Surface waves in piezothermoelastic transversely isotropic layer lying over piezothermoelastic transversely isotropic ha
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O R I G I NA L PA P E R
Siddhartha Biswas
Surface waves in piezothermoelastic transversely isotropic layer lying over piezothermoelastic transversely isotropic half-space
Received: 28 July 2020 / Revised: 15 September 2020 / Accepted: 23 September 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In this article, the propagation of Rayleigh surface waves in a piezothermoelastic transversely isotropic layer lying over a piezothermoelastic transversely isotropic half-space is investigated in the context of the Green–Naghdi model type III of hyperbolic thermoelasticity. The secular equation of Rayleigh surface waves is derived, and different cases are discussed. Phase velocity, attenuation coefficient and specific loss of surface waves are computed and presented graphically with respect to frequency, and a comparison of different wave characteristics for classical and generalized thermoelastic models is presented in the figures.
1 Introduction The paradox of infinite speed of heat propagation is inherent in classical coupled thermoelasticity [1]. Generalized thermoelasticity was developed to remove this physical absurdity. Lord and Shulman [2] first modified the classical coupled thermoelasticity by introducing a thermal relaxation time, and this model is known as LS model. Later, Green and Lindsay [3] developed a more general theory of thermoelasticity by introducing two thermal relaxation times, and this model is known as GL model. Green and Naghdi [4–6] developed three models for generalized thermoelasticity which are known as GN model type I, II and III. The GN-II model is known as thermoelasticity without energy dissipation, and the GN-III model is known as thermoelasticity with energy dissipation. Detailed information regarding these models is available in [7,8]. Piezoelectric materials have been integrated with structural systems to form a class of ‘smart materials’. The piezoelectric materials are capable of altering the structure’s response through sensing, actuation and control. Piezoelectricity literally means pressure electricity and it has many applications. This phenomenon of piezoelectricity was first discovered by Curie and Curie [9]. The development of quartz transducers to generate and detect under-water acoustic waves has been successfully used for submarine detection. One of the most important applications of piezoelectricity was radio communications, which was finally put into use in the form of the first quartz crystal controlled transmitter. The thermo-piezoelectricity theory was first proposed by Mindlin [10], and the governing equations of thermo-piezoelectric plate were also derived by Mindlin [11]. The effect of rotation on wave characteristics in piezoelectric crystals has been discussed by various authors such as Gates [12] and Soderkvist [13]. According to Wren and Burdess [14] and Clarke and Burdess [15], the surface acoustic waves (SAWs) in elastic solids are greatly affected by rotation, and the speeds of disturbed waves are dependent upon rotation rate. F
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