Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non-linear micropolar medium

Ерофеев, В. И.; Leontieva, A. V.; Malkhanov, Alexey O.

doi:10.1002/zamm.201600146

Cited by 5 publications

(4 citation statements)

References 1 publication

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“…The work continues the studies of wave processes begun in [22][23][24][25], generalizing them with allowance for the micropolarity of the medium, and also continues the studies begun in [26], generalizing them with allowance for the electrical conductivity of a nonlinear micropolar continuum.…”

Section: Introductionmentioning

confidence: 82%

“…Further, in the strain tensor and the bending-torsion tensor, we will consider both linear and nonlinear terms in the rotation and displacement gradients (geometric nonlinearity) [26]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Further, in the strain tensor and the bending‐torsion tensor, we will consider both linear and nonlinear terms in the rotation and displacement gradients (geometric nonlinearity) [26]:

\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{\gamma }_{ji} = {u}_{i,j}\ + {u}_{i,j}{u}_{i,j} - {\epsilon }_{kji}{\varphi }_k,}\\[6pt] {{\kappa }_{ji} = {\varphi }_{i,j}\ + {\varphi }_{i,j}{\varphi }_{i,j}.} \end{array} \end{equation}

…”

Section: Mathematical Modelmentioning

confidence: 99%

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Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Ерофеев

Malkhanov

2023

Z Angew Math Mech

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A nonlinear model of an electrically conductive micropolar medium interacting with an external magnetic field is proposed. The deformable state of such a medium is described by two asymmetric tensors: tensor of deformations and bending‐torsion tensor. Both tensors consider both linear and nonlinear terms in rotation and displacement gradients (geometric nonlinearity). The components of the bending‐torsion tensor which have the same indices, describe torsional deformations, while the rest describe bending deformations. The stress state of the medium is described by two asymmetric tensors: stresses tensor and moment stresses tensor. It is assumed, as is customary in magnetoelasticity, that the action of an electromagnetic field on a strain field occurs through Lorentz forces. From the system of Maxwell's equations follow the equations for electric and magnetic induction, which together with electromagnetic equations of state, should be added to the group of equations which describe the dynamics of a micropolar medium. In the frames of the proposed model, a one‐dimensional nonlinear magnetoelastic shear‐rotation wave is considered. In the equations of dynamics, a nonlinear term is considered. This term makes the most significant contribution to wave processes. It is shown that two factors will influence the wave propagation: dispersion and nonlinearity. Nonlinearity leads to the emergence of new harmonics in the wave, which contributes to the appearance of sharp drops in the moving wave profile. Dispersion, on the contrary, smoothed out differences due to differences in phase velocities of harmonic component waves. The combined action of these factors can lead to the formation of stationary waves that propagate at a constant speed without changing shape. Only those cases where a constant component is absent in the deformation wave are physically realizable. Stationary waves can be either periodic or aperiodic. The latter are spatially localized waves—solitons. It is shown that the behavior of “subsonic” and “supersonic” solitons will be qualitatively different.

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Section: Introductionmentioning

confidence: 82%

“…Further, in the strain tensor and the bending-torsion tensor, we will consider both linear and nonlinear terms in the rotation and displacement gradients (geometric nonlinearity) [26]:…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Further, in the strain tensor and the bending‐torsion tensor, we will consider both linear and nonlinear terms in the rotation and displacement gradients (geometric nonlinearity) [26]:

\begin{equation} \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{\gamma }_{ji} = {u}_{i,j}\ + {u}_{i,j}{u}_{i,j} - {\epsilon }_{kji}{\varphi }_k,}\\[6pt] {{\kappa }_{ji} = {\varphi }_{i,j}\ + {\varphi }_{i,j}{\varphi }_{i,j}.} \end{array} \end{equation}

…”

Section: Mathematical Modelmentioning

confidence: 99%

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Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Ерофеев

Malkhanov

2023

Z Angew Math Mech

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“…Said et al (2017) studied two-temperature rotation in micropolar thermoelastic medium under the influence of magnetic field. Erofeev et al (2017) studied the longitudinal thermoelastic waves and the waves of the rotation type in the non-linear micropolar medium.…”

Section: Introductionmentioning

confidence: 99%

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

Chawla

Ahuja

Rani

2017

MMMS

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Purpose The purpose of this paper is to study the fundamental solution in transversely isotropic micropolar thermoelastic media. With this objective, the two-dimensional general solution in transversely isotropic thermoelastic media is derived. Design/methodology/approach On the basis of the general solution, the fundamental solution for a steady point heat source on the surface of a semi-infinite transversely isotropic micropolar thermoelastic material is constructed by six newly introduced harmonic functions. Findings The components of displacement, stress, temperature distribution and couple stress are expressed in terms of elementary functions. From the present investigation, a special case of interest is also deduced and compared with the previous results obtained. Practical implications Fundamental solutions can be used to construct many analytical solutions of practical problems when boundary conditions are imposed. They are essential in the boundary element method as well as the study of cracks, defects and inclusions. Originality/value Fundamental solutions for a steady point heat source acting on the surface of a micropolar thermoelastic material is obtained by seven newly introduced harmonic functions. From the present investigation, some special cases of interest are also deduced.

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Linear Reduced Elastic Isotropic Cosserat Medium Subjected to the External Follower Viscoelastic Torque as a Smart Acoustic Metamaterial

Grekova,

Isaeva

2023

Advanced Structured Materials

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Stationary longitudinal thermoelastic waves and the waves of the rotation type in the non-linear micropolar medium

Cited by 5 publications

References 1 publication

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Spatially localized nonlinear magnetoelastic waves in an electrically conductive micropolar medium

Fundamental solution for a two-dimensional problem in transversely isotropic micropolar thermoelastic media

Linear Reduced Elastic Isotropic Cosserat Medium Subjected to the External Follower Viscoelastic Torque as a Smart Acoustic Metamaterial

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