140
G. Yu. Levi et al.
to calculate the temperature distribution as a result of the action of time-dependent
forces and heat sources.
The development of modern technologies causes a considerable interest in the
processes of excitation of mechanical vibrations due to the effect of laser radiation (Muratikov 1998). A fairly complete overview of the work in this direction
is given in (Achenbach 2003; Xu et al. 2008). In the majority of works, different
approaches are used for research, which allow efficiently analyzing various sides of
dynamic processes in thermoelastic. These are, first of all, the propagation features
of volume (Singh et al. 1985; Sharma et al. 1986; El-Maghraby 2008) and interface
(Kumar et al. 2013; Verma 2002) waves, Rayleigh waves (Stan Chirita, 2013), Lamb
(Al-Qahtani et al. 2004; Kumar et al. 2008) and cylindrical waves (Sharma 2001).
Questions of viscoelastic effects (Elhagary 2013; Levi et al. 2015), as well as the
presence of initial stresses (Singh 2010), occupy a special place in the problem of the
propagation of thermoelastic waves in semibounded bodies. In article (Sheydakov
2008), following the approach considered in the monograph (Lurie 1980), consecutive linearization of nonlinear equations of a thermoelastic medium was carried
out, and equations of motion and determining relationships of the dynamics of a
prestressed thermoelastic medium were constructed. The equations are constructed
in tensor form, admitting generalization to curve-linear coordinates. The issues of
thermoelastic bodies contact interaction are of considerable interest (Levi et al. 2019;
Belyankova et al. 1999; Belyankova et al. 2012; Levi et al. 2017; Belyankova et al.
2016). In (Belyankova et al. 1999; Belyankova et al. 2012), the problems of contact
interaction of a thermoelastic layer and half-space were investigated. The equations
of motion constructed in (Sheydakov 2008) and the defining relations, taking into
account the presence of initial stresses, preliminary heating, etc., are generalized to
prestressed thermoelectronic stresses.
In the present work, within the framework of the linearized theory of propagation
of coupled thermoelastic waves (Sheydakov 2008), the boundary problem of oscillation of a non-uniform half-space under the action of a thermal load given on the
surface of the medium is considered. The effect of preheating and initial strain on
layered thermoelastic half-space phase velocity is investigated.
10.2 Formulation of the Problem
We consider a structurally inhomogeneous half-space, which is a homogeneous thermoelastic layer rigidly coupled with a homogeneous thermoelastic half-space. The
body is subject to prestressing, which is set as deformation and thermal effects. A load
acts on a surface in a certain area, imposing mechanical stress or heat flux. Outside
this area, the surface is thermally insulated and free from mechanical stress. At the
boundary between the layer and the half-space, the conditions of rigid coupling and
thermal insulation are assumed.
G. Yu. Levi et al.
to calculate the temperature distribution as a result of the action of time-dependent
forces and heat sources.
The development of modern technologies causes a considerable interest in the
processes of excitation of mechanical vibrations due to the effect of laser radiation (Muratikov 1998). A fairly complete overview of the work in this direction
is given in (Achenbach 2003; Xu et al. 2008). In the majority of works, different
approaches are used for research, which allow efficiently analyzing various sides of
dynamic processes in thermoelastic. These are, first of all, the propagation features
of volume (Singh et al. 1985; Sharma et al. 1986; El-Maghraby 2008) and interface
(Kumar et al. 2013; Verma 2002) waves, Rayleigh waves (Stan Chirita, 2013), Lamb
(Al-Qahtani et al. 2004; Kumar et al. 2008) and cylindrical waves (Sharma 2001).
Questions of viscoelastic effects (Elhagary 2013; Levi et al. 2015), as well as the
presence of initial stresses (Singh 2010), occupy a special place in the problem of the
propagation of thermoelastic waves in semibounded bodies. In article (Sheydakov
2008), following the approach considered in the monograph (Lurie 1980), consecutive linearization of nonlinear equations of a thermoelastic medium was carried
out, and equations of motion and determining relationships of the dynamics of a
prestressed thermoelastic medium were constructed. The equations are constructed
in tensor form, admitting generalization to curve-linear coordinates. The issues of
thermoelastic bodies contact interaction are of considerable interest (Levi et al. 2019;
Belyankova et al. 1999; Belyankova et al. 2012; Levi et al. 2017; Belyankova et al.
2016). In (Belyankova et al. 1999; Belyankova et al. 2012), the problems of contact
interaction of a thermoelastic layer and half-space were investigated. The equations
of motion constructed in (Sheydakov 2008) and the defining relations, taking into
account the presence of initial stresses, preliminary heating, etc., are generalized to
prestressed thermoelectronic stresses.
In the present work, within the framework of the linearized theory of propagation
of coupled thermoelastic waves (Sheydakov 2008), the boundary problem of oscillation of a non-uniform half-space under the action of a thermal load given on the
surface of the medium is considered. The effect of preheating and initial strain on
layered thermoelastic half-space phase velocity is investigated.
10.2 Formulation of the Problem
We consider a structurally inhomogeneous half-space, which is a homogeneous thermoelastic layer rigidly coupled with a homogeneous thermoelastic half-space. The
body is subject to prestressing, which is set as deformation and thermal effects. A load
acts on a surface in a certain area, imposing mechanical stress or heat flux. Outside
this area, the surface is thermally insulated and free from mechanical stress. At the
boundary between the layer and the half-space, the conditions of rigid coupling and
thermal insulation are assumed.