space scales,it is imperative to establish a generalized thermoelasticity that can describe the heat wave effect of heat and describe the non-local effect.Based on the recently proposed generalized thermoelasticity theory considering nonlocal effects,the following problems are studied:(1)The dynamic response of a half-space with temperature-dependent,thermal shock and stress shock is studied.The coupling control equations of G-L fractional nonlocal one dimensional generalized thermo-elastic problem are established.The distribution of temperature,displacement and stress are obtained by using analytical and numerical techniques based on Laplace transforms and their inversions and illustrating graphically.The results show that the nonlocal elastic effect has no effect on the temperature,and the effect on the displacement and stress is more significant.(2)The dynamic response of one-dimensional magneto-thermo-elastic coupling problem of fixed rods with both ends and subjected to a moving heat source is studied.The non-localized generalized magneto-thermal coupling governing equations of L-S are established for the first time.The governing equations are expressed in the Laplace transform domain and solved in that domain.The influence of nonlocal elasticity and magnetic field on the distribution of temperature,displacement and stress are obtained.The results show that the nonlocal effect parameters and the magnetic field have significant effects on the displacement and stress,while the temperature is barely affected by the two parameters.