18
A. M. Antonov et al.
The main laws of propagation of Rayleigh waves are as follows: the absence of
dispersion, i.e., wave speed does not depend on its frequency and is constant for
each material; this speed reaches 0.87–0.96 from the velocity of a volume shear
wave; the displacement vector has longitudinal and transverse components, while
the transverse component always exceeds the longitudinal one.
In recent years, Rayleigh waves of ultrasonic range have found wide application.
With their help, it is possible to monitor the state of the surface layer of the sample
(detection of surface and near-surface defects in samples of metal, glass, plastic, and
other materials—ultrasonic surface flaw detection). The influence of the properties
of the surface layer of the sample on the velocity and attenuation of Rayleigh waves
allows the latter to be used to determine the residual stresses of the surface metal
layer and the thermal and mechanical properties of the surface layer of the sample
(Klyuev 2004; Uglov et al. 2009).
Along with the model of the classical continuum, the models of generalized
continua are widely used in the mechanics of a deformable solid body (Maugin
and Metrikine 2010; Altenbach and Eremeyev 2013; Altenbach et al. 2011, 2013,
2016, 2018a, b, 2019; Bagdoev et al. 2016; Maugin 2017; dell’Isola et al. 2012,
2015, 2016a, b, c, 2018; Abali et al. 2017, 2019; Neff et al. 2014; Alibert et al. 2003;
Auffray et al. 2013; Sciarra et al. 2007; Rahali et al. 2015).
The appearence of the model of the generalized continua that belong, in particular,
to the gradient-elastic medium, dates back to the beginning of the twentieth century
and is associated with the names of Le Roux (Le Roux 1911, 1913) and Jaramillo
(Jaramillo 1929).
The famous Cosserat continuum model (Cosserat et al. 1909), when the dependence of the rotation vector on the displacement rotor (constrained rotation)
(Erofeyev 2003) is rigidly fixed, also reduces to the gradient-elastic medium model.
One of the great applications of generalized continuum theories is designing of
new artificial microstructured metamaterials (Barchiesi et al. 2019; Del Vescovo and
Giorgio 2014). An example of mechanical metamaterial is pantographic structure
(dell’Isola et al. 2016, 2019a, b; Placidi et al. 2016, 2017).
The Rayleigh surface waves in the framework of the gradient-elastic model have
not been practically studied. An exception is the work (Sabodash and Filippov 1971),
in which, on the basis of the studies performed, it is stated that the velocity of a surface
wave in a gradient-elastic medium can exceed the velocity of a bulk shear wave.
The paper studies the main laws of propagation of the Rayleigh waves along
the boundary of the gradient-elastic half-space, in particular, it verifies the assertion
contained in (Sabodash and Filippov 1971). The problem of the generation of a
surface wave by a source moving at superspeeds along the border of a gradientelastic half-space is considered. The dependence of the amplitude of the wave, the
Mach cone on the source load, and its velocity is determined.
A. M. Antonov et al.
The main laws of propagation of Rayleigh waves are as follows: the absence of
dispersion, i.e., wave speed does not depend on its frequency and is constant for
each material; this speed reaches 0.87–0.96 from the velocity of a volume shear
wave; the displacement vector has longitudinal and transverse components, while
the transverse component always exceeds the longitudinal one.
In recent years, Rayleigh waves of ultrasonic range have found wide application.
With their help, it is possible to monitor the state of the surface layer of the sample
(detection of surface and near-surface defects in samples of metal, glass, plastic, and
other materials—ultrasonic surface flaw detection). The influence of the properties
of the surface layer of the sample on the velocity and attenuation of Rayleigh waves
allows the latter to be used to determine the residual stresses of the surface metal
layer and the thermal and mechanical properties of the surface layer of the sample
(Klyuev 2004; Uglov et al. 2009).
Along with the model of the classical continuum, the models of generalized
continua are widely used in the mechanics of a deformable solid body (Maugin
and Metrikine 2010; Altenbach and Eremeyev 2013; Altenbach et al. 2011, 2013,
2016, 2018a, b, 2019; Bagdoev et al. 2016; Maugin 2017; dell’Isola et al. 2012,
2015, 2016a, b, c, 2018; Abali et al. 2017, 2019; Neff et al. 2014; Alibert et al. 2003;
Auffray et al. 2013; Sciarra et al. 2007; Rahali et al. 2015).
The appearence of the model of the generalized continua that belong, in particular,
to the gradient-elastic medium, dates back to the beginning of the twentieth century
and is associated with the names of Le Roux (Le Roux 1911, 1913) and Jaramillo
(Jaramillo 1929).
The famous Cosserat continuum model (Cosserat et al. 1909), when the dependence of the rotation vector on the displacement rotor (constrained rotation)
(Erofeyev 2003) is rigidly fixed, also reduces to the gradient-elastic medium model.
One of the great applications of generalized continuum theories is designing of
new artificial microstructured metamaterials (Barchiesi et al. 2019; Del Vescovo and
Giorgio 2014). An example of mechanical metamaterial is pantographic structure
(dell’Isola et al. 2016, 2019a, b; Placidi et al. 2016, 2017).
The Rayleigh surface waves in the framework of the gradient-elastic model have
not been practically studied. An exception is the work (Sabodash and Filippov 1971),
in which, on the basis of the studies performed, it is stated that the velocity of a surface
wave in a gradient-elastic medium can exceed the velocity of a bulk shear wave.
The paper studies the main laws of propagation of the Rayleigh waves along
the boundary of the gradient-elastic half-space, in particular, it verifies the assertion
contained in (Sabodash and Filippov 1971). The problem of the generation of a
surface wave by a source moving at superspeeds along the border of a gradientelastic half-space is considered. The dependence of the amplitude of the wave, the
Mach cone on the source load, and its velocity is determined.