Investigation of harmonic plane waves: detailed analysis of recent thermoplastic model with single delay term (original) (raw)

Analysis of the Effects of Phase-lags on Propagation of Harmonic Plane Waves in Thermoelastic Media

Computational Methods in Science and Technology, 2010

The present paper attempts to investigate the propagation of harmonic plane waves of assigned frequency by employing the thermoelasticity theory with three phase-lags, recently proposed by Roychoudhuri (2007). The solutions of dispersion relation for the longitudinal plane waves are determined analytically and asymptotic expansions of several characterizations of the wave fields-phase velocity, specific loss and penetration depth of the dilatational waves are obtained for both the high frequency and low frequency values. Computational work for numerical values of the above quantities is also carried out with the help of Mathematica. A detailed analysis of the effects of phase-lags on the plane wave is presented by contrasting the theoretical as well as numerical results of the present work with the corresponding results of the theory of thermoelasticity type III (Green and Naghdi, 1993) as reported earlier.

Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags

International Journal of Engineering Science, 2010

The present paper deals with the investigation of the propagation of harmonic plane waves with assigned frequency by employing the thermoelasticity theory with dual-phase-lags (Tzou [7], Chandrasekharaiah [10]). The exact dispersion relation solutions for the plane wave are obtained analytically and asymptotic expressions of several characterizations of the wave fields, such as phase velocity, specific loss, penetration depth and amplitude ratios are obtained for both the high frequency as well as low frequency values. In order to illustrate the analytical results, the computational tool Mathematica is used to find the numerical values of different wave fields at intermediate values of frequency and results are depicted in different figures. A detailed analysis of the effects of phase-lags on plane wave is presented on the basis of analytical and numerical results and significant points are highlighted.

Effects of Thermal Relaxation Time on Plane Wave Propagation Under Two-Temperature Thermoelasticity

International Journal of Engineering Science, 2010

The present paper is concerned with an in-depth investigation of the propagation of harmonic plane waves in elastic media in the context of the linear theory of two-temperature generalized thermoelasticity. The exact dispersion relation solutions for the longitudinal plane wave are determined analytically. Asymptotic expansions of several characterizations of the wave field, like phase velocity, specific loss and penetration depth of the dilatational waves, are obtained for both the high frequency as well as low frequency values. The effects of thermal relaxation parameter on the plane wave is analyzed in details by comparing the theoretical as well as numerical results of the present work with the corresponding results in the context of classical two-temperature thermoelasticity theory as reported earlier.

On the wave propagation in the time differential dual-phase-lag thermoelastic model

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2015

We study the propagation of plane time harmonic waves in the infinite space filled by a time differential dual-phase-lag thermoelastic material. There are six possible basic waves travelling with distinct speeds, out of which, two are shear waves, and the remaining four are dilatational waves. The shear waves are found to be uncoupled, undamped in time and travels independently with the speed that is unaffected by the thermal effects. All the other possible four dilatational waves are found to be coupled, damped in time and dispersive due to the presence of thermal properties of the material. In fact, there is a damped in time longitudinal quasi-elastic wave whose amplitude decreases exponentially to zero when the time is going to infinity. There is also a quasi-thermal mode, like the classical purely thermal disturbance, which is a standing wave decaying exponentially to zero when the time goes to infinity. Furthermore, there are two possible longitudinal quasi-thermal waves that a...

On the Wave Propagation in the Thermoelasticity Theory with Two Temperatures

Journal of Elasticity, 2020

This paper considers the thermoelastic theory with two temperatures that involves higher gradients of thermal and mechanical effects. The wave propagation question is addressed within the class of waves of assigned wavelength. Considering harmonic in time wave solutions, it is found that the transverse waves are undamped in time and nondispersive, and they are not altered by the thermal effects. Conversely, the longitudinal waves are dispersive and damped in time; the dispersion relation is established like a cubic equation and the effects of conductive temperature are explicitly presented. Rayleigh surface waves are also studied and an explicit secular equation is derived by using wave solutions damped in time. Illustrative examples are numerically analyzed and graphically depicted. The results achieved are meaningful because they are able to bring information about the propagation of waves with assigned length and, moreover, they are in agreement with the results regarding the wave speed of travelling discontinuities. Also the structure of the wave solutions provides information upon asymptotic stability.

Dispersion of Thermoelastic Waves in a Plate With and Without Energy Dissipation

2001

In this paper, the dispersion and energy dissipation of thermoelastic plane harmonic waves in a thin plate bounded by insulated traction-free surfaces is studied on the basis of three generalized theories of thermoelasticity. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained. Some limiting and particular cases of the frequency equations are then discussed. Results obtained in three theories of generalized thermoelasticity are compared. The results for the coupled thermoelasticity can be obtained as particular cases of the results by setting thermal relaxations times equal to zero. Numerical evaluations relating to the lower modes of the symmetric and antisymmetric waves are presented for an aluminum alloy plate.

On the propagation of thermoelastic waves in temperature rate-dependent materials

Journal of Elasticity, 1992

The one-dimensional propagation of thermoelastic waves in isotropic homogeneous half spaces within the theory of Green and Lindsay [1] is studied. Padr-extended ray methods are employed to obtain the desired information. Comparisons between the predictions of the Green and Lindsay theory and the theory of Lord and Shulman [2] are made. Our ray series solutions show that for discontinuous thermal disturbances the displacement according to the Green and Lindsay theory is also discontinuous. This violates the fundamental continuum hypothesis that matter is impenetrable. For a simple numerical example we show also that a compressive behaviour in the displacement may be associated with a tensile behaviour in the stress and vice versa. This prediction of the Green and Lindsay theory is also unrealistic from the physical point of view.

Wave propagation in temperature rate dependent thermoelasticity with two temperatures

The present investigation is concerned with two problems. (i) Reflection and transmission of thermoelastic waves between two thermoelastic half-spaces with two temperature at an imperfect interface; and (ii) Propagation of Rayleigh waves at the free surface of thermoelastic solid with two temperature. In problem (i) the amplitude ratios for reflection and transmission coefficients are obtained and deduced for normal force stiffness, transverse force stiffness, thermal contact conductance and perfect bonding. The numerical results obtained have been illustrated graphically to understand the behavior of amplitude ratios versus angle of incidence of longitudinal wave (P-wave), thermal wave (T-wave) and SV-wave. It is found that the amplitude ratios of various reflected and transmitted waves are affected by the stiffness and two temperature effects. In problem (ii) the phase velocity and attenuation coefficient are obtained and presented graphically to depict the effect of two temperatures. Some special cases of interest have been deduced from the two problems also.

On the propagation of elasto-thermodiffusive surface waves in heat-conducting materials

Journal of Sound and Vibration, 2008

The present paper deals with the study of the propagation of Rayleigh surface waves in homogeneous isotropic, thermodiffusive elastic half-space. After developing the formal solution of the model, the secular equations for stress free, thermally insulated or isothermal, and isoconcentrated boundary conditions of the half-space have been obtained. The secular equations have been solved by using irreducible Cardano's method with the help of DeMoivre's theorem in order to obtain phase velocity and attenuation coefficient of waves under consideration. The motion of the surface particles during the Rayleigh surface wave propagation is also discussed and found to be elliptical in general. The inclinations of wave normal with the major axis of the elliptical path of a typical particle have also been computed. Finally, the numerically simulated results regarding phase velocity, attenuation coefficient, specific loss and thermo-mechanical coupling factors of thermoelastic diffusive waves have been obtained and presented graphically. Some very interesting and useful characteristics of surface acoustic waves have been obtained, which may help in improving the fabrication quality of optical and electronic devices in addition to construction and design of materials such as semiconductors and composite structures. Therefore, this work finds applications in the geophysics and electronics industry. r diffusion is used to introduce ''dopants'' in controlled amounts into the semiconductor substance. In particular, diffusion is used to form the base and emitter in bipolar transistors, integrated resistors, and the source/drain regions in MOS transistors and dope polysilicon gates in MOS transistors. Thermal diffusion utilizes the transfer of heat across a thin liquid or gas to accomplish isotope separation. Today, thermal diffusion remains a practical process to separate isotopes of noble gases (e.g. xenon) and other light isotopes (e.g. carbon) for research purposes. In most of the applications, the concentration is calculated using what is known as Fick's law. This is a simple law that does not take into consideration the mutual interaction between the introduced substance and the medium into which it is introduced or the effect of the temperature on this interaction. However, there is a certain degree of coupling with temperature and thermal gradients as temperature speeds up the diffusion process. The thermoelastic diffusion in elastic solids is due to coupling of the fields of temperature, mass diffusion (MD) and that of strain in addition to heat and mass exchange with the environment. Angstrom [1] was the first to publish an experimental and theoretical study of diffusion waves. In this pioneering work, he calculated the thermal diffusivity of solids as measured by periodically heating a long bar and then detecting the alternating temperature field at a point in the bar some distance away from the heat source. Nowacki developed the theory of thermoelastic diffusion by using a coupled thermoelastic model. Dudzviak and Kowalski [6] and Olesiak and Pyryev [7], respectively, discussed the theory of thermo diffusion and coupled quasi-stationary problems of thermal diffusion for an elastic cylinder. They studied the influence of cross effects arising from the coupling of the fields of temperature, MD, and strain due to which the thermal excitation results in additional mass concentration and this generates additional fields of temperature.

On the propagation waves in the theory of thermoelasticity with microtemperatures

Mechanics Research Communications, 2016

The present paper studies the propagation of plane time harmonic waves in an infinite space filled by a thermoelastic material with microtemperatures. It is found that there are seven basic waves traveling with distinct speeds: (a) two transverse elastic waves uncoupled, undamped in time and traveling independently with the speed that is unaffected by the thermal effects; (b) two transverse thermal standing waves decaying exponentially to zero when time tends to infinity and they are unaffected by the elastic deformations; (c) three dilatational waves that are coupled due to the presence of thermal properties of the material. The set of dilatational waves consists of a quasi-elastic longitudinal wave and two quasithermal standing waves. The two transverse elastic waves are not subjected to the dispersion, while the other two transverse thermal standing waves and the dilatational waves present the dispersive character. Explicit expressions for all these seven waves are presented. The Rayleigh surface wave propagation problem is addressed and the secular equation is obtained in an explicit form. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.