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Compared with the fractional order generalized themoelastic theory, the generalized thermoelastic theory based on the memory-dependent derivative has following significant advantages: First, the generalized thermoelastic theory with memory-dependent derivative has more specific physical meanings and can excellently describe that the present state of a system is dependent on its past states; Second, the memory-dependent derivative is based on the integer order calculus, which is more convenient to operate than fractional order model; Particularly, for different kernel functions, the time-dealy factor has different choice to adapt to different specific problems, which makes it greatly possible to describe the real thermoelastic response of medium. In present work, the transient response of an infinite rotating hollow cylindrical conductor with variable material properties subjected to a thermal shock at its inner surface is investigated based on the generalized thermoelastic theory with memory-dependent derivative. The hollow cylinder is placed in an external magnetic field with constant intensity, whose outer surface is traction free. The governing equations are formulated and then solved by using Laplace transform and its numerical inversion. The distributions of the dimensionless temperature, displacement, induced electric field, induced magnetic field, hoop stress as well as radial stress in the cylinder are obtained and illustrated graphically. The obtained results show that the kernel function, the time-delay factor and the temperature-dependent material properties influence the distributions of the considered variables more or less, while, the angular velocity significantly influence the variations of the dimensionless displacement, hoop stress and radial stress. [ABSTRACT FROM AUTHOR]

The present work is devoted to investigating the transient responses of a sandwich structure based on the generalized thermoelastic diffusion theory with memory-dependent derivative. Both the left and the right bounding surfaces are subjected to a thermal shock and a chemical potential shock simultaneously. It is assumed that the values of thermal contact resistance and diffusional contact impedance at the interface are zero with ideal adhesion. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The influences of the material characteristic parameters at the interface on the structural responses are emphatically discussed, and the non-dimensional temperature, chemical potential, displacement, stress as well as concentration at different values of time delay factors and kernel functions are obtained and illustrated graphically. The results show that: the changes of the time delay factors, kernel functions, and material characteristic parameters have the varying degrees of influences on the considered variables. Based on the above conclusions, the sandwich structure working under the thermoelastic diffusion coupling condition can be designed reasonably. [ABSTRACT FROM AUTHOR]

In the generalized thermoelasticity with nonlocal effect and memory-dependent derivative, the dynamic response of a finite thermoelastic rod fixed at both ends and subjected to a moving heat source is investigated. The corresponding governing equations are formulated and solved by means of Laplace transform and its numerical inversion. In simulation, the effects of the time-delay factor, the kernel function and the nonlocal parameter on the distributions of the non-dimensional temperature, displacement and stress are examined, respectively, and illustrated graphically. The results show that: the time-delay factor and the kernel function significantly affect the peak values of the considered variables; the nonlocal parameter barely influences the distributions of the non-dimensional temperature, slightly influences the peak values of the non-dimensional displacement, while remarkably influences the peak values of the non-dimensional stress. [ABSTRACT FROM AUTHOR]

In present work, the transient responses of a hollow cylindrical conductor based on the generalized thermoelastic theory with memory-dependent derivative are investigated. The conductor with temperature-dependent mechanical properties is subjected to a thermal shock on its internal surface. The hollow cylindrical conductor is placed in a magnetic field along the axial direction of the cylinder. The effects of memory-dependent derivative and temperature-dependent properties influenced by the variable material property factors on the heat conduction and structural responses are emphatically discussed. The coupled governing equations containing time delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The distributions of the non-dimensional induced electric field, induced magnetic field, hoop stress, radial stress, temperature and displacement at different values of time delay factors, kernel functions and variable material property factors are obtained and illustrated graphically. Finally, some conclusions are summed up, based upon which guidelines may be provided in the design of a hollow cylindrical conductor working in a thermo-mechanical coupling environment. [ABSTRACT FROM AUTHOR]

In the context of a memory-dependent generalized thermoelasticity, the thermal-induced transient response in an infinite elastic body containing a spherical shell is investigated. A thermal shock is applied on the inner surface of the spherical shell. The infinite body and the spherical shell are assumed to be isotropic but two dissimilar materials. By using an analytical technique based on the Laplace transform along with its numerical inversion, the governing equations of the problem are solved and the non-dimensional physical quantities in the two materials, i.e., temperature, displacement and stress, are obtained and illustrated graphically respectively. In simulation, the accuracy of memory-dependent derivative (MDD) is verified by degrading the present model into L-S model to compare the results obtained from the cases with interfacial thermal resistance and without interfacial thermal resistance. In addition, the effects of the different kernel functions as well as the ratios of the two materials, including the ratios of the density, the thermal-conductivity and the time-delay, on the distributions of the considered variables are obtained and demonstrated graphically respectively. [ABSTRACT FROM AUTHOR]

The dynamic response of a one-dimensional thermo-piezoelectric problem with variable material properties is investigated in the context of fractional order theory of thermoelasticity. The system of governing equations for the thermo-piezoelectric problem is formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered non-dimensional displacement, temperature, and stress are obtained and illustrated graphically. The effects of fractional order parameter and temperature-dependent properties on the considered quantities are investigated and the results show that they have significant influence on the variations of the considered quantities. [ABSTRACT FROM AUTHOR]

Based on the generalized thermoelastic diffusion theory with memory-dependent derivative in both the generalized heat conduction law and the generalized diffusion law, the transient response is investigated of a half-space subjected to a thermal shock and a chemical potential shock on its bounding surface. The coupled governing equations containing time-delay factors and kernel functions, which can be chosen freely according to specific problems, are solved by the Laplace transform together with its numerical inversion. The non-dimensional temperature, chemical potential, displacement, stress, as well as concentration at different values of time, time-delay factors, and kernel functions are obtained and illustrated graphically. The results show that: all the considered variables have obvious changes with the passage of time; the thermal time-delay and kernel functions hardly influence the distributions of the non-dimensional chemical potential, modestly influence the distributions of the non-dimensional concentration, while appreciably influence the distributions of the non-dimensional temperature, displacement, and stress; the diffusion time-delay and kernel functions barely affect the distributions of the non-dimensional temperature, slightly affect the distributions of the non-dimensional concentration, while remarkably affect the distributions of the non-dimensional chemical potential, displacement and stress. [ABSTRACT FROM AUTHOR]

The transient thermo-piezoelectric response of a functionally graded piezoelectric rod subjected to a moving heat source is investigated in the context of fractional order theory of thermoelasticity proposed by Sherief. The material properties of the functionally graded piezoelectric rod are assumed to vary exponentially along the length, except for the thermal relaxation time and the specific heat, which are taken to be constant. To solve the governing equations of the problem, Laplace transform is applied, eliminating the time effect; the analytical solutions of the displacement, stress, temperature, and electric field in Laplace domain are obtained. Subsequently, the solutions of the considered variables in time domain are obtained by numerical Laplace inversion and illustrated graphically. In calculation, the effect of the fractional order parameter on the variations of the considered variables is presented. [ABSTRACT FROM PUBLISHER]

The dynamic response of a piezoelectric-thermoelastic rod made of piezoelectric ceramics (PZT-4) subjected to a moving heat source is dealt with in the context of the fractional order theory of thermoelasticity. The piezoelectric-thermoelastic governing equations for the problem are formulated and then solved by means of Laplace transform together with its numerical inversion. The distributions of the considered nondimensional temperature, displacement, stress, and electric potential are obtained and illustrated graphically. The effects of fractional order parameter and the velocity of heat source on the variations of the considered variables are investigated, and the results show that they have significant influence on the variations of the considered variables. The present investigation could be helpful for better understanding the multi-field coupling effect of mechanical, electric, and thermal fields in real piezoelectric ceramics structures, and provide some guidelines in the optimal design of actuators or sensors made of piezoelectric ceramics serving in a thermoelastic environment. [ABSTRACT FROM PUBLISHER]

The dynamic response of a two-dimensional generalized thermoelastic diffusion problem for a half-space is investigated in the context of the generalized thermoelastic diffusion theory. The half-space is subjected to a thermal shock and a chemical potential shock on its bounding surface. The governing equations of this problem are formulated, and due to the complexity of the equations, a numerical method, i.e., hybrid Laplace transform-finite element method, is used to solve them. The non-dimensional temperature, displacement and chemical potential are obtained and illustrated graphically. The results show that the non-zero values of all the considered variables are only in a bounded region and vanish identically beyond this region, and the propagating speed of diffusive wave is larger than that of thermoelastic wave. [ABSTRACT FROM AUTHOR]