Study On Relaxation Effect Of Generalized Electromagnetic Thermoelastic Coupling Of Rotating Hollow Cylinder

In classical heat transfer theory,the speed of heat transfer is infinite,but this is contrary to the experimental obervation results.With the development of high and new technology,accompanied by the emergence of very fast heat transfer,extremely high / low temperature heat transfer and other unconventional heat transfer processes,the traditional heat transfer equation suitable for steady-state heat transfer has been greatly challenged in solving such problems,and its applicability has been questioned,Then,the scholars modified the classical thermoelastic theory and developed the generalized thermoelastic theory,such as L-S generalized thermoelastic theory,G-L generalized thermoelastic theory and G-N generalized thermoelastic theory,and the generalized thermoelastic theory considering fractional order or memory-dependent derivative on the basis of these theories.Compared with the traditional fractional order heat conduction model,the new generalized thermoelasticity theory with memory-dependent derivative not only has a clear physical meaning,it can also well describe that the instantaneous rate of change is affected by the past situation;moreover,because the memory dependent model is based on the integral order calculus operation,it is more convenient than the fractional order model in operation;especially,for different kernel functions Time delay factor also has different choices to adapt to different complex environment,which provides great possibility to describe the real mechanical response of media.With the development of laser processing technology,the research on the mechanism of the thermoelastic process of ultra fast heating becomes more and more important,and the influence of strain rate is also more and more important in the generalized thermoelastic theory.Although the thermoelastic model considering temperature rate has been studied by many scholars for a long time,there are few thermoelastic models considering strain rate.In this paper,by introducing strain relaxation into the L-S generalized thermoelastic theory and using continuum mechanics,the L-S generalized thermoelastic model considering strain rate is established and its control equation is derived.In the existing research,although some scholars have solved the problem of generalized electromagnetic thermoelastic coupling of hollow cylinder considering memory-dependent derivative,they have not considered the effect of rotation on the problem;for the generalized thermoelastic theory considering the effect of strain rate,there is a lack of the study of introducing both the thermal relaxation time and thestrain relaxation time into the L-S generalized thermoelastic theory.Based on the L-S generalized thermoelastic theory and memory dependent differential,this paper analyzes the generalized electromagnetic thermoelastic coupling of a rotating infinite hollow cylinder by using Laplace transform and its inverse transform method.The specific research contents are as follows:(1)Based on the L-S generalized thermoelasticity theory and memory-dependent derivative,the dynamic response of a rotating infinite hollow cylinder subjected to internal surface thermal shock is studied.The effects of different kernel function,time delay factor,angular velocity component and material characteristic parameters on non-dimensional hoop stress,radial stress,temperature and displacement,induced electric field and induced magnetic field were investigated.The results show that the kernel function,the time delay factor and the material characteristic parameters related to temperature all have certain influence on the physical parameters,while the angular velocity component has significant influence on the non-dimensional displacement,the hoop stress and the radial stress.(2)Based on the L-S generalized thermoelastic theory,the strain relaxation factor is introduced into it,and the governing equation of L-S generalized thermoelastic theory considering strain relaxation is derived.The dynamic response of a rotating infinite hollow cylinder under the action of internal surface thermal shock is studied.The effects of different thermal relaxation factors,strain relaxation factors and angular velocity components on non-dimensional hoop stress,radial stress,temperature and displacement,as well as induced electric field and induced magnetic field were investigated.The results show that both the thermal relaxation factor and the strain relaxation factor have obvious influence on the physical quantities except the on non-dimensional induced magnetic field,while the rotation effect has little influence on the non-dimensional temperature,the non-dimensional induced electric field.At the same time,the curves of the non-dimensional displacement,the induced magnetic field,the hoop stress and the radial stress are smoother at the peak.