Multi-field Coupled Dynamic Response Of A Hollow Cylinder Considering Memory-dependent Effects

The environment to which the components are exposed is becoming more and more extreme with the development of advanced science,technology and materials.The complex mechanical environment poses a serious challenge to the refined study of the mechanical properties of the components,and a more reasonable and accurate model must be available.In extreme environments,the thermal environment has a particular impact on the components.However,the classical Fourier heat transfer model cannot accurately describe or even fail in extreme environments.The classical Fourier model of heat conduction has a natural flaw in that it assumes that the heat wave velocity is infinite.To remedy this deficiency,many scholars obtained a series of modified heat conduction models,i.e.,non-Fourier heat conduction models,by modifying the classical models.Based on these models,a series of generalized thermoelastic theories have been developed to solve problems such as the dynamic response of components in complex environments.With the application of piezoelectric materials,fiber-reinforced materials,porous materials,and other materials that have a prominent role in some aspects,it is imperfect to rely solely on the generalized thermoelastic theory to model the coupling.Therefore,a modified fractional order(i.e.,memory-dependent differential)is further introduced into the generalized thermoelastic theory to improve the theory.After extensive literature research,there are many papers that study hollow cylinders based on the generalized thermoelastic coupling theory.However,with the complexity of the environment in which the member is located.It is difficult to rely solely on simply generalized thermoelasticity to accurately describe the dynamic response of the member.To address this situation,this paper focuses on(1)the dynamic response of a hollow cylinder in a thermal shock environment based on the generalized thermoelastic theory considering the size effect and the memory-dependent effect.A hollow cylinder whose material is metallic copper is used as an arithmetic example for discussion.(2)The dynamic response of hollow cylinders is investigated by introducing the memory-dependent differential in the case of hygrothermal coupling.The hollow cylinder with fiber-reinforced material is used as an arithmetic example for discussion.The specific study is outlined as follows.(1)Based on the generalized thermoelasticity theory with nonlocal effects and memorydependent differential corrections,the dynamic response of an infinitely long hollow cylinder subjected to thermal shock on the inner surface is investigated in the case of linear variation of the heat transfer coefficient with temperature.The outer surface is insulated and the inner and outer surfaces are stress-free.The controlling equations of the problem are established and solved by Laplace transform,and the distribution laws of temperature,displacement and stress characterized by modified Bessel functions are obtained.In the numerical calculations,the effects of the nonlocal parameters are examined first,followed by the effects of the variable heat transfer coefficients,and finally,the effects of the freely combined hysteresis factors and kernel functions on the individual physical quantities are examined.The results show that: the non-local parameters have almost no effect on temperature and significant effect on displacement and stress;the variable thermal conductivity has significant effect on temperature,displacement and stress;the hysteresis factor has effect on the peak value of physical quantities.The obtained results can be applied to the design of materials under thermal shock to meet some special engineering requirements.(2)The memory-dependent differential is introduced into the heat transfer equation and the diffusion equation,and a memory-dependent differential generalized hygrothermal coupling model is established.The dynamic response of a hollow cylinder subjected to a hygrothermal shock is studied for hygrothermal elasticity.In this paper,the Laplace transform method is used to find the closed-form solutions of each physical quantity.The effects of the hysteresis factor and kernel function on it are analyzed.After Laplace inverse transformation,the time course of the hygrothermal coupling is investigated.The numerical results show that the larger the ratio of temperature gradient hysteresis factor to heat flux hysteresis factor,the faster the wave speed.Also,the hysteresis factor affects the wave crest.For the time course of hygrothermal,it is once again verified that the hygrothermal wave has a finite propagation velocity,and at the same time we can get the conclusion that the preliminary phase is dominated by fluctuations after the occurrence of hygrothermal shock.The above research conclusions have a reference value for the structural design and optimization of the tube in the damp heat environment.