THERMOELASTIC LAMB WAVES IN ELECTRICALLY SHORTED TRANSVERSELY ISOTROPIC PIEZOELECTRIC PLATE

The propagation of Lamb waves in a homogeneous, transversely isotropic, piezothermoelastic plate, which is stress free, electrically shorted, and thermally insulated (or isothermal), is investigated. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave mode propagation are derived in completely separate terms. It is shown that the motion of the purely transverse shear horizontal (SH) mode gets decoupled from the rest of the motion and remains unaffected due to piezoelectric, pyroelectric, and thermal effects. The secular equations for stress-free piezoelectric, thermoelastic, and elastic plates are deduced as special cases in the current analysis. At short wavelength limits the secular equations for symmetric and skew symmetric modes reduce to Rayleigh surface wave frequency equation, because a finite-thickness plate in such a situation behaves like a semi-infinite medium. The amplitudes of dilatation, electrical potential, and temperature change are also computed during the symmetric and skew symmetric motion of the plate. Finally, numerical solutions of various secular equations and other relevant relations are carried out for cadmium selenide (6 mm class) material. The dispersion curves, attenuation coefficients and amplitudes of dilatation, temperature change, and electrical potential for symmetric and antisymmetric wave modes are presented graphically to illustrate and compare the analytical results. The theory and numerical computations are found to be in close agreement. The coupling between the thermal/electric/elastic fields in piezoelectric materials provides a mechanism for sensing thermomechanical disturbances from measurements of induced electric potentials and for altering structural responses via applied electric fields. Therefore, the analysis will be useful in the design and construction of Lamb wave sensors, temperature sensors, and surface acoustic wave filter devices.     

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.     

The Inhomogeneous Waves in Pyroelectrics

In this paper, the general theory of inhomogeneous waves in pyroelectric medium is addressed. The difference from the homogeneous wave is that the wave propagation vector is not coincident with the attenuation vector. The attenuation angle, defined by the angle between wave propagation vector and attenuation vector, is found to be limited in the range of (?90°, 90°). It is found that increasing the attenuation angle will introduce more dissipation and anisotropy. In both L–S theory and inertial entropy theory, four wave modes are found in pyroelectric medium, which are temperature, quasitransverse I, II and quasilongitudinal. Although there is no independent wave mode for the electric field, it can still propagate with other wave modes. The variations of phase velocities and attenuations with propagation angle and attenuation angle are discussed. Phase velocity surfaces on anisotropic and isotropic planes are presented for different attenuation angle. It is found that attenuation angle almost doesn't influence the phase velocities of elastic waves in both anisotropic and isotropic planes. In contrast, the roles it plays on temperature wave are obvious. The effects of the positive and negative attenuation angles are not the same in anisotropic plane. In inertial theory, the results indicate that the temperature wave is almost the same with L–S theory, whereas the coefficient of the inertial entropy should be less than certain value.     

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.     

PROPAGATION OF GENERALIZED VISCOTHERMOELASTIC RAYLEIGH–LAMB WAVES IN HOMOGENEOUS ISOTROPIC PLATES

The present paper is aimed at studying the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's, Green and Lindsay's, and Green and Nagdhi's are employed to understand the thermomechanical coupling and thermal and mechanical relaxation effects. Secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. In the absence of mechanical relaxations (viscous effect), the results for generalized and coupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. The various forms and regions of Rayleigh–Lamb-type secular equation have been obtained and discussed in addition to Lame modes, decoupled shear horizontal (SH) modes, and thin-plate results. At short-wavelength limits, the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and stress-free isothermal plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. Finally, the numerical solution is carried out for copper material. The dispersion curves, and amplitudes of temperature change and displacements for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results.     

Thermoelasticity and P-wave simulation based on the Cole-Cole model

Abstract

The classical Zener model of thermoelasticity can be represented by a mechanical (or viscoelastic) model based on two springs and a dashpot, commonly called standard-linear solid, whose parameters depend on the thermal properties and a relaxation time, and yield the isothermal and adiabatic velocities at the low- and high-frequency limits. This model differs from the more general Lord-Shulman theory of thermoelasticity, whose low-frequency velocity is the adiabatic one. These theories are the basis of thermoelastic attenuation in inhomogeneous media, with heterogeneities much smaller than the wavelength, such as Savage’s theory of thermoelastic dissipation in a medium with spherical pores. In this case, the shape of the relaxation peak differs from that of the Zener and Lord-Shulman models. In these effective homogeneous media, the anelastic behavior of real materials can better be described by using a stress-strain relation based on fractional derivatives. In particular, wave propagation (dispersion and attenuation) is well described by a Cole-Cole stress-strain equation, as illustrated by the agreement with Savage’s theory. We propose a time-domain algorithm based on the Grünwald-Letnikov numerical approximation of the fractional time derivative involved in the time-domain representation of the Cole-Cole model. The spatial derivatives are computed with the Fourier pseudospectral method. We verify the results by comparison with the analytical solution, based on the Green function. The numerical example illustrates wave propagation at an interface separating a porous medium and a purely solid phase.     

Propagation of Inhomogeneous Waves in a Generalized Thermoelastic Anisotropic Medium

The thermal constants and frequency are grouped together to define two thermal coefficients that steer the thermoelastic effects on wave propagation. The four quasi-waves propagate in generalized thermoelastic anisotropic media. The complex value of one of the thermal coefficients makes the four waves attenuating. The complex slowness vector of attenuating waves is resolved into propagation and attenuation vectors. The attenuation part is, further, separated into homogeneous and inhomogeneous waves. The simple procedure is presented to obtain such a specification of complex slowness vector, for given direction of propagation. A non-dimensional inhomogeneity parameter defines the strength of inhomogeneous waves. The propagation velocities, magnitudes and angles of attenuation of inhomogeneous waves depend on inhomogeneity parameter and direction of propagation. The variations of propagation characteristics of attenuating waves, with the inhomogeneity parameter, are computed, for the numerical model of a reservoir rock. The effects of frequency, thermal conductivity, thermoelastic coupling, relaxation time, specific heat on the velocities and attenuations of quasi-waves are exhibited numerically through the different values of thermal parameters defined in the study.     

On electromagneto-thermoelastic plane waves under Green–Naghdi theory of thermoelasticity-II

The present work attempts to investigate the propagation of one-dimensional electromagneto-thermoelastic plane waves in an isotropic unbounded thermally and electrically conducting media with finite conductivity in the context of the theory of thermoelasticity of Green and Naghdi type-II. The heat conduction equation is affected with the Thomson coe?cient. Basic governing equations are modified by using Green–Naghdi theory of type-II. Our problem formulation derives two different systems. The first system is found to be coupled with the thermal field and represents the longitudinal wave. However, the second system represents transverse wave that is uncoupled with the thermal field. In both the cases, we identify waves that are affected with the magnetic field. Asymptotic expansions of dispersion relation solutions and various components of plane waves such as phase velocity, specific loss, and penetration depth are derived analytically for high- and low-frequency values in all cases. Analytical results predicting the limiting behavior of longitudinal and transverse waves are verified with the numerical results. The results of the present study are compared with the results of the thermoelastic case, and a detailed analysis of the effects of presence of the magnetic field under this theory has been presented.     

Waves in Pyroelectrics

The propagation of waves in an infinite pyroelectric medium is studied in this paper. The governing equations for the pyroelectrics are written in three versions which are (1) the version containing heat flow, (2) the stiffened version and (3) the compact version. The results obtained by using versions (1), (2) and (3) are the same. Four characteristic wave velocities are found, three being analogous to those of elastic waves and the fourth wave, which is predominantly a temperature disturbance, corresponding to the heat pulse known as the second sound. It is found that all the velocities and attenuation coefficients are related to the wave normal and the material constants. The effect of the electric properties on the wave propagation is considered, which indicates that the temperature wave is not sensitive to pyroelectricity and piezoelectricity in the discussed case. The effects of relaxation time τ are estimated by several different values, and the results indicate that τ has very little effect on the mechanical velocities; whereas it plays a large role on the velocity and attenuation of temperature wave. The effects of the terms containing τ on the attenuation are researched in detail in one-dimensional case for clarity.     

Effect of orifice plate on the transmission mechanism of a detonation wave in hydrogen-oxygen mixtures

In this paper, a square orifice plate with 60 mm thick and the blockage ratio (BR) of 0.889 is employed to systematically explore the transmission regime of a steady detonation wave in hydrogen-oxygen mixtures. The influence of hydrogen mole fraction is also considered. The average velocity of combustion wave can be determined by evenly mounting eight high-speed pressure sensors on the tube wall, and the detonation cellular patterns can be also registered by the soot foil technique. The experimental results indicate that for the condition of smooth tube, the hydrogen concentration limits range of detonation successful propagation is 37.5%–73.68%. Two propagation modes can be obtained, i.e., the regimes of fast flame and steady detonation. The hydrogen concentration limits range is narrowed to 42.53%–69.51% in the tube with a square orifice plate. Three propagation regimes are observed: (1) near the low limit, a steady detonation wave can be produced before the obstacle, and the phenomenon of detonation decay is seen across the square orifice plate because of the influence of diffraction resulting in the mechanism of detonation failure. The failed detonation wave is not re-ignited because of the lower hydrogen concentration; (2) as the hydrogen mole fraction is increased to 42.53%, the mechanism of detonation re-ignition can be seen after the detonation decay. Well within the limits, the same detonation re-initiation phenomenon also can be observed; (3) as the hydrogen concentration is further enhanced to 69.7% beyond the upper limit, a stable detonation wave is not produced prior to the orifice plate, and the combustion wave front maintain the mode of fast flame until the end of the channel. Finally, it can be found that the detonation wave can successfully survive from the diffraction only when the effective diameter (d_eff) is at least greater than one cell size (λ).     

Mechanical and thermal couplings in helical strands*

Abstract

A generalized Timoshenko rod model is developed for helical strands and helically reinforced cylinders. The thermomechanical constitutive law has five effective elastic moduli, and two thermal coefficients, which can be obtained with the finite element method, or partly from analytic solutions. The model predicts nonclassical bending and thermoelastic behavior of helical strands. First, bending–shearing coupling is explicitly captured, which leads to non-planar bending under a transverse shear force, or a bending moment. Second, torsion and thermal expansion are coupled due to structural chirality. The dispersion relation of harmonic thermoelastic waves is governed by four non-dimensional parameters: two thermoelastic coupling constants, one chirality parameter and the Fourier number. The quasi-longitudinal and the quasi-torsional waves (“quasi” meaning the longitudinal mode is always coupled with a small torsional motion, and vice versa, due to chirality) are dispersive and damped, and dependent on temperature. The adiabatic-isothermal transition of the wave propagation is determined by the Fourier number.     

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.     

Numerical simulation of detonation wave propagation through a rigid permeable barrier

The results of calculation of the detonation propagation in a porous medium for hydrogen-air mixture are presented. The porous medium was specified explicitly and consisted of sets of individual obstacles in the form of solid walls or the sets of finite-size plates. Various modes of detonation propagation depending on obstacle parameters are obtained: propagation in a cellular mode, stationary propagation with destruction of the cellular structure of the detonation front, propagation of a monotonically attenuating detonation wave with destruction of the cellular structure of the front. The possibility of reducing the detonation propagation velocity by replacing solid plates with finite-size ones was shown. The effect of the geometrical parameters of the plates and the step of it installation on the degree of detonation attenuation was estimated. It was determined that an increase in the number of plates leads to a stronger attenuation of the detonation.     

Surface waves in nonlocal thermoelastic medium with state space approach

Abstract

In this paper, a new model based on Eringen’s nonlocal thermoelasticity is constructed. The propagation of Rayleigh surface waves in homogeneous isotropic medium is considered under the purview of this new nonlocal thermoelasticity theory in the context of energy dissipation theory. The normal mode analysis is employed to the considered equations to obtain vector matrix differential equation which is then solved by state space approach. The frequency equations for different cases are derived. The phase velocity, attenuation coefficients, specific loss and penetration depth of Rayleigh surface waves are computed numerically and presented graphically with respect to frequency and the effects of non-locality on the considered parameters are presented in the figures.     

EFFECTS OF THERMAL RADIATION ON THE SOUND WAVE PROPAGATION IN A GAS-PARTICLE TWO-PHASE MEDIUM

A study is made of the sound wave propagation through a radiating gas medium that contains solid particles in suspension. The relaxation models are introduced to describe the temporal momentum and thermal nonequilibrium interactions between gas and particles. The gray gas differential approximation is used for radiation. It is found that the radiation induces the attenuation mode, the position of which is varied with the absorption coefficient in addition to the immovable mode by suspended particles. The attenuation because of radiation is greatly influenced by the absorption coefficient of the radiative medium while the dispersion remains almost unchanged. As the absorption coefficient increases, the attenuation mode because of radiation shifts to the higher frequency zone. This radiation effect is significantly reduced as the particle mass loading increases, since the convection becomes much more dominant.     

Effect of initial pressure on flame–shock interaction of hydrogen–air premixed flames

By utilizing a newly designed constant volume combustion bomb (CVCB), turbulent flame combustion phenomena are investigated using hydrogen–air mixture under the initial pressures of 1 bar, 2 bar and 3 bar, including flame acceleration, turbulent flame propagation and flame–shock interaction with pressure oscillations. The results show that the process of flame acceleration through perforated plate can be characterized by three stages: laminar flame, jet flame and turbulent flame. Fast turbulent flame can generate a visible shock wave ahead of the flame front, which is reflected from the end wall of combustion chamber. Subsequently, the velocity of reflected shock wave declines gradually since it is affected by the compression wave formed by flame acceleration. In return, the propagation velocity of turbulent flame front is also influenced. The intense interaction between flame front and reflected shock can be captured by high-speed schlieren photography clearly under different initial pressures. The results show that the propagation velocity of turbulent flame rises with the increase of initial pressure, while the forward shock velocities show no apparent difference. On the other hand, the reflected shock wave decays faster under higher initial pressure conditions due to the faster flame propagation. Moreover, the influence of initial pressure on pressure oscillations is also analyzed comprehensively according to the experimental results.     

Rayleigh surface wave propagation in orthotropic thermoelastic solids under three-phase-lag model

The present article deals with the propagation of Rayleigh surface waves in a homogeneous, orthotropic thermoelastic half-space in the context of three-phase-lag model of thermoelasticity. The frequency equations in closed form are derived and the amplitude ratios of surface displacements and temperature change during the Rayleigh wave propagation on the surface of half-space have been computed analytically. The path of particles during Rayleigh wave propagation is found elliptical and eccentricity of the ellipse is derived. To illustrate the analytical developments, the numerical solution is performed and the computer-simulated results in respect of phase velocity, attenuation coe?cient, and specific loss are presented graphically.     

A study of plane wave propagation in anisotropic three-phase-lag and two-phase-lag model

The present paper deals with the study of plane wave propagation in anisotropic medium in the context of the theory of three-phase-lag model and two-phase-lag model. It is found that there exist one quasi-longitudinal wave (QL) and two transverse waves (QSH, QSV) and one quasi-longitudinal thermal wave (QLT). The governing equations for homogeneous transversely isotropic three-phase-lag are reduced as a special case and obtained that three coupled quasi waves and one quasi-transverse wave which is decoupled from rest of the motion. From the obtained results the different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically.     

Application of CESE method to simulate non-Fourier heat conduction in finite medium with pulse surface heating

This study employs the space–time conservation element and solution element (CESE) method to simulate the temperature and heat flux distributions in a finite medium subject to various non-Fourier heat conduction models. The simulations consider three specific cases, namely a single phase lag (SPL) thermal wave model with a pulsed temperature condition, a SPL model with a surface heat flux input, and a dual phase lag (DPL) thermal wave model with an initial deposition of thermal energy. In every case, the thermal waves are simulated with respect to time as the thermal wave propagates through the medium with a constant velocity. In general, the simulation results are found to be in good agreement with the exact analytical solutions. Furthermore, it is shown that the CESE method yields low numerical dissipation and dispersion errors and accurately models the propagation of the wave form even in its discontinuous portions. Significantly, compared to traditional numerical schemes, the CESE method provides the ability to model the behavior of the SPL thermal wave following its reflection from the boundary surface. Further, a numerical analysis is performed to establish the CESE time step and mesh size parameters required to ensure stable solutions of the SPL and DPL thermal wave models, respectively.     

The propagation mechanism of detonation wave in a round tube filled with larger blockage ratio orifice plates

In this study, the detonation propagation mechanisms for the stoichiometric hydrogen-oxygen mixture are explored systematically in a circular tube with 6-m in length and an inner diameter of 90-mm. The continuous orifice plates with BR = 0.93 are adopted to investigate the characteristics of detonation diffraction, failure and initiation. High-speed piezoelectric pressure transducers are used to obtain the average velocity, and the smoked foil technique is adopted to record the detonation cellular patterns. The results indicate that three various propagation regimes can be observed, i.e., steady detonation, quasi-detonation and fast flame. In the smooth tube, only the steady detonation and fast flame modes are seen. When the initial pressure is greater than the critical value, the detonation can propagate at about the theoretical CJ velocity. Near the critical pressure, a sudden velocity drop is observed. Of note is that the single-headed spin and double-headed detonation cannot occur because of the limitation of the aspect ratio. In the tube filled with obstacles, the averaged wave velocity is decayed severely. Only the mechanisms of the quasi-detonation and fast flame can be seen. In the quasi-detonation mode, the critical value of d/λ is greater than 7.36, which is far larger than 1. Two different detonation ignition regimes produced by the shock reflection from the wall are observed, i.e., the initiation positions occur in the vicinity of the tube wall and the surface of the orifice plate.