Non-local Dynamic Response Of Temperature-dependent One-dimensional Problem Of Material Properities Under Fractional Thermoelastic Theory

With the development and progress of science and technology,the classical heat transfer theory and the classical thermoelastic theory have been severely challenged because its applicable conditions are no longer satisfied,which has given rise to the development of the generalized thermoelastic theory.The development of the generalized thermoelastic theories has undergone several stages such as non-Fourier heat conduction,the generalized thermoelastic theory,the fractional-order generalized thermoelasticity,and etc.Compared with the classical thermoelastic theory,the generalized thermoelastic theories mainly eliminate the paradox that heat propagates in media with an infinite speed.At present,the generalized thermoelastic theories have been applied mostly to studying the dynamic response of generalized thermoelastic coupling problems in which the thermal interaction time is very short while the geometrical dimension of the elastic body still belongs to the macroscopic scale.With the miniaturization of devices,when the characteristic length scale of the elastic body also tends to be microscale,the mechanical behaviors of the material will take on a strong effect of size-dependence.To depict such size-dependence effect,scholars have made great efforts in revising the theory of the classical continuum mechanics and proposed the nonlocal continuum mechanics theory.In present thesis,based on the fractional generalized thermoelastic theory with non-local effect,the nonlocal generalized dynamic responses of rods with temperature-dependent properties are investigated,and the specific research contents include:1)The nonlocal dynamic response of a finite length piezoelectric rod with temperature-dependent properties is investigated.The piezoelectric rod is fixed at both end and subjected to a moving heat source,undergoing thermal expansion deformation.The governing equations of the problem are formulated in the context of the fractional order generalized thermoelasticity and solved by means of Laplace transform and its numerical inversion.The distributions of the temperature,displacement,electrical potential and stress are obtained numerically.In calculation,the effects of the nonlocal parameter,the fractional-order parameter and the temperature-dependent properties on the considered variables are considered and the obtained results show that the influence effects are significant.2)The nonlocal dynamic response of a semi-finite thermoelastic rod withtemperature-dependent properties is investigated.The thermoelastic rod is subjected simultaneously to a thermal shock and a stress shock at its end.The governing equations of the problem are established based on the fractional order generalized thermoelasticity and solved by means of Laplace transform and its numerical inversion.The distributions of the temperature,displacement and stress are obtained numerically.In calculation,the effects of the nonlocal parameter,the fractional-order parameter and the temperature-dependent properties on the considered variables are examined.The obtained results indicate that the non-local parameter has almost no effect on the temperature and has significant influence on the displacement and the stress;The fractional-order parameter has almost no effect on the displacement and the stress;The temperature-dependent properties affect both the temperature and the stress.