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Magneto-thermo-piezo-elastic wave in an initially stressed rotating monoclinic crystal in a two-temperature theory

Yadav Anand Kumar

International Journal of Applied Mechanics and Engineering

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2023

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Vol. 28, no. 3

127--158

EN

This research problem is an investigation of wave propagation in a rotating initially stressed monoclinic piezoelectric thermo-elastic medium under with the effect of a magnetic field. A two-temperature generalized theory of thermo-elasticity in the context of Lord-Shulman’s theory is applied to study the waves under the magnetic field. The governing equations of a rotating initially stressed monoclinic piezoelectric thermo-elastic medium with a magnetic field are formulated. This research problem is solved analytically, for a two-dimensional model of the piezo-electric monoclinic solid, and concluded that there must be four piezo-thermoelastic waves, three coupled quasi waves (qP (quasi-P), qT (quasi-thermal), and qSV (quasi-SV)) and one piezoelectric potential (PE) wave propagating at different speeds. It is found that at least one of these waves is evanescent (an evanescent wave is a non-propagating wave that exists) and that there are therefore no more than three bulk waves. The speeds of different waves are calculated and the influence of the piezoelectric effect, two-temperature parameter, frequency, rotation, and magnetic field on phase velocity, attenuation coefficient, and specific loss is shown graphically. This model may be used in various fields, e.g. wireless communications, signal processing, and military defense equipment are all pertinent to this study.

2

Propagation of Harmonic Plane Waves in a Rotating Elastic Medium under Two-Temperature Thermoelasticity with Relaxation Parameter

Prasad R., Mukhopadhyay S.

Computational Methods in Science and Technology

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2012

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Vol. 18, No. 1

25-37

EN

The present work investigates the propagation of harmonic plane waves in an isotropic and homogeneous elastic medium that is rotating with uniform angular velocity by employing the two-temperature generalized thermoelasticity, recently introduced by Youssef (IMA Journal of Applied Mathematics, 71, 383-390, 2006). Dispersion relation solutions for longitudinal as well as transverse plane waves are obtained analytically. Asymptotic expressions of several important characterizations of the wave fields, such as phase velocity, specific loss, penetration depth, amplitude coefficient factor and phase shift of thermodynamic temperature are obtained for high frequency as well as low frequency values. A critical value of the two-temperature parameter for the low frequency case is obtained. Using Mathematica, numerical values of the wave fields at intermediate values of frequency and for various values of the twotemperature parameter are computed. A detailed analysis of the effects of rotation on the plane wave is presented on the basis of analytical and numerical results. An in-depth comparative analysis of our results with the corresponding results of the special cases of absence of rotation of the body and with the case of generalized thermoelasticity is also presented. The most significant points are highlighted.

3

Effect of rotation on surface wave propagation in a elastic layer lying over a thermodiffusive elastic half-space having imperfect boundary

Kumar R., Chawla V.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

37-55

EN

The present investigation deals with the propagation of surface waves at an imperfect boundary between an isotropic elastic layer of finite thickness and a homogenous isotropic thermodiffusive elastic half- space with rotation in the context of generalized theory of thermoelastic diffusion. Lord and Shulman (L-S) theory in which thermal and thermo-mechanical relaxation time is governed by time constant and diffusion relaxation time is governed by other different time constants is selected for the study. The secular equation for surface waves in a compact form is derivied after developing the mathematical model. The phase velocity and attenuation coefficient are obtained for stiffness and then deduced for normal stiffness, tangential stiffness and welded contact. The dispersion curves for these quantities are illustrated to depict the effect of stiffness and thermal relaxation times. The amplitudes of displacements, temperature and concentration are computed at the free plane boundary and depicted graphically. Specific loss of energy is obtained and presented graphically. The effects of rotation are shown for phase velocity, attenuation coefficient and amplitudes of displacements, temperature change and concentration. Some special cases of interest are also deduced and compared with known results.

4

Generalized thermoelastic plane harmonic waves in materials with voids

Sharma J. N., Kaur D.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 4

1019-1043

EN

The aim of the present paper is to give a detailed account of the plane harmonic generalized thermoelastic waves in solids containing vacuous voids based on the modified fourier law of heat conduction. The general characteristic equation being quartic suggests that there are four longitudinal waves, namely: quasi-elastic [...], quasi-thermal [...], volume fraction [...] and micro-thermal [...], in addition to transverse waves, which can propagate in such solids. The transverse waves get decoupled from the rest of the field quantities and hence remain unaffected due to temperature variation and porosity effects. These waves travel without attenuation and dispersion. The other generalized thermoelastic waves are significantly influenced by the interacting fields and hence suffer both attenuation and dispersion. The general complex characteristic equation has been solved by using descartes algorithm along with irreducible case of cardano's method with the help of demoivre's theorem in order to obtain phase speeds, attenuation coefficients and specific loss factor of energy dissipation. The propagation of waves in non-heat conducting solids has also been discussed. Finally, the numerical solution of the secular equation is carried out to compute phase velocities, attenuation coefficients and specific loss factors of thermoelastic waves which are presented graphically.