Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space
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O R I G I NA L PA P E R
Siddhartha Biswas
Rayleigh waves in a nonlocal thermoelastic layer lying over a nonlocal thermoelastic half-space
Received: 17 April 2020 / Revised: 29 May 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract The paper deals with Rayleigh wave propagation in a nonlocal thermoelastic layer, and the layer is lying over a nonlocal thermoelastic half-space. The problem is treated in the context of Eringen’s nonlocal thermoelasticity and Green–Naghdi model type III of hyperbolic thermoelasticity. The frequency equation of Rayleigh waves is derived, and different cases are also discussed. The effect of the nonlocal parameter on phase velocity, attenuation coefficient, specific loss, and penetration depth is presented graphically.
1 Introduction The theory of nonlocal elasticity has attracted the attention of many authors because of its early success in solving an old problem in fracture mechanics. The nonlocal elasticity solution of Eringen [1,2] showed that the stress at the tip of a crack is finite; it rises to a maximum and then diminishes with the distance from the crack tip. Eringen [3,4] found the nonlocal solution of the discrete dislocation problem. Nonlocal field theories contain very interesting physics, in fact, all physics, excluding quantum effects and elementary particle physics. This can be extended further to include the nonlocal mixture theory, diffusion, and other allied phenomena. Some nonclassical thermoelasticity theories have been developed depending on the strategies to incorporate additional atomistic features based on Eringen’s nonlocal elasticity theory [5] which is now well established. In the local elasticity model, Eringen [5] assumed that the stress field at a particular point in an elastic continuum not only depends on the strain field but also on strains at all other points of the body. Altan [6] studied the uniqueness in the linear theory of nonlocal elasticity. The nonlocal elasticity models characterized by the presence of nonlocality residuals of fields have been proposed by Eringen and Edelen [7]. Eringen extended the concept of nonlocality to various other fields in his works cited in [8–10]. Nonlocal elasticity theories are now well established and are being applied to the problems of wave propagation in elastic and thermoelastic solids. Pramanik and Biswas [11] investigated the propagation of Rayleigh surface waves in nonlocal thermoelastic solids. Biswas [12] considered the propagation of Rayleigh surface waves in a porous nonlocal thermoelastic orthotropic medium. Khurana and Tomar [13] studied wave propagation in a nonlocal microstretch solid. Jun et al. [14] discussed nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity. Khurana and Tomar [15] investigated Rayleigh-type waves in a nonlocal micropolar solid half-space. The generalized thermoelasticity theories have been developed with the aim of removing the paradox of infinite speed of heat propagation inherent in the classical coupled dynamical t
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