Propagation Of Thermoelastic Waves Research Articles

Band structure analysis of Green-Naghdi thermoelastic wave propagation in a GPLs/CNTs-reinforced metamaterial with energy dissipation

In this paper, the band structure analysis of the thermoelastic wave propagation in a phononic crystal (PC), which it is reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs), is presented. The reinforced PC beam is made of periodic unit-cells including a metal section and a GPLs/CNTs-reinforced epoxy section. The Green-Naghdi theory of the generalized coupled thermoelasticity with energy dissipation and a new modified micromechanical model to predict the mechanical properties of the reinforced section are employed in the analysis. An analytical solution and the transfer matrix method are adopted to compute the band structures. The frequency band-gaps are obtained and the effects of the GPLs and CNTs volume fractions on the width and location of the band-gaps are analyzed and discussed in details. The results show that the GPLs influence the frequency band-gaps and the band structures of the thermoelastic wave propagation in the reinforced PC beam much more remarkably than the CNTs. The proposed analytical solution method, the modified micromechanical model and the presented results can be employed for designing the reinforced PC structures by the GPLs, CNTs or both of them and also for tuning the band-gaps in the future researches.

Analytical Solution for Thermoelastic Stress Wave Propagation in an Orthotropic Hollow Cylinder

The problem of thermoelastic stress wave propagation in an orthotropic hollow cylinder is investigated using analytical methods. The fully coupled classical theory of thermoelasticity is used to extract the equations for an orthotropic cylinder. To solve the boundary value problem, heat conduction equation and equation of motion are divided into two different sets of equations, the first set consists of uncoupled equations with considering boundary conditions and the second set comprises coupled ones with initial conditions. Finite Hankel transform (Fourier-Bessel expansion) is utilized to solve the problem with respect to radial variable. Two different cases, pure mechanical load and pure thermal load, were studied numerically to show the effect of considering the thermomechanical coupling term in the heat conduction equation. To show the effect of considering the coupling term in the heat conduction equation, the temperature history is plotted for the pure mechanical load case, where the temperature rises without applying any thermal load. By applying boundary conditions on the inner surface of the cylinder, initiation of the stress waves from the inner surface of the cylinder, propagation through the thickness in the radial direction and reflection from the outer surface were observed in the plotted figures.

The Propagation of Thermoelastic Waves in Different Anisotropic Media Using Matricant Method

Thermoelasticity is a generalization of classical theories of elasticity and thermal conductivity and describes a wide range of phenomenon. The theory can precisely predict the propagation of thermoelastics waves in case of an isotropic medium. However, the propagation of thermoelastic waves in the anisotropic medium is not fully understood. In this case, the theory of elasticity employs an approximate theory of temperature stress which does not take into consideration the interactions of temperature and deformations. In this paper, an analytical study has been carried out by using method of matricant to investigate the propagation of longitudinal elastic and heat waves in the anisotropic medium of a monoclinic, trigonal, hexagonal, and cubical crystal systems. In this article, a solution to the problem of the propagation of thermal waves and the propagation of a thermal wave along z -axis has been obtained. The attenuation coefficient and phase velocity of thermal waves for various materials are determined. Specifically, the problem of propagation of heat waves in one dimension has been solved.

A deep learning approach based on the physics-informed neural networks for Gaussian thermal shock-induced thermoelastic wave propagation analysis in a thick hollow cylinder with energy dissipation

This paper proposes a novel approach based on the physics-informed neural networks (PINNs) as an efficient deep learning approach to solve a broad range of the coupled partial differential equations (PDEs). For the first time, the PINN methodology is successfully applied to the thermoelastic wave propagation analysis with energy dissipation in a thick hollow cylinder based on the Green-Naghdi (GN) theory of coupled thermoelasticity. The assumed thick hollow cylinder is subjected to Gaussian thermal shock loading applied on the inner bounding surface. This research presents a PINN architecture with self-adaptive weights, which does not suffer from the curse of dimensionality as opposed to the numerical methods. An in-depth discussion is provided on the method and its capabilities to address PDE-related issues. Moreover, the PINN-based parametric studies are performed to show the effects of the materials coefficients on the thermoelastic wave propagation and dynamic behaviors of the fields’ variables. Numerous examples of thermoelastic wave propagation analysis with and without energy dissipation are solved via this approach. The framework generates satisfactory results in terms of accuracy and stability, as summarized in the paper.

Thermoelastic wave propagation damping in a hollow FG-GPLRC cylinder with the spinning motion

This analysis deals with generalized thermoelasticity via Lord–Shulman’s theory for hollow cylinders reinforced with graphene platelets (GPL). The viscosity effect is also considered for applied materials. The second-order correlation homogenization techniques are utilized to obtain the equivalent thermo-mechanical properties. The hollow cylinder with spinning motion is modeled based on the linear thermoelastic constitutive law. The GPLs are functionally distributed along the cylinder’s radius based upon a power-law function. The Kelvin–Voigt type of viscosity behavior which is a differential state of viscous materials, is employed. The energy equation is attained based on the coupled and generalized framework. After obtaining the motion and energy equations in dimensionless form, the generalized differential quadrature (GDQ) and Newmark time marching methods are implemented to extract the temporal evolution and wave propagation of temperature, displacement, and stresses that occurred in the structure. After validating the responses with the available theoretical article, some numerical results are demonstrated to examine the effect of thermo-mechanical properties on the thermoelastic behavior of chosen nanocomposite cylinder.

Automated design of phononic crystals under thermoelastic wave propagation through deep reinforcement learning

This article presents a novel concept of deep reinforcement learning (DRL) to facilitate the reverse design of layered phononic crystal (PC) beams with anticipated band structures focusing on the band structure analysis of thermoelastic waves propagating. To this end, we define the reverse design of phononic crystals (PCs) as a game for the DRL agent. To achieve the desired band structure, the DRL agent needs to obtain the topological system of PC. We trained a DRL agent called deep deterministic policy gradient (DDPG). An environment is developed and used to simulate the reverse design of layered PCs with the acquisition of a reward function. The presented reward function encourages the agent to achieve the desired bandgaps. The trained DDPG agent can maximize the game’s score by attaining the desired bandgap. The presented concept allows the user to instantly generate the design parameters through the trained DDPG agent without unnecessary search over the design space. We demonstrated that the DRL agent could perform very well for the automated design of PCs with hundred design cases.

Thermoelastic wave propagation due to local thermal shock on the functionally graded media

The present study is based on investigating the effect of locally applied thermal shock on the ceramic side of the functionally graded (FG) domain using nonlinear Lord-Shulman generalized thermoelastic theory. The constituent materials and therefore their properties in the two-dimensional FG domain are considered to be graded as a function of horizontal or vertical coordinates according to the power law. The finite element (FE) form of the nonlinear coupled differential equation is solved using the Picard method at each time-step in the framework of the Newmark time-integration scheme. The gradation of the material properties due to FGM is incorporated using graded finite elements in the FE formulation. The numerical results concerned with studying the effect of volume fraction index and orientation of the gradation of material properties across the FG domain are presented. It is observed from the study that both the gradation of material properties, as well as the direction of orientation of material gradation, have a substantial effect on the propagation of the thermal and elastic waves in the domain. Moreover, the thermal waves appear to be more dominant than the elastic waves at the time of application of thermal shock, which may also alter as time progresses.

Plane waves in nonlocal generalized thermoelasticity

AbstractThe Lord–Shulman (LS) model of generalized thermoelasticity and the Eringen's model of nonlocal elasticity are used to formulate the new constitutive relations and the field equations. The propagation of plane thermoelastic waves are then probed in a homogeneous isotropic nonlocal thermoelastic solid by employing this new model. We found two sets of the coupled longitudinal waves and one independent shear‐type wave. All these waves are found to be dispersive and attenuating in nature in the presence of nonlocality in the medium. We found that the shear‐type wave faces a critical frequency, while the coupled longitudinal waves may face critical frequency conditionally. A reflection of thermoelastic waves at a stress‐free thermally insulated and isothermal boundary of a thermoelastic half‐space are also considered in case of incident coupled longitudinal thermoelastic wave. The amplitude ratios of the reflected waves to that incident wave are determined analytically. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, attenuation coefficients and reflection coefficients. To investigate the effect of elastic nonlocal parameter on the variations of phase speeds, attenuation coefficients and amplitude ratios of the reflected waves are presented graphically. Some interesting results are noticed: All the waves are detected to be influenced by the nonlocality of the medium. The longitudinal waves are influenced by the thermal parameters but the shear‐type wave is independent of the thermal effect. Moreover the presence of elastic nonlocality reduces the classical shear‐type wave speed.

Effects of variable thermal properties on thermoelastic waves induced by sinusoidal heat source in half space medium

Aim of the present study is to characterize the effects of changing thermal conductivity on the propagation of thermoelastic waves in the half space medium when it is exposed to a periodic heat source. Closed form solutions of all significant physical fields such as conductive temperature, stress and displacement are evaluated in their dimensionless form in the Laplace transform domain. Impact of changing thermal conductivity parameter is exhibited on all field variables with the help of quantitative outcomes in time-domain. Following this pattern, the effects of time parameter is also observed on the field quantities.

Scale Effects on Thermoelastic Coupling Wave Propagation of Micro-Beam Resonator Using Nonlocal Stain Gradient and Generalized Thermoelasticity

Coupled thermoelastic analysis in the study of microscale solid mechanics has attracted considerable attention along with the miniaturization and functionalization of devices. Higher-order continuum mechanics theories have considered scale effects; however, the theories to predict thermoelastic performances of structures in micro-scale are still incomplete. The purpose of this paper is to study scale and thermal-induced effects by considering stress nonlocality and strain gradient elasticity in micro-structure resonators. The thermoelastic constitutive relations are established based on the nonlocal strain gradient (NSG) theory. The wave propagation problem of a Timoshenko micro-beam in conjunction with Green and Naghdi’s generalized thermoelastic (G–N) theory is investigated. The governing equations are derived and analytically solved by the eigenvalue method. Finally, the dispersion relation of a frequency spectrum is determined and the influences of scale parameters and coupled thermoelastic effect are discussed; in addition, the analysis results are compared with those under different size-dependent theories accordingly.

Strain gradient and Green–Naghdi-based thermoelastic wave propagation with energy dissipation in a Love–Bishop nanorod resonator under thermal shock loading

The thermoelastic wave propagation analysis is developed in a Love–Bishop nanorod resonator employing the strain gradient elasticity and Green–Naghdi theories with energy dissipation for the first time. The assumed nanorod resonator is subjected to thermal shock loading. The variational principle is applied to derive the coupled system of partial differential equations for temperature and displacement fields in a Love–Bishop nanorod. An analytical solution is proposed to solve the governing equations in Laplace domain. To obtain the temporal variation of fields’ variables, a proper Laplace inversion technique is employed in the problem. The size effects in the nano-sized Love–Bishop rods are taken into account with five small-scale parameters including three higher-order materials length parameters, the micro-length inertia and thermal parameters. Two types of thermal shock loadings such as laser pulse-induced suddenly increasing temperature are utilized in this work, and the laser shock-induced thermoelastic wave propagations in both temperature and displacement fields are illustrated. The effects of the higher-order materials length parameters and the micro-length inertia and thermal parameters on the propagation of thermal and elastic waves are studied in detail.

Band structure analysis of Green-Naghdi-based thermoelastic wave propagation in cylindrical phononic crystals with energy dissipation using a meshless collocation method

In this paper, a meshless collocation method based on the generalized finite difference (GFD) method is employed for the band structure analysis of thermoelastic waves propagating in the cylindrical phononic crystal (PC). The Green-Naghdi (GN) theory of the generalized coupled thermoelasticity with energy dissipation and the Bloch's theorem are adopted to compute the dispersion relation of thermoelastic waves. The proposed GFD-based meshless collocation method is used to predict the frequency range of the band-gaps and to analyze the effects of the material parameters and the thickness of each layer (sub-cylinder) in a unit-cell on the band-gap property of thermoelastic waves propagating in the cylindrical PCs. The effects of the variations in the layer thicknesses in each unit-cell on the thermoelastic wave band structures are studied in detail. Also, the influences of the key material parameters on the frequency band structures of the thermoelastic waves are investigated. It will be shown that the dimensionless speed of the thermal wave influences the band-gaps more remarkably than other dimensionless parameters such as the dimensionless speeds of the purely elastic dilatational and shear waves, the damping coefficient and the thermoelastic coupling parameter.

Gaussian thermal shock-induced thermoelastic wave propagation in an FG multilayer hybrid nanocomposite cylinder reinforced by GPLs and CNTs

In this paper, a new modified micromechanical model is proposed to obtain the mechanical and thermal properties of a reinforced functionally graded (FG) multilayer hybrid nanocomposite cylinder for thermoelastic wave propagation analysis with energy dissipation using Green–Naghdi theory. The FG multilayer hybrid nanocomposite cylinder is assumed to be under Gaussian thermal shock loading and also it is reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs). The cylinder is assumed to be made of multi-layers (sub-cylinders), and each layer is reinforced by a uniform distribution of GPLs and CNTs. A modified micromechanical model is proposed to calculate the thermo-mechanical properties with nonlinear grading patterns of the GPLs and CNTs along the radial direction of the cylinder. The nonlinear grading patterns of the GPLs and CNTs distributions along the radial direction of the whole cylinder can be created using a suitable arrangement of the layers (sub-cylinders). An effective meshless collocation method based on the generalized finite difference (GFD) method and the Newmark method are employed to solve the coupled governing equations of the GN-based coupled thermoelasticity analysis. The effects of the key parameters such as the weight fraction of the GPLs and CNTs and volume fraction index on the thermoelastic wave propagations and dynamic behaviors of the field variables are studied in detail. Also, the effects of the reinforcement by GPLs and/or CNTs in a hybrid nanocomposite on the transient behaviors of cylinder in both temperature and displacement fields are compared. The accuracy and stability of the presented meshless method and also the proposed new modified micromechanical model is verified by the published reference data.

Thermoelastic wave and thermal shock based on dipolar gradient elasticity and fractional-order generalized thermoelasticity

In the current work, the thermoelastic wave propagation and the thermal shock problems are studied based on the dipolar gradient elasticity and fractional order generalized thermoelasticity in order to take into account the microstructure effect and the thermal effect at a small scale. First, the fractional-order governing equations for coupled thermoelastic wave propagation are derived and the effects of microstructure parameters and fractional order on the dispersion and the attenuation are discussed; next, the transient problems by the thermal shock and the mechanical shock on the surface of half-space are studied. The Laplace transformation method and the state transfer equation method are used to solve this problem. The numerical results for the temperature, the displacement, the stress and the high order stress distributions are provided and shown graphically. The effects of the fractional order and the microstructure parameter on the thermoelastic behavior are investigated. Some interesting phenomenons and conclusions are presented at last.

Thermoelastic wave propagation in a piezoelectric layered half-space within the dual-phase-lag model

Thermoelastic wave propagation in a piezoelectric layered half-space within the dual-phase-lag model

Refined couple stress dynamic modeling of thermoelastic wave propagation reaction of LEMV/CFRP composite cylinder excited by multi relaxation times

This composition presents a multi-phase-lags thermos-elasticity model for the thermos-elastic wave propagation reaction of a composite hollow circular cylinder with the interface layer LEMV/CFRP (Linear Elastic Material with void/Carbon Fiber Reinforced Polymer) using new modified couple stress theory. Three partial differential equations of the modified couple stress and multiphase lag model of composite hollow cylinder are derived for axisymmetric mode and solved exactly using linear theory of elasticity. The frequency equations are achieved for the traction free outer surface with continuity conditions at the interfaces. The influences of changing wave number and thickness on the field quantities like frequency, temperature, displacements, are investigated. Some comparisons are tabulated and presented graphically to estimate the effects of various thermos-elasticity theories and coupled stress parameter.

Heat Transfer Due to Thermoelastic Wave Propagation in a Porous Rod

Abstract This paper investigates the propagation of thermoelastic waves in a homogeneous, linear, and isotropic porous solid. For physical and mathematical simplicity, one-dimensional wave propagation in a porous solid rod is considered to explain the concept of heat transfer caused by motion. The solutions of governing equations show that the transfer of heat in a porous rod is not only due to the conduction but also produced by the local particle displacement phenomenon. It is observed that the time-averaged transfer of heat depends on the circular frequency, porosity, thermal conductivity, thermal relaxation, specific heat, and other material coefficients.

Investigation of Thermoelastic Wave Propagation in Euler–Bernoulli Beam via Nonlocal Strain Gradient Elasticity and G-N Theory

The size-dependent effect arising in micro/nano-structures has attracted considerable attention in academic and industrial communities. The theories developed to characterize such effect mainly include the nonlocal elasticity theory, the strain gradient theory, the modified coupled stress theory and the more recent nonlocal strain gradient elasticity etc. Meanwhile, the thermal-induced deformation or stress in micro/nano-structures is increasingly becoming a vital issue in their designs and applications. Nevertheless, theoretical investigations to predict the thermoelastic performances of micro/nano-structures are not so common, especially in the case of nonlocal strain gradient elasticity incorporating thermoelastic coupling effect. In present work, investigation of thermoelastic wave propagation in micro-beam is conducted in the context of the nonlocal strain gradient elasticity and the G-N theory, taking the thermoelastic coupling effect into account. The governing equations are formulated based on the Euler–Bernoulli beam model and the G-N theory. By assuming the wave-type solutions, the equations are solved and the dispersion relation between frequency and wave number and the relation between phase velocity and wave number are determined respectively. In calculation, the above two relations are fully investigated and comparisons on them under different theories are provided accordingly. Some new findings are presented and discussed in detail. It is hoped that the present work may provide some guidelines in designing and optimizing micro-structures.

Thermoelastic waves in double porosity materials

The focus of this paper is on the propagation of thermoelastic waves with assigned wavelength within the context of theory of thermoelasticity for materials with double porosity. It is shown that there exist two shear waves that are undamped in time, non-dispersive and that are unaltered by the presence of pore system or by thermal effects. Furthermore, there also exist other four longitudinal wave solutions that are dispersive and damped in time: one longitudinal quasi-elastic wave and two quasi-pore modes and one quasi-thermal mode. The dispersion relation is explicitly established like a fifth degree algebraic equation with real coefficients and hence it always allows some real roots, thus predicting existence of some standing waves. A numerical analysis for Berea sandstone shows that the speed of propagation of the longitudinal quasi-elastic wave is larger than the wave speed for its counterpart from the classical elastic model or that in the double porosity elastic model. The propagation of the Rayleigh surface waves is addressed and the corresponding secular equation is explicitly established. As an illustrative example it is used Berea sandstone when the secular equation is solved by means of the graphical method to prove that the Rayleigh surface wave problem admits a solution.

A novel theory of generalized thermoelasticity based on thermomass motion and two-temperature heat conduction

The present paper constructs a new theory of two-temperature generalized thermoelasticity based on thermomass motion consideration. The governing equations of the theory are formulated for heterogeneous, anisotropic, and homogenous materials. Moreover, the uniqueness theorem of the equations of the new theory is proved. The theory based on the motion of thermomass predicts the propagation of thermoelastic waves in the micro-scale heat conduction with finite speed. The two-temperature parameter has significant effects on the conductive temperature increment, dynamical temperature increment, strain, displacement, and stress distributions. The two-temperature generalized thermoelasticity with thermomass motion theory introduces a successful thermoelastic model.