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The flexural vibrations of homogeneous, transversely isotropic, generalized (non-Fourier) thermoelastic simply-supported thin beam resonators due to thermal and mechanical loads have been investigated under Euler–Bernoulli hypothesis. The model equation governing the transverse vibrations has been solved by using double Laplace transform technique (LTT) with respect to space and time. A mesh-less computational method, Adomian decomposition method (ADM), has also been employed to solve the model equation in the space domain for the comparison purpose. The inversion of the transformed solution has been carried out by using Durbin׳s technique in order to obtain the results in physical time domain. The natural frequencies and the corresponding mode shapes of the beam have been computed. The effects of thermal variations and other parameters on the deflection and temperature profiles of the thin beam have been studied. The effect of thermal relaxation time (second sound) on the vibration characteristics of beam has also been observed. The results computed by using LTT and ADM have been compared and are found to be in good agreement. It is noticed that ADM is an accurate, computer friendly and provides a unified, systematic powerful mathematical tool for solving the static and dynamic vibration problems for the considered beams.

This article deals with the transverse vibrations in a homogeneous isotropic, thermoelastic-diffusive thin beam based on the Euler–Bernoulli theory under clamped–clamped boundary conditions. The analytical expressions for deflection, thermal moment, mass moment, frequency shift, and damping due to thermoelastic-diffusion in the beam has been derived. The effects of mass diffusion, thermomechanical coupling, surface conditions, and beam dimensions on energy dissipation and other field quantities induced by thermoelastic-diffusion have been investigated. The analytical results have been numerically analyzed with the help of MATLAB software. The numerically computed results for deflection, temperature change, thermal moment, mass moment, damping factor, and frequency shift have been presented graphically. The computed values of effective flexural rigidity have been given in tabular form. The study may find applications in medical science, engineering, accelerometers, sensors, resonators, etc.

The flexural vibrations in a homogenous isotropic, thermoelastic-diffusive thin cantilever beam have been analyzed in closed form based on the Euler–Bernoulli theory. The analytical expressions for deflection, thermal moment, mass moment, frequency shift and thermoelastic-diffusive damping (inverse quality factor) have been obtained for clamped-free (cantilever) beam. It is found that the thermoelastic-diffusive damping and frequency shift of beam vibrations significantly depend on diffusive properties. The analytical results have been analyzed numerically with the help of MATLAB software. The values of effective flexural rigidity have also been computed and presented in tabular form. The numerical computed results have been presented graphically. This study may be useful in the design and construction of sensors, gyrometers, charge detectors, radio frequency filters, communicators and energy harvesters etc due to mass concentration change in the materials.

This article is devoted to model and analyze the transverse deflection and thermal moment of transverse vibrations in a transversely isotropic, thermo-elastic beam resonator under the action of time harmonic concentrated load. The governing equations of flexural vibrations and thermal moment in a transversely isotropic, thermo-elastic Euler–Bernoulli beam have been derived in a closed form. A time harmonic point load is assumed to act on the beam at a given distance from the origin. The beam is assumed to be at either clamped-clamped (CC), simply supported-simply supported (SS), clamped-simply supported (CS), or clamped-free (CF) conditions at its ends. The Laplace transform technique has been used to find the transverse deflection and thermal moment in the transform domain due to the action of concentrated load in a beam under above conditions in case of both free and forced vibrations. The analytic expressions obtained in the physical domain after inversion of Laplace transforms have been computed numer...

The aim of this article is to study the disturbance in a homogeneous, transversely isotropic (6 mm class), linear generalized piezothermoelastic, cylindrical continuum subjected to continuous mechanical and thermal point loads. A combination of integral transforms, Laplace and Hankel, has been employed to solve the model consisting of partial differential equations and boundary conditions. The transform technique reduces the system of partial differential equations to ordinary differential equations. The formal solution of the resulting system of coupled ordinary differential equations has been obtained by using the eigenvalue approach. A numerical technique for inverting the integral transforms along with Des Cartes’ procedure and the Gauss elimination method has been used to obtain the results in physical domain. The stresses, temperature change and electric displacement have been computed numerically from the relevant expressions and relations for PZT-5A material. The computer simulated results have be...

A statistical analysis is presented to investigate the influence of temperature, rotation, viscosity and thermal relaxation time on the propagation characteristics of different waves in an elastic medium. The solution of complex secular equation governing the characteristics of the bulk waves in an infinite homogenous isotropic, Kelvin-Voigt type generalized viscothermoelastic rotating media is carried out by employing both direct and perturbation methods. The analytical developments are supported with numerical illustrations for copper material in respect of phase velocities, attenuation coefficients and specific loss factor of various possible waves. The computer simulated results have been presented graphically with respect to Kibel number. In order to explore and analyze the effects of viscosity and temperature on the elastic waves, the Karl-Pearson correlation coefficient has been used. The student t-test is used to judge and decide the suitability of Cardano’s method vis-à-vis perturbation one for computing different characteristics. The present study may be useful in geophysics and gyroscopic sensor applications and industry.

The three-dimensional free vibrations in a simply supported homogeneous isotropic, thermally conducting, circular cylinder of finite length with an eccentrically located inner circular cavity have been studied. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The three-dimensional linear theory of coupled thermoelasticity has been employed to model the problem. The displacement potential functions have been introduced to decouple purely shear and longitudinal motions. The purely transverse wave has been found to remain unaffected due to thermal field. The translation addition theorem for cylindrical wave functions along with orthogonal series expansions has been used to develop the exact solution. To illustrate the analytical results, the numerical solution of some relations and equations have been obtained to compute lowest frequency and dissipation factor versus eccentricities, for selected length to radius ratio and radius ratio of hol...

In this article, the closed form expressions for the transverse vibrations of a piezothermoelastic beam, based on Euler–Bernoulli theory, have been derived. The effects of electric potential, relaxation times, thermomechanical coupling, and beam dimensions on energy dissipation induced by thermoelastic damping microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS) resonators have been investigated under free edge conditions. Analytical expressions for damping and frequency shift of vibration due to electric potential and thermal variations are obtained. The vibrations of such resonators are significantly affected due to surface conditions. Some numerical results with the help of MATLAB programming software in the case of lead zirconate titanate (PZT)-5A material have been presented graphically for illustration of analytical developments.

PurposeThe purpose of this paper is to analyze the free vibrations in a stress free and thermally insulated (or isothermal), homogeneous, transversely isotropic, solid cylinder based on three‐dimensional coupled thermoelasticity, which is initially undeformed and kept at uniform temperature.Design/methodology/approachThe displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple the purely shear and longitudinal motions. The system of governing partial differential equations is reduced to four second‐order coupled ordinary differential equations in radial coordinate by using the method of separation of variables. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. The convergence analysis of matrix Frobenius method has been successfully carried out.FindingsThe purely transverse mode is found to be independent of the rest of the motion and temperature change. The natural frequency, dissipation factor, inverse quality factor and frequency shift of vibrations in a stress free solid cylinder get significantly affected due to thermal variations and thermo‐mechanical coupling.Originality/valueA new procedure is used and compared to other methods available in the literature.

In the present paper, the theory of generalized thermo-microstretch elasticity has been employed to study the propagation of straight and circular crested waves in microstretch thermoelastic plates bordered with inviscid liquid layers (or half-spaces), with varying temperature on both sides. The secular equations governing the wave motion in both rectangular and cylindrical plates have been investigated. The results in the case of thin (long wavelength) and thick (short wavelength) plates have also been obtained and discussed as special cases of this work. The secular equation in the case of microstretch coupled with thermoelastic, micropolar thermoelastic and thermoelastic plates can be obtained from the present analysis by an appropriate choice of relevant parameters. 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 sandwiched in the inviscid liquid. The computer simulated results in respect of phase velocity, attenuation coefficient, specific loss factor of energy dissipation and relative frequency shift due to liquid layers on both sides of the plate are presented graphically.

The aim of the paper is to study three-dimensional free vibrations in a homogeneous transversely isotropic, thermoelastic hollow cylinder, which is initially undeformed and at uniform temperature. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The displacement potential functions have been introduced in the equations of motion and heat conduction to decouple purely shear and longitudinal motions. The purely transverse wave is not affected by thermal field. By using the method of separation of variables, the system of governing partial differential equations is reduced to four second-order coupled ordinary differential equations in radial coordinate. The Matrix Frobenius method of the extended power series is employed to obtain the solution in radial direction. To illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the lowest frequency, frequency shift and damping fac...

The governing equations of flexural vibrations in a transversely isotropic thermoelastic beam are derived in closed form based on Euler–Bernoulli theory. The out-of- plane vibrations have been studied under different beam dimensions and boundary conditions. The analytical expressions for thermoelastic damping and frequency shift of vibrations are obtained. The damping and frequency shift of beam vibrations significantly depend on thermal relaxation time and surface conditions at resonance. The expressions for displacement and temperature fields in the beam resonator are obtained. Some numerical results with help of MATLAB software have been computed and presented graphically for silicon material beams.

The present work deals with the propagation of interfacial surface waves in a composite consisting of homogeneous, transversely isotropic, piezoelectric halfspace underlying a thin layer of non-piezoelectric semiconductor material. The mathematical model of the problem is depicted by partial differential equations of motion for the structure and boundary conditions to be satisfied at the interface and free surface of the composite. After obtaining formal wave solution of the model the secular equation that governs the propagation of surface waves in the considered composite structure has been derived in compact form. The numerical solution of secular equation is being carried out for the composites Si–CdSe, Ge–CdSe and Ge–PZT by employing functional iteration method along with irreducible Cardano method using MATLAB programming. The computer simulated results in respect of dispersion curves, attenuation coefficient and specific loss factor of energy dissipation are presented graphically for Si–CdSe composite to illustrate the analytical developments. We have extended our analysis to Ge–CdSe and Ge–PZT composites also. However, to avoid clustering of profiles and also to have clear understanding of the variations, the computer simulated values of phase velocity and attenuation coefficient are presented in tabular form for all three considered composite structures. This work may be useful for designing and construction of surface acoustic wave (SAW) devices and electronics industry.

The present paper deals with the disturbances due to periodic strip thermal sources, acting on the rigidly fixed, charge free (open circuit) or electrically shorted (closed circuit) surface of a homogeneous, transversely isotropic, thermally conducting generalized piezothermoelastic half-space. The Laplace and Fourier transform technique have been employed to solve the model consisting of partial differential equations and boundary conditions in the transformed domain. In order to obtain the displacements, temperature change, stresses, electric potential and electric displacement in the physical domain, the integral transforms have been inverted by using a numerical inversion technique. Finally, to illustrate the analytical results, the numerical computations of various field parameters have been carried out from the relevant expressions and relations for cadmium selenide (CdSe) material by developing a FORTRAN code. The computer simulated results are presented graphically in respect of different considered field functions with load frequency and epicentral distance for 6 mm cadmium selenide (CdSe) material half-space.

The present paper deals with the propagation of body waves in a homogenous isotropic, rotating, generalized thermoelastic solid. The complex cubic secular equation has been solved by using Cardano’s and perturbation methods to obtain phase velocities, attenuations and specific loss factors of three attenuating and dispersive waves, which are possible to exist in such media. These wave characteristics have also been computed numerically for magnesium crystal and are presented graphically. Statistical analysis has been performed to compare the computer simulated results obtained by using both methods. This work may find applications in geophysics and gyroscopic sensors.

The present article is devoted to investigate the propagation of elasto-thermodiffusive (ETNP) surface waves in a homogeneous isotropic, thermally conducting semiconductor material of half-space with relaxation of heat and charge carrier fields. The secular equation, a more general functional relation, that governs the propagation of elasto-thermodiffusive (ETNP) surface waves in homogeneous isotropic, thermoelastic semiconductor material halfspace with relaxation of heat and charge carrier fields has been derived by solving a system of coupled partial differential equations. A hybrid numerical technique consisting of Descartes algorithm for solving complex polynomial characteristic equation along with functional iteration scheme has been successfully used to solve the secular equation in order to obtain dispersion curves, attenuation coefficient and specific loss factor of energy dissipation for p-type germanium (Ge) semiconductor. Some particular forms of the general secular equation governing the propagation of elasto-thermodiffusive (ETN/ETP), thermoelastic (ET), elastodiffusive (EP/EN) and thermodiffusive (TP/TN) surface waves have been also deduced and discussed. In order to illustrate the analytical development, the numerical solution of the secular equation and other relevant relations under different situations is also carried out for Ge semiconductor materials to characterize the elasto-thermodiffusive (ETP) and thermodiffusive (TP) surface waves. The computer simulated results have been presented graphically in respect of the dispersion curves, attenuation coefficient and specific loss factor.

The propagation of Lamb waves in a homogeneous, transversely isotropic (6 mm class), piezothermoelastic plate rotating with uniform angular velocity about normal to its boundary has been investigated. The generalized (non-classical) theories of thermoelasticity in contrast to Sharma and Pal [Sharma, J.N., Pal, M., 2004. Lamb wave propagation in transversely isotropic piezothermoelastic plate. J. Sound Vib. 270, 587–610] have been used to investigate the problem. The surfaces of the plate are subjected to stress free, thermally insulated/isothermal and electrically shorted boundary conditions. Secular equations for wave propagation modes in the plate are derived from a coupled system of governing partial differential equations of linear piezothermoelasticity. After obtaining the complex characteristic roots with the help of Descartes' algorithm, the transcendental secular equations have been solved by functional iteration numerical technique to compute phase velocity and attenuation coefficient. Finally, in order to illustrate the analytical development, numerical solution of secular equations is carried out for PZT-5A piezo-thermoelastic material. The corresponding simulated results of various physical quantities such as phase velocity, attenuation coefficients, specific loss factor of energy dissipation, thermo-mechanical coupling factor and relative frequency shifts have been presented graphically for both rotating and non-rotating plates for comparison purpose. There is a scope for extension of the present work to other classes of piezo/pyroelectric crystals. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric surface acoustic wave (SAW) devices.

In this paper the propagation of plane and circular crested viscothermoelastic waves in a homogeneous isotropic, Kelvin–Voigt type viscoelastic thermally conducting, plate sandwiched between inviscid liquid layers is investigated in the context of classical and non-classical theories of thermoelasticity. The secular equations for the symmetric and skew-symmetric modes of plane and circular crested waves are derived in closed form and isolated mathematical conditions. It is noticed that the motion for both the plane and cylindrical waves in plates is governed by Rayleigh–Lamb-type secular equations. The secular equations for thin plate and short wave length waves are also obtained and discussed. The results in the absence of fluid loading, coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. The dispersion curves, attenuation profiles and specific loss in case of symmetric and skew-symmetric wave modes are also presented graphically for a polymethyl methacrylate material plate under fluid loadings. The effect of dissipation due to viscosity is noticed to be quite significant and clearly visible from various curves in the graphs.

The present article is aimed at an investigation of the propagation of elasto-thermodiffusive (ETN) surface waves in a homogenous isotropic, thermoelastic semiconductor material half-space underlying a viscous or inviscid fluid half-space or layer of finite thickness with varying temperature. The relaxation times of heat and charge carrier fields are also taken into consideration during the study. The secular equation that governs the propagation of elasto-thermodiffusive surface (interfacial) waves in the considered composite structures has been derived in compact form after obtaining the general wave solution of the model. Some particular forms of the general secular equation are also deduced and investigated. Numerical solution of secular equation and other relevant relations is carried out for silicon (Si) semiconductor material under different situations with the help of functional iteration numerical technique along with the irreducible case of Cardano's method. The computer-simulated results in res...

The present paper represents an analysis of Rayleigh surface waves in a homogeneous, transversely isotropic, generalized piezothermoelastic half-space rotating with uniform angular velocity about normal to its boundary and subjected to stress free, electrically shorted/charge free and thermally insulated/isothermal boundary conditions. The secular equations for stress free, generalized piezothermoelastic half-space in closed form and isolated mathematical conditions are derived. The characteristics of surface waves propagating in generalized piezothermoelastic solid half-space and their dependence upon various geometric and physical parameters have been investigated. Finally, in order to illustrate and compare the theoretical results, numerical solution of various secular equations and other relevant relations are derived for cadmium selenide (6 mm) class material by adopting functional iteration scheme after employing Descartes’ algorithm to compute the characteristic roots of coupled differential equation system. The corresponding simulated results of various physical quantities such as phase velocity, attenuation, specific loss, frequency shifts and electromechanical coupling have been presented graphically for rotation and non-rotation cases. The study will be useful in design and construction of gyroscope, rotation sensors, temperature sensors and other pyro/piezoelectric SAW devices.

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.

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...

The paper is aimed at an investigation of the propagation of elasto-thermodiffusive (ETN) surface waves in homogenous isotropic, thermally conducting, semiconductor material half-space with relaxation of heat and charge carrier fields. Secular equations, in isolated mathematical conditions and compact form, for the thermoelastic diffusive surface waves in semiconducting material half-space are derived. Some particular forms of the general secular equation are also deduced and investigated. The secular equations for thermoelastic (ET) and elastodiffusive (EN) surface waves have been obtained and discussed as special cases. The surface displacements during the wave propagation have also been obtained and discussed. The paths of surface particles of ETN, ET, and EN surface waves are found to be elliptical in nature. Numerical solution of various secular equations and other relevant relations is carried out for silicon (Si) semiconductor material with the help of functional iteration numerical technique. In o...

The present paper deals with the study of rotation effect on the characteristics of Rayleigh waves propagating in a homogeneous, transversely isotropic piezothermoelastic half space in the framework of linear theory including Coriolis and Centrifugal forces. The medium is subjected to stress free, thermally insulated, electrically shorted/charge free boundary conditions and is rotating about an axis perpendicular to its plane. Characteristics of surface waves propagating in thermoelastic piezoelectric solids and their dependence upon various geometric and physical parameters are derived. After deriving secular equations in closed form and isolated mathematical conditions, the effect of rotation on dispersion curves and attenuation profiles is studied. The specific loss factor and relative frequency shift are also obtained in case of open and closed circuit electric surface conditions. Finally, in order to illustrate and verify the analytical results, numerical solution of various secular equations and other relevant relations are derived for cadmium selenide (6mm) class material. The analysis shows that the rotation sensitivity at long wavelengths (in the vicinity of the surface) is substantially greater than those at short wavelengths (deep into the half space). The study is very helpful in the development of rotation sensors and other piezoelectric devices.

In this article the effect of anisotropy and temperature on the dispersive wave propagation in composite substrate has been investigated. The propagation of guided waves in coated homogeneous anisotropic thermoelastic media is of interest in electronics and related areas. In recent years, cladded fiber-reinforced composites are being developed for use as aerospace structures. This paper deals with the guided wave propagation in a cladded (or coated) thermoelastic homogeneous anisotropic medium in the context of linear generalized thermoelasticity. The cladding (coating) is assumed to be thin homogeneous isotropic layer, which is bonded to a transversely isotropic substrate with the axis of symmetry parallel to the layer. It is shown that the anisotropy of the substrate affects the dispersion behaviour in a manner that is substantially different than that in case of isotropic substrate. In addition, the effect of variation of temperature on the dispersion curves and attenuation coefficient of thermoelastic waves is also studied. The results in case of classical coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) can be obtained as special cases from the present analysis by omitting thermal relaxation time and thermo mechanical coupling effects, respectively. Finally, the numerical solution of the model is obtained by computer simulations for a magnesium material half-space in different situations and the computed dispersion curves and attenuation coefficient profiles have been presented graphically in order to illustrate different phenomenon involved.

The aim of present paper is to study 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/rigidly fixed, thermally insulated or isothermal boundary conditions. Coupled dynamical thermoelasticity is employed to study the problem. We derive complex secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases from the derived secular equations. In general, the obtained secular equations are complex each of these on separating real and imaginary parts leads to two real frequency equations. These equations contain complete information regarding wavenumber, phase velocity, group velocity and attenuation coefficients of different propagating modes. The regions and the corresponding forms of Rayleigh–Lamb-type secular equations have been obtained and discussed in addition to Lame modes, decoupled shear horizontal modes and thin plate results. At short wavelength limits, the secular equations for symmetric and skew-symmetric waves in stress-free insulated and stress-free isothermal plate reduce to Rayleigh surface wave frequency equations. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. In order to illustrate and compare the theoretical results, the numerical solution is carried out for copper material by using the functional iteration method. The dispersion curves, attenuation coefficients, amplitudes of temperature change, and displacements in case of symmetric and skew-symmetric wave modes are presented graphically.

This article is aimed at studying the propagation of surface waves in a homogeneous, isotropic, thermally conducting elastic solid bordered with layers or half spaces of inviscid liquid in the context of generalized theories of thermoelasticity. After developing formal solutions, secular equations for the solid in closed form and isolated mathematical conditions for leaky Rayleigh waves, leaky Lamb waves, and nonleaky Lamb waves in completely separate terms are derived. The thin-plate wave results for leaky Lamb waves have also been derived. The amplitude ratios of displacement in liquid layers and half spaces are also obtained and computed analytically. The results have been deduced and compared with the relevant publications available in the literature at the appropriate stages of the work. Finally, the numerical solution is carried out for an aluminum–epoxy composite material solid (half space) or plate bordered with water layers of finite and infinite thickness. The dispersion curves, attenua...

The propagation of circularly crested generalized thermoelastic waves in a homogeneous isotropic, thermally conducting plate, bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides, is investigated in the context of conventional coupled thermoelasticity, and Lord-Shulman and Green-Lindsay theories of thermoelasticity. We derive secular equations for a circular homogeneous isotropic plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms. Results for the uncoupled theory of thermoelasticity have been obtained as a particular case from the present one. Special cases, such as Lam6 modes, short wavelength waves, and thin plate waves of the secular equation, are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for aluminum epoxy composite material bordered with water. The dispersion curves for symmetric and antisymmetric wave modes and amplitudes of displacement and temperature change in the case of fundamental symmetric (SO) and skew symmetric (AO) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.

The Kelvin–Voigt model of linear viscoelasticity, which describes the viscoelastic nature of a material, is used to investigate the transient waves due to thermal loads acting on the boundary of the thermoviscoelastic media. The Laplace and Hankel transform technique has been employed to solve the boundary-value problem in the transform domain in the context of various theories of generalized thermoelasticity. The Laplace transforms have been inverted by using a numerical technique and then the inverse Hankel transform integrals are evaluated by using Romberg integration to obtain the results in the physical domain. The temperature and stresses are computed numerically and presented graphically in different situations for copper material. A comparison of the results for different theories of generalized thermoelasticity and viscoelasticity is also presented at appropriate stages of this work.

The paper is concerned with the investigation of the steady-state response of an applied load moving with constant speed for infinite long time over the top surface of a homogeneous thermoelastic layer lying over an infinite half-space. The governing field equations of motion and heat conduction have been solved by using the Fourier transform technique. The algebraic expressions as a function of time and horizontal distance for the displacements and temperature change have been obtained and are valid for all epicentral distances. The displacements and temperature change so obtained in the physical domain at the free surface of the layer and its interface with the half-space have been computed numerically and are presented graphically. The paper may attract the attention of engineers and designers because of its significance in engineering problems of ground motion under a pressure wave.

In this work, based on three-dimensional piezoelectric thermoelasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel is presented. Displacement and electric potential functions are introduced in order to solve the equations of motion, Gauss equation and heat conduction equation. It is noticed that a purely transverse mode is independent of piezoelectric and pyroelectric effects and gets decoupled from rest of the motion. The equations for free vibration problem are further reduced to five second-order ordinary differential equations, after expanding the displacement, temperature change and electric potential functions with an orthogonal series. The dispersion relation for electrically-shorted/charge-free, thermally insulated/isothermal and simply supported cylindrical panel with stress-free edges have been obtained and discussed. A modified Bessel function solution with complex arguments is directly used for complex eigenvalues. In order to clarify the developed method and compare the results to the existing ones, numerical examples are presented for PZT-5A material, and the computed functions are illustrated graphically.

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 ...

A mathematical model has been developed and solved for predicting the response of a thick thermoelastic axisymmetric solid plate subjected to sudden lateral mechanical and thermal loads. The governing equations of motion and heat conduction have been solved by using Laplace and Fourier transform methods to predict the response of the plate in the physical time domain. A modified Bessel function solution with complex argument is directly used. The model is also formulated and solved with the help of the finite element method (FEM). The results for radial and axial displacements and temperature change have been computed numerically and illustrated graphically for different theories of generalized thermoelasticity. The comparison of exact analysis with that of FEM is also discussed. Excellent agreement is found between the finite element analysis and analytical and classical solutions.

The propagation of magnetic-thermoelastic plane wave in an initially unstressed, homogeneous isotropic, conducting plate under uniform static magnetic field has been investigated. The generalized theory of thermoelasticity is employed, by assuming electrical behaviour as quasi-static and the mechanical behaviour as dynamic, to study the problem. The secular equations for both symmetric and skew-symmetric waves have been obtained. The magneto-elastic shear horizontal (SH) mode of wave propagation gets decoupled from rest of the motion and it is not influenced by thermal variations and thermal relaxation times. 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. Thin plate results are also deduced at the end. Dispersion curves are represented graphically for various modes of wave propagation in different theories of thermoelasticity. The amplitudes of displacement, perturbed magnetic field and temperature change are also obtained analytically and computed numerically. The result in case of elastokinetics, magneto-elasticity and coupled magneto-elasticity has also been deduced as special cases at appropriate stages of this work.

The propagation of circularly crested waves in a homogeneous, transversely isotropic, thermally conducting plate bordered with layers of inviscid liquid or half space of inviscid liquid on both sides is investigated in the context of conventional coupled thermoelasticity, Lord–Shulman and Green–Lindsay theories of thermoelasticity. Secular equations for circular homogeneous transversely isotropic plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for isotropic materials and uncoupled theories of thermoelasticity have been obtained as particular cases. The special cases such as short wavelength waves, thin plate waves and leaky Lamb waves of the secular equation are also deduced and discussed. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for transversely isotropic circular plate of cobalt material bordered with water. The dispersion curves for symmetric and antisymmetric wave modes, attenuation coefficient and amplitudes of displacement and temperature change in case of fundamental symmetric ( S 0 ) and skew symmetric ( A 0 ) modes are presented in order to illustrate and compare the theoretical results. The analytical and numerical results are found to be in close agreement.

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 temperatur...

We investigated the problem of thermoelastic wave reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity, namely, Lord-Shulman, Green-Lindsay, Green-Nagdhi, coupled thermoelasticity, and uncoupled thermoelasticity. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave incidence cases. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for aluminum-epoxy composite material in case of incident P- and SV-waves from the stress-free and rigidly fixed thermally insulated boundaries. The results obtained are discussed and compared in various models of thermoelasticity.

Analysis for the propagation of thermoelastic waves in a homogeneous, transversely isotropic, thermally conducting plate bordered with layers of inviscid liquid or half space of inviscid liquid on both sides, is investigated in the context of coupled theory of thermoelasticity. Secular equations for homogeneous transversely isotropic plate in closed form and isolated mathematical conditions for symmetric and anti-symmetric wave modes in completely separate terms are derived. The results for isotropic materials and uncoupled theories of thermoelasticity have been obtained as particular cases. It is shown that the purely transverse motion (SH mode), which is not affected by thermal variations, gets decoupled from rest of the motion of wave propagation and occurs along an in-plane axis of symmetry. The special cases, such as short wavelength waves and thin plate waves of the secular equations are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. The amplitudes of displacement components and temperature change have also been computed and studied. Finally, the numerical solution is carried out for transversely isotropic plate of zinc material bordered with water. The dispersion curves for symmetric and anti-symmetric wave modes, attenuation coefficient and amplitudes of displacement and temperature change in case of fundamental symmetric (S0) and skew symmetric (A0) modes are presented in order to illustrate and compare the theoretical results. The theory and numerical computations are found to be in close agreement.

The propagation of thermoelastic waves in a homogeneous isotropic, thermally conducting plate bordered with layers of inviscid liquid or half-space of inviscid liquid on both sides is investigated in the context of coupled thermoelasticity. Secular equations for the plate in closed form and isolated mathematical conditions for symmetric and antisymmetric wave modes in completely separate terms are derived. The results for coupled and uncoupled theories of thermoelasticity have been obtained as particular cases. The different regions of secular equations are obtained; and special cases, such as Lame modes, thin plate waves, and short wavelength waves, of the secular equations are also discussed. The secular equations for leaky Lamb waves are also obtained and deduced. Finally, the numerical solution is carried out for an aluminum-epoxy composite material plate bordered with water. The dispersion curves for symmetric and antisymmetric wave modes are presented in order to illustrate and compare the theoretic...

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 Lame modes are also obtained and discussed for different regions. The results for coupled and uncoupled ...

In this article, based on three-dimensional thermoelasticity, an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel is presented in the context of L ord-Shulman (L S), Green-L indsay (GL), and Green-Nagdhi (GN) theories of thermoelasticity. Three displacement potential functions are introduced so that the equations of motion and heat conduction are uncoupled and simplified. It is noticed that the purely transverse mode is independent of temperature change and rest of the motion. The equations for free vibration problems are further reduced to four second-order ordinary differential equations after expanding the potential and temperature functions with an orthogonal series. A modified Bessel function solution with complex arguments is then directly used for complex eigenvalues. Numerical examples are presented to clarify the developed method and compare the results to the existing one.

The disturbance due to mechanical point loads and thermal sources acting on the boundary of a homogeneous isotropic thermoelastic half-space has been investigated upon applying the Laplace and Hankel transforms in the context of generalized theories of thermoelasticity. The integral transforms have been inverted using a numerical technique to obtain the displacements, temperature, and stresses in the physical domain. The numerical technique expresses the integrand as a Fourier series representation with respect to the Laplace transform parameter and evaluates the inverse Hankel transform integral via Romberg integration with an adaptive stepsize after using the results from successive refinements of the extended trapezoidal rule followed by extrapolating the results to the limit when the stepsize tends to zero. The results for various physical quantities are computed and presented graphically. A comparison of the results for different generalized theories of thermoelasticity are also presented.

The disturbance due to a time-harmonic normal point load and thermal source in a homogeneous isotropic thermoelastic, half-space is investigated by applying the Hankel transform technique in the context of generalized theories of thermoelasticity. The inverse transform integrals are evaluated using Romberg integration with adaptive stepwise after using the results from successive refinements of the extended trapezoidal rule followed by extrapolation of the results to the limit when the step-size tends to zero. The displacement, temperature, and stresses so obtained in the physical domain are computed numerically and presented graphically in Figures 1-12 in different situations for Aluminium-epoxy composite material. A comparison of the results for different theories of generalized thermoelasticity is also presented.

The paper concentrates on the study of reflection and transmission characteristics of waves at the interface of a thermoelastic-diffusive solid half-space underlying an inviscid liquid. The analytic expressions for amplitude ratios, reflection and transmission coefficients, in terms of incident angles and material parameters have been obtained for quasi-longitudinal (qP) and quasi-transverse (qSV) wave incidence. The normal and grazing incidence cases have also been derived and discussed. The total reflection phenomenon has also been discussed. The energy law has been shown to be obeyed by the incidence, reflected and transmitted waves by deriving energy equation and its simulation. The numerical computations of reflection and transmission coefficients have been carried out for copper material half-space in contact with water at the interface by using MATLAB software. The computer simulated results have been presented graphically in order to bring out clear comparison of various situations.

This article is aimed at investigating the plane strain problems in generalized theory of thermoelasticity in a homogeneous, transversely isotropic medium by employing an eigenvalue approach after applying the technique of Laplace and Fourier transforms. An example of a half-space having a step input of temperature has been presented in order to illustrate the application of the approach. The results for coupled thermoelasticity and in the case of homogeneous isotropic medium have also been deduced as particular cases. The results obtained can be used for a broad class of problems in generalized thermoelasticity. The integral transforms have been inverted numerically to obtain the displacement, temperature, and stress fields in the physical domain. The results for these quantities are given and illustrated graphically.

The state space approach to generalized thermoelasticity is reformulated, and it is established that the solutions to the generalized thermoelastic fields can be formed by an entirely different approach as was illustrated by Sosa and Bahar for coupled thermoelastic problems. The article is concemed with a one-dimensional description of a semi-infinite body subjected to two types of boundary conditions; namely: (i) a step input of temperature and zero stress and (ii) a step input of stress and zero temperature. The various results obtained are found to be discontinuous for certain values of time in both the Lord and Shulman and the Green and Lindsay theories of thermoelasticity, and most of the jumps are shown to decay exponentially with time. The results for conventional coupled theory of thermoelasticity are obtained as a particular case of the generalized theory.

In this article a two-dimensional axisymmetric problem in a homogeneous transversely isotropic medium has been studied by employing the eigenvalue approach after applying the technique of Laplace and Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The results for coupled thermoelasticity and in the case of a homogeneous isotropic medium have also been deduced. The results obtained can be used for a broad class of problems in generalized thermoelasticity. The integral transforms have been inverted by using a, numerical technique to obtain the displacements, temperature, and stresses in the physical domain. The results for these quantities are given and illustrated graphically.

In this paper the general axisymmetric and plane strain problems in generalized theories of thermoelasticity have been investigated by employing the eigenvalue approach after applying the Laplace and the Hankel transforms technique. Examples of an infinite space and a half space have been presented in order to illustrate the application of the approach. The results for the coupled thermoelasticity can be obtained as particular cases of the obtained results by setting thermal relaxation times equal to zero. The obtained results can be used for a broad class of problems in generalized thermoelasticity.

The distribution of displacement, temperature, and stress in a homogeneous, isotropic, thermally conducting, infinitely extended, stretched elastic plate resulting from a flat-nosed, cylindrical projectile have been investigated in the context of the Lord-Shulman theory of thermoelasticity. The Laplace transform technique is used to obtain the solutions. Because the second-sound effects are of short duration, the discussion is confined to small time approximations. The displacement is found to be continuous, but temperature and stress are found to be discontinuous. The long time solutions are also discussed. The jumps have been computed numerically and are represented graphically for carbon-steel material.

The present paper deals with the investigations of the distribution of deformation, temperature, stresses and magnetic field in a homogeneous isotropic, thermally and electrically conducting, uniformly rotating elastic half-space, in contact with vacuum, due to (i) normal load and (ii) impulsive load, at the plane boundary, in the context of generalised theory of thermoelasticity. The Laplace transform on time has been used to obtain the solutions. Because ‘second sound’ effects are short-lived, so small time approximations have been considered. The standard results of the previous investigations have also been deduced as particular cases.