Reflection and transmission between an orthotropic thermoelastic half-space and an initially stressed orthotropic rotating thermoelastic diffusive half-space

Abstract

The purpose of present investigation is to study the reflection and transmission phenomena at the plane interface between an orthotropic thermoelastic half-space and an initially stressed orthotropic thermoelastic rotating half-space with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. The amplitude and energy ratios of the reflected and transmitted waves are derived and the numerical computations have been carried out with the help of MATLAB programing. The effects of initial stress, rotation and diffusion parameters on the amplitude ratios are depicted graphically. It has been verified that at each angle of incidence, there is no dissipation of energy at the interface during reflection and transmission phenomena. Moreover, the effect of anisotropy is also depicted on the velocities of various reflected and transmitted waves. The velocities of these waves are found to depend on the angle of propagation in an orthotropic medium. This dependence of velocities on the direction of propagation is shown graphically.     

Propagation of waves in an initially stressed generalized electromicrostretch thermoelastic medium with temperature-dependent properties under the effect of rotation

In the present article, a model of the equations of generalized electromicrostretch thermoelasticity in an initially stressed perfectly conducting elastic medium under the effect of temperature-dependent properties is studied. The entire elastic medium is rotating with a uniform angular velocity. Reflection phenomena of plane waves in electromicrostretch thermoelasticity is investigated under two theories proposed by Lord and Shulman (L–S) and Green and Lindsay (G–L). Amplitude ratios and energy ratios of various reflected waves are presented when an elastic wave is made incident obliquely at the plane boundary of an electromicrostretch thermoelastic solid half-space. It has been verified that there is no dissipation of energy at the boundary surface during reflection. Numerical examples calculate the amplitude ratios to evince the effects of initial stress parameter, rotation, and temperature-dependent properties, and the results obtained are depicted graphically.     

Waves in nonlocal thermoelastic solids of type II

The present article deals with the investigation of the propagation of thermoelastic plane harmonic waves in a nonlocal thermoelastic medium. The Green and Naghdi theory II (without energy dissipation) of generalized thermoelasticity with elastic nonlocal effect is adopted to address this problem. The problem of reflection of thermoelastic waves due to an incident coupled longitudinal elastic wave from the rigid and thermally insulated boundary of a homogeneous, isotropic nonlocal thermoelastic half-space is also studied. The amplitude ratios of the reflected waves and their respective energy ratios are determined analytically. For a particular model, the effect of elastic nonlocality parameter on the variations of phase speeds, attenuation coefficients, amplitude ratios and corresponding energy ratios of the reflected waves is presented graphically and analysis of these results is given.     

Reflection of magneto-thermoelasticity waves with temperature dependent properties in generalized thermoelasticity

The model of the equations of generalized magneto-thermoelasticity in an isotropic perfectly conducting elastic medium under the effect of temperature dependent properties is established. The modulus of elasticity is taken as a linear function on reference temperature. Reflection of plane harmonic waves in magneto generalized thermoelasticity theories is investigated. The formulation is applied under four theories of the generalized thermoelasticity: Lord-Shulman (LS) with one relaxation time, Green-Naghdi theory GN-II, without energy dissipation and Chandrasekharaiah-Tzou (CT) theory with dual-phase-lag, as well as the coupled theory (CD). The expressions for the reflection coefficients, which are the relations of the amplitudes of the reflected waves to the amplitude of the incident waves are obtained. Effects of dependence of modulus of elasticity on the amplitude ratios have been depicted graphically for a (LS), (GN-II) and (CT) theories.     

Fundamental solution of steady oscillations equations in nonlocal thermoelastic medium with voids

Abstract

A new nonlocal theory of generalized thermoelasticity with voids based on Eringen’s nonlocal elasticity is established. The propagation of plane harmonic waves in nonlocal thermoelastic medium with voids is investigated in the context of dual-phase-lag model of generalized thermoelasticity. There exist three longitudinal waves, namely elastic (E-mode), thermal (T-mode) and volume fraction (V-mode) in addition to transverse waves which get decoupled from the rest of motion and not affected by thermal and volume fraction fields. The fundamental solution of the system of differential equations in case of steady oscillations in terms of the elementary functions has been constructed. The effect of nonlocal parameter and the effect of voids on phase velocities, attenuation coefficients and penetration depths are presented graphically.     

Reflection and refraction of incident p-, T-, and SV-waves at interface between magnetized two solid-liquid media with heat sources and initial stress with and without thermal relaxation times

We investigate the problem of reflection and refraction of thermoelastic waves at a magnetized solid-liquid interface in presence of initial stress. In the context of Green-Lindsay and coupled thermoelastic theories of thermoelasticity, the problem has been solved and the effect of magnetic field, external heat sources, and initial stress on p-, T-, and SV-waves propagation have been discussed. The boundary conditions at the interface for displacement continuity, vanishing the tangential displacement, continuity of normal force, tangential force, and continuity of temperature are applied. The amplitudes ratios for the incident p-, T-, and SV-waves have been obtained. The effect of the initial stress, heat sources, and magnetic field on the reflection and transmitted coefficients for the incident waves have been discussed.     

Analysis of the quality factor of micro-beam resonators based on heat conduction model with a single delay term

The present article investigates the quality factor of thermoelastic damping in micro-beam resonator from the standpoint of a very recent thermoelasticity theory proposed by Quintanilla (2011). In recent years, significant attention is being paid to micro- and nano-resonators due to their wide applications in micro- and nano-electromechanical systems (MEMS/NEMS). The quality performance of a micro-beam resonator is usually measured by the quality factor and thermoelastic damping is considered to be the most important intrinsic dissipative mechanism in micro and nanoscale devices. In the present article, we consider the heat conduction model with a single delay term given by Quintanilla (2011) and derive an expression for thermoelastic damping by applying complex frequency approach. The variation of thermoelastic damping versus normalized frequency and thickness of Silicon micro-beam resonator for different aspect ratios have been studied. We compare the results of present model with the corresponding results of thermoelasticity theories of type GN-III, three-phase-lag (TPL), and Lord-Shulman (LS) models and investigate that the new model with a single delay term (NMSDT) gives high Q-factor of the micro-beam resonator’s sensitivity in comparison to LS and TPL models and the results under this model have more similarity to the results of GN-III model.     

Reflection and refraction of plane wave at the interface between elastic and thermoelastic media with three-phase-lag model

The problem of reflection and refraction phenomenon due to longitudinal and transverse waves incident obliquely at a plane interface between uniform elastic solid half-space and thermoelastic solid with three-phase-lag model half-space has been studied. In thermoelastic solid medium, potential functions are introduced to represent two longitudinal waves and one transverse wave. The amplitude ratios of various reflected and refracted waves to that of incident wave are derived. These amplitude ratios are further used to find the expressions of energy ratios of various reflected and refracted waves to that of incident wave. The graphical representation is given for these energy ratios for different directions of propagation. The law of conservation of energy at the interface is verified.     

Electric and Thermal Relaxation Times Effects on Reflection and Transmission Coefficients at the Boundary of Electromicrostretch Thermoelastic Media

In this work, the propagation of plane waves at an interface of two electromicrostretch thermoelastic solid half-spaces is studied. Amplitude ratios of various reflected and transmitted waves are presented, when a plane wave is made incident obliquely at an interface of electromicrostretch thermoelastic solid half-spaces. The amplitude ratios are influenced by angle of incidence and the properties of media. Numerical computations are performed for a specific model to determine the amplitude ratios and the obtained results are described graphically with angle of incidence. The influence of electric and thermal relaxation effects is observed on reflection and transmission coefficients. Some special cases of interest have also been concluded from the present investigation.     

Reflection of plane waves in a thermoelastic diffusive medium under the effect of microtemperatures

Abstract

The present analysis is aimed to model and study the characteristics of various reflected waves in a homogeneous and isotropic thermoelastic diffusive half-space with microtemperatures. It is shown that there exist four kinds of coupled longitudinal waves in addition to transverse and microtemperature waves in such type of medium. The reflection coefficients and energy ratios of these reflected waves have been computed numerically with the help of MATLAB programing when (i) a set of coupled longitudinal waves is made incident and (ii) a transverse wave is made incident. The numerical values of modulus of reflection coefficients are presented graphically to depict the effect of thermodiffusive parameter. It has been verified that there is no dissipation of energy at the free plane boundary during reflection phenomena.     

Structure and intrinsic properties of dispersion relation in hyperbolic thermoelasticity

For a system of field equations of hyperbolic thermoelasticity, we derive a propagation condition for a thermoelastic disturbance in a form of homogeneous plane wave in deformation and temperature. The corresponding dispersion relation is given in an explicit form, together with the dependence of characteristic coefficients on the principal invariants of the tensor of isothermal elasticity, heat conductivity, and thermoelasticity. Discussion of different types of homogeneous thermoelastic plane waves is given as well. Derived methodology is applied in the analysis of Green–Naghdi model.     

CIRCULAR CRESTED THERMOELASTIC WAVES IN HOMOGENEOUS ISOTROPIC PLATES

The propagation of circularly crested thermoelastic waves in a homogeneous isotropic cylindrical plate subjected to stressfree and isothermal conditions is investigated in the context of conventional coupled thermoelasticity (CT), Lord-Shulman (LS), Green-Lindsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. The secular equation for the circular plate in closed form and isolated mathematical conditions for symmetric and skew symmetric wave mode propagation in completely separate terms are derived. It is shown that the motion for SH modes gets decoupled from the rest of the motion and remains unaffected due to thermomechanical coupling and thermal relaxation effects. The phase velocities for SH modes have also been obtained. It is noticed that the rest of the motion for circular crested waves is again governed by Rayleigh-Lamb-type secular equations. The secular equations for these plate and Lamé modes are also obtained and discussed for different regions. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. At short wavelength limits, the secular equations for symmetric and skew symmetric waves in stressfree insulated and isothermal circular plate reduces to Rayleigh surface wave frequency equations. Finally, the numerical solution is carried out for aluminium-epoxy composite material, and dispersion curves for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.     

Wave propagation in an initially stressed magneto-thermoelastic medium with voids and microtemperatures

Abstract

Present analysis is concerned with the propagation of plane waves in an initially stressed magneto-thermoelastic half-space with microtemperatures and voids. It is noticed that there exist four kinds of coupled dilatational waves in addition to shear and microtemperature waves in such type of medium. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves have been presented in closed form when (i) a set of coupled dilatational waves is made incident and (ii) a shear wave is made incident. Amplitude ratios of various reflected waves are presented graphically to explore the effects of magnetic field, initial stress and void parameter. It is verified that there is no loss of energy at the free surface during reflection phenomena.     

Ray expansion theory in the problem of impact of a thermoelastic rod against a heated wall

Abstract

The impact of a thermoelastic rod against a rigid heated barrier is considered using the hyperbolic theory of dynamic coupled thermoelasticity with thermal relaxation. The ray method which is based on the theory of discontinuities is used as a method of solution. The longitudinal coordinate dependence of the desired values at each fixed instant of the time beginning from the moment of rod’s impact against the wall up to the moment of its rebound has been constructed. It has been found that the contact duration of the thermoelastic rod with the heated rigid wall is dependent not only on the arrival to the place of contact of elastic and thermal waves reflected from the free rod’s end, but on the relaxation processes occurring in the thermoelastic rod as well.     

Propagation of waves in transversely isotropic micropolar generalized thermoelastic half space

The propagation of waves in a transversely isotropic micropolar medium possessing thermoelastic properties based on Lord and Shulaman (L–S), Green and Lindsay (G–L) and Coupled thermoelasticity (C-T) theories are discussed. After developing the solution, the phase velocities and attenuation quality factor have been obtained. The expressions for amplitudes of stresses, displacements, microrotation and temperature distribution have been derived and computed numerically. The numerical results have been plotted graphically.     

SV-waves incidence at interface between solid-liquid media under electromagnetic field and initial stress in the context of three thermoelastic theories

In this article, we studied the propagation of SV-waves under the effect of electromagnetic field and initial stress for three models in thermoelasticity: The couple and Green–Lindsay theories as well as the dual-phase-lag theory. The problem of reflection and transmission of thermoelastic waves at a solid–liquid interface in the presence of electromagnetic fields and initial stress we investigated subjected to certain boundary conditions. The appropriate expressions to find the amplitude ratios of the incident waves (SV-waves) were obtained. The reflection and transmission coefficients for the incident SV-waves were computed numerically. The effect of electric field, magnetic field, and initial stress were illustrated graphically. Comparisons were made with the obtained results in the presence and absence of considered variables and displayed graphically. The results indicate that the effect of electric field, magnetic field, and initial stress on SV-waves incidence at the interface between solid–liquid media are very pronounced.     

ON THE PROPAGATION OF THERMOELASTIC WAVES IN MEDIA WITH LONG-RANGE COHESIVE FORCES

Abstract

After establishing the fundamental equations of nonlocal coupled thermoelasticity in Fourier space, nonlocal longitudinal thermoelastic waves in an infinite space are analyzed. Identification of the elastic dispersion equation obtained with its counterpart derived in lattice dynamics leads to values of the nonlocal elastic moduli. Similar identification of the velocity of thermal waves with its counterpart in second sound theory yields the values of the nonlocal thermal moduli. A numerical example involving solid helium is given.     

A Unified Generalized Thermoelasticity Formulation; Application to Thick Functionally Graded Cylinders

In this article a new unified formulation for the generalized coupled thermoelasticity theories is presented. The generalized coupled thermoelasticity theories proposed by Lord–Shulman, Green–Lindsay, and Green–Naghdi are combined into a unified formulation introducing the unified parameters. The formulation is given for the general anisotropic heterogeneous linear thermoelastic materials and then is reduced to the system of equations for the isotropic heterogeneous materials. As an example, a functionally graded cylinder is considered and the thermoelastic waves based on the new unified formulation, using the generalized theories, are obtained and discussed. Utilizing the transfinite element method, the equations for a long thick circular cylinder are solved in the Laplace domain and the results are inverted to the real time domain using a numerical inversion technique of the Laplace transform. The results for the propagation of thermoelastic waves based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models are derived and compared.     

Thermoelastic Damping in Nanomechanical Resonators with Finite Wave Speeds

ABSTRACT

The operation of micro-/nanobeams vibrating at very high frequencies, such as encountered in micro-/nanoelectromechanical systems (MEMS/NEMS), hinges on the minimization of intrinsic material losses. We study the associated thermoelastic damping in such beams from the standpoint of a generalized theory of thermoelasticity with one relaxation time. Some of our results relate to: (i) the cooling (instead of heating) in the compressed surface of the beam; (ii) the existence of not one damping peak appearing in the classical theory, but many peaks, with a decreasing amplitude as the frequency tends to infinity; (iii) the relevance of thermoelasticity with finite wave speeds for frequencies on the order of 10¹² Hz.     

Propagation of Rayleigh Surface Waves in Microstretch Thermoelastic Continua Under Inviscid Fluid Loadings

The present article is aimed at an investigation of the propagation of generalized Rayleigh surface waves in a homogeneous, isotropic, microstretch thermoelastic solid half-space underlying an inviscid liquid half-space or layer of finite thickness, in the context of classical (coupled) and non-classical (generalized) theories of thermoelasticity. The secular equations in close form and isolated mathematical conditions are derived for generalized Rayleigh waves in the considered composite structure after obtaining general wave solutions of the model. The fluid overlying the solid half-space has been successfully modeled as thermal load in addition to normal (hydrostatic pressure) one. Some special cases of dispersion equations have also been deduced and discussed. The analytic expressions for the amplitudes of displacement, microstretch, microrotation and temperature change at the interfacial surface during the Rayleigh wave propagation are also derived. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of this work. Finally, the analytical developments have been illustrated numerically for aluminum–epoxy-like material half-space under the action of inviscid liquid (water) half-space or layer of finite thickness. The computer simulated results in respect of phase velocity, attenuation coefficient, specific loss factor of energy dissipation and relative frequency shift due to fluid loadings are presented graphically in normalized form to observe their distinctions from those in the context of the well established theory of coupled thermoelasticity.