Chapter 10
The Effect of Preheating
on the Thermoelastic Structurally
Inhomogeneous Medium Spectral
Properties in the Presence of an Initial
Strain
Galina Yu. Levi, Leonid Igumnov, and Mikhail O. Levi
Abstract The boundary problem of a prestressed thermoelastic layered half-space
oscillations subjected to the action of a mechanical or thermal load is considered.
Initial stresses are induced in the body by stretching or compression and by the action
of temperature. The two-dimensional Green’s function of the medium is constructed.
We made the analysis of its real poles behavior, and their distribution is presented
graphically. The effect of preheating, pinching, and initial deformation of the first
mode phase velocity is studied.
Keywords Thermoelasticity · Half-space · Initial strain · Preheating · Green’s
function · Phase velocity
10.1 Introduction
Thermoelasticity studies the interaction of deformation and thermal fields. It deals
with a dynamic system, the interaction of which with the environment is limited to
mechanical work, external forces, and heat transfer. It also includes thermal conductivity, stress, and deformation due to heat flow. In addition, the change in body
temperature is caused not only by external and internal sources of heat, but also by
the deformation process itself. For this reason, thermoelasticity should be considered
as a multifield discipline governed by the interaction of the temperature deformation
field. This allows one to determine the stresses created by the temperature field and
G. Yu. Levi · L. Igumnov (B)
Research Institute for Mechanics of Lobachevsky State University of Nizhny Novgorod, Gagarin
ave., 23, 603950 Nizhny Novgorod, Russia
e-mail: igumnov@mech.unn.ru
G. Yu. Levi · M. O. Levi
Southern Scientific Center of Russian Academy of Sciences, st. Chehova, 41, 344006
Rostov-on-Don, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_10
139
The Effect of Preheating
on the Thermoelastic Structurally
Inhomogeneous Medium Spectral
Properties in the Presence of an Initial
Strain
Galina Yu. Levi, Leonid Igumnov, and Mikhail O. Levi
Abstract The boundary problem of a prestressed thermoelastic layered half-space
oscillations subjected to the action of a mechanical or thermal load is considered.
Initial stresses are induced in the body by stretching or compression and by the action
of temperature. The two-dimensional Green’s function of the medium is constructed.
We made the analysis of its real poles behavior, and their distribution is presented
graphically. The effect of preheating, pinching, and initial deformation of the first
mode phase velocity is studied.
Keywords Thermoelasticity · Half-space · Initial strain · Preheating · Green’s
function · Phase velocity
10.1 Introduction
Thermoelasticity studies the interaction of deformation and thermal fields. It deals
with a dynamic system, the interaction of which with the environment is limited to
mechanical work, external forces, and heat transfer. It also includes thermal conductivity, stress, and deformation due to heat flow. In addition, the change in body
temperature is caused not only by external and internal sources of heat, but also by
the deformation process itself. For this reason, thermoelasticity should be considered
as a multifield discipline governed by the interaction of the temperature deformation
field. This allows one to determine the stresses created by the temperature field and
G. Yu. Levi · L. Igumnov (B)
Research Institute for Mechanics of Lobachevsky State University of Nizhny Novgorod, Gagarin
ave., 23, 603950 Nizhny Novgorod, Russia
e-mail: igumnov@mech.unn.ru
G. Yu. Levi · M. O. Levi
Southern Scientific Center of Russian Academy of Sciences, st. Chehova, 41, 344006
Rostov-on-Don, Russia
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_10
139