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This article, published in the International Journal of Applied Mechanics, discusses a new theory of fractional-order rate-dependent piezoelectric thermoelasticity and its application in analyzing the structural transient response of smart piezoelectric composite laminates. The authors develop unified forms of fractional-order strain and heat conduction by adopting different types of fractional derivatives. They establish a fractional-order rate-dependent piezoelectric thermoelasticity theory and derive constitutive and governing equations using an extended thermodynamics framework. The theory is then applied to investigate the dynamic thermo-electromechanical responses of smart piezoelectric composite laminates with imperfect interfacial conditions. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on wave propagations and structural thermo-electromechanical responses are evaluated and discussed. [Extracted from the article]

Functionally graded sandwich micro/nano-structures have attracted great attention due to the capability to resist high noise and thermal stress in a non-isothermal environment. Additionally, the design of high quality-factor micro/nano-resonators requires accurate estimation of their thermoelastic damping. However, the classical thermoelastic damping models fail at the micro/nano-scale due to the influences of the size-dependent effects related to heat transfer and elastic deformation. This work aims to investigate the influences of the size-dependent effects on the thermoelastic damping of functionally graded sandwich micro-beam resonators by combining the nonlocal dual-phase-lag heat conduction model and the nonlocal elasticity model. It is assumed that the functionally graded sandwich micro-beam resonators consist of a ceramic core and functionally graded surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of thermoelastic damping is obtained by complex frequency method. Numerical results are analyzed for the effects of the thermal nonlocal parameter, the elastic nonlocal parameter, the power-law index, and the vibration modes on the thermoelastic damping of functionally graded sandwich micro-beam resonators. The results show that the thermoelastic damping of functionally graded sandwich micro-beam resonators can be adjusted by the suitably modified parameters, which strongly depends on the double nonlocal effects and the power-law index. [ABSTRACT FROM AUTHOR]

In order to capture the memory-dependent effect and size-dependent effect, present work aims to develop a novel thermo-viscoelastic nonlocal model in micro-scale for the first time to include the simultaneous effects of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function. Then, the theory is applied to studying the dynamic response of a polymer microbeam heated by a ramp-type heating. In calculation, the influences of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function on the variations of the considered variables are presented and discussed in detail. [ABSTRACT FROM AUTHOR]

Ultra-slow relaxation process of polymers has the memory-dependent feature, integer-order thermoviscoelastic models may fail to describe the dynamic behaviors of viscoelastic structures accurately. Additionally, it is noticed that the small-scale effect of elastic deformation and heat conduction in a non-isothermal temperature environment is becoming significant due to the development of micro-devices. To better capture the memory-dependent effect and the small-scale effect of viscoelastic micro-structures in heat transfer environment, as a first attempt, present work focuses on developing a refined fractional Kelvin-Voigt thermoviscoelastic model by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). Then, the model is applied to investigating the transient response of a polymer microbeam subjected to a harmonic thermal loading. The governing equations involving the modified parameters are formulated and then solved by Laplace transform method. Some parametric results are demonstrated to display the impacts of the nonlocal thermal parameter, the material length-scale parameter and the fractional-order parameter on the considered physical quantities. The results show that the small-scale effect and the memory-dependent effects strongly depend on the polymer micro-structure characteristics in thermal environment. [ABSTRACT FROM AUTHOR]

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]

Nano sandwich-like storage structure or device is commonly designed as diaphragm to extend nano-battery working life, or fabricated as nanocomposite anode materials to maximumly improve electrochemical performance in nano-battery systems. This work aims to investigate size-dependent dynamic mechanical-diffusion responses of multi-layered laminated sandwich-like nanocomposites subjected to shock loadings of molar concentration in the context of nonlocal diffusion-elasticity model by a semi-analytical technique via Laplace transformation. The results reveal that the diffusion isolation will be maximally improved and lager harmful chemical stresses can be reduced to some extent for proper materials nonlocal parameters and constants ratios of selected. [ABSTRACT FROM AUTHOR]

Thermotropic yield characteristic of the ceramic–alloy composite beam induced by a unilateral heat source is investigated by using the Hamilton principle and the variation method based on the first‐order shear deformation theory. The mathematical essence of the yield problem of the composite beam is that the variation of the Lagrange function of the system to the space coordinates equals zero. The Tamura–Tomota–Ozawa model and the linear rule of mixtures are used to simulate the composite material properties of functionally graded material (FGM), and the constitutive equations are established with the linear hybrid hardening model. The von‐Mises yield condition is introduced to judge whether the beam enters the yield state. The governing equations are established by using the Hamilton principle and variation method. The thermotropic yield surfaces, the yield stresses, and the critical temperature rises of the yield functionally graded beam are obtained, and the deflections of the beam are calculated by analytical method. The results reveal that the yield interfaces, the yield stresses, the critical temperature rises, and the deflections of the beam vary with material parameters, geometric parameters, and so on. [ABSTRACT FROM AUTHOR]

The applicability of the generalized thermoelastic theories with integer-order derivative in solving anomalous or transient thermoelastic diffusion problems is questionable. Due to the feature of memory-dependence and heredity, the fractional-order derivative and the memory-dependent derivative are introduced to modify the generalized thermoelastic theories for extending their applicability. To demonstrate the features of such theories, the thermoelastic-diffusive dynamic response of an infinite elastic medium containing a spherical cavity with variable material properties is investigated in three different generalized theories with memory-dependent effect, which are incorporated in a unified form. Of them, two are based on fractional-order derivative and the other one is based on the memory-dependent derivative. The corresponding governing equations are formulated and then solved by Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress, concentration and chemical potential under the three theories are obtained and illustrated graphically for comparing with those obtained from one of the integer-order theories. The effects of the fractional-order parameter, the time-delay factor, the variable thermal conductivity and diffusivity on the variations of the considered variables are considered and discussed in detail. [ABSTRACT FROM AUTHOR]

Porous materials have been widely used in aerospace, electronic communication, petrochemical and bio-medicine, etc. due to their attractive attributes such as low relative density, thermal and acoustical insulation and good permeability. For porous materials suffering high temperature gradient or ultrafast heating, etc., it is crucial to reveal the behaviors of the thermal-induced stress and deformation within them for guiding their potential applications and optimizations. In present work, the thermoelastic dynamic behaviors of a porous half-space subjected to a ramp-type heating is investigated based on the theory for thermoelastic porous materials and the three-phase-lag heat conduction model. The governing equations of the problem are formulated, and then, solved by using Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, stress and volume fraction within the half-space are obtained and illustrated graphically. In calculation, the effects of time, ramp-heating time factor and thermal time-delay factors on the considered physical quantities are examined and discussed in detail. Comparisons of the variations of the considered quantities under three different theories are carried out and presented. [ABSTRACT FROM AUTHOR]

With the rapid development of ultrafast heating technologies and its application in the micro-machining of micro/nano-electromechanical devices, where the nonlocal effects on elastic deformation and heat/mass transfer will increase and classical/generalized theory of thermoelastic diffusion coupling does not hold any more. In this work, a nonlocal theory of thermoelastic diffusive materials is developed, and the spatial nonlocal effects of heat and mass transport are both considered for the first time. With the aid of thermodynamic principles, the constitutive relations involving size-dependent characteristic lengths are derived. In the aspect of the application, the proposed theoretical model is further used to investigate the dynamic thermo-elasto-diffusive responses of a one-dimensional semi-infinite medium with one end subjected to time-dependent shock loads, and the semi-analytical techniques based on Laplace transform methods are applied to obtain the transient solutions. The effects of nonlocal parameters on structural dynamic thermo-elasto-diffusive responses are also evaluated and discussed to be expected to provide new insights on the thermoelastic diffusion coupling at the micro/nanoscale. [ABSTRACT FROM AUTHOR]

The present work devotes to investigating the transient responses of a half-space with variable thermal material properties based on the generalized thermoelastic theory with memory-dependent derivative. The bounding surface is assumed to be traction free and heated by a non-Gaussian laser beam. The material characteristic parameters are assumed as the linear function of temperature. The coupled governing equations containing thermal time-delay factor and kernel function, which can be chosen to adapt to specific problems, are formulated and solved by the Laplace and Kirchhoff transformations. Numerical results of the non-dimensional temperature, displacement as well as stress under different time, variable thermal conductivity, thermal time-delay factor and kernel function are obtained and illustrated graphically. It is hoped that the obtained results would be helpful in designing the temperature-dependent structures heated by a non-Gaussian laser beam in engineering. [ABSTRACT FROM AUTHOR]

Viscoelastic laminated sandwich composite structure has been used as a new class of high-efficient structural damping in the passive vibration control systems. This work aims to investigate transient thermo-viscoelastic responses of viscoelastic laminated sandwich composite structure. The effects of fractional order parameters and material constants ratio on the structural transient thermo-viscoelastic responses are evaluated and discussed. For each homogeneous isotropic layer, the governing equations are formulated and solved by Laplace transformation techniques. The results are expected to provide new insights on the vibration control and thermal management of viscoelastic laminated sandwich composite structure under extreme non-isothermal conditions. [ABSTRACT FROM AUTHOR]