Waves in thermoelastic solid half‐space containing voids with liquid loadings

Abstract

The influence of the voids in the propagation of time‐harmonic plane waves in a semi‐infinite homogeneous isotropic thermoelastic medium in contact with inviscid liquid half‐space has been explored under the Lord‐Shulman theory of thermoelasticity. The incompressible and non‐viscous liquid is taken in the upper half‐space and the effect of gravity on the whole system is assumed to be negligible. The mathematical model is developed and the exact expressions for the considered variables are obtained by using the normal mode analysis method. The compact secular equation for the considered model is derived for thermally insulated and isothermal cases respectively. There exist four waves in the generalized thermoelastic porous solid half‐space and one wave exists in the liquid half‐space. In the solid half‐space, one is a transverse wave and the remaining three is the set of coupled dilatational waves. The coupling among these waves is because of the presence of voids and thermal effects, also the amplitude of oscillation of these waves decreases with time. The transverse wave in the solid half‐space is undamped in time and remains independent of the effects of voids and heat. The particle's motion is deduced for Rayleigh wave propagation and found to be elliptical in solid half‐space and circular in liquid half‐space. Also, the plane of particle motion is tilted due to the presence of void parameters in the medium. Magnesium crystal has been chosen for the numerical computation and the discussion of various graphs depicting the profiles are presented in the last section.

Impact of memory-dependent heat transfer on Rayleigh waves propagation in nonlocal piezo-thermo-elastic medium with voids

“…However, this research advances significantly by emphasizing the pivotal role of voids in this context. Inspiration is drawn from previous studies (Singh, 2007; Sharma and Kaur, 2010; Iovane and Nasedkin, 2010b; Pathania and Joshi, 2021) examining voids in various materials and enabling the extrapolation and definition of void parameters, as summarized in Table 1. This approach deepens the understanding of the paramount influence of voids in the realm of Rayleigh wave propagation.…”

Generalized Plane Waves in a Rotating Thermoelastic Double Porous Solid

“…The phase velocity of the waves is complex in nature because the characteristics of roots 2 j m are also complex in nature as investigated by [26,27,30]. After obtaining the complex roots…”

“…Reflection of plane waves from the free surface of a rotating orthotropic magneto-thermoelastic solid half-space with diffusion, fractional-order initially stressed, was studied by Yadav [19, 20, 21, 22, 23, and 24]. Barak and Dhankhar [25] evaluated the effect of inclined load on a functionally graded fiber-reinforced thermoelastic medium with temperature-dependent properties, and the effect of Lamb-type waves in a porothermoelastic plate immersed in the inviscid fluid was analyzed by Pathania and co-researchers [26,27]. Kumari et al [28,29] studied the distinctive characteristics of reflection coefficients and energy sharing at both open-pore and sealed-pore border surfaces and measured the horizontal and vertical motion at the surface of partially saturated soils.…”

“…j Q , and get modified due to the volume fraction of type-I and type-II voids as well as thermal variations and rotation effect. The specific loss ( SL ) and penetration depth ( PD ) have been obtained by Pathania and Joshi[27] and Sharma et al[30] as follows:* * * Im ( ) Re ( )…”

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

“…Linh et al [16] investigated the propagation of Lamb waves in an orthotropic elastic sandwich plate and obtained explicit dispersion equations. Pathania and Joshi [17] investigated the surface waves in a half-space of a poro-thermoelastic solid coupled with a half-space of the inviscid liquid and derived the secular equation in the cases of thermally insulated and isothermal boundaries.…”