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Magnetoelastic vibrations and stability of magnetically active plates and shells

Record Type:	Electronic resources : Monograph/item
Title/Author:	Magnetoelastic vibrations and stability of magnetically active plates and shellsby Gevorg Y. Baghdasaryan, Marine A. Mikilyan.
Author:	Baghdasaryan, Gevorg Y.
other author:	Mikilyan, Marine A.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xiii, 273 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	MagnetostrictionMathematical models.
Online resource:	https://doi.org/10.1007/978-3-031-60307-5
ISBN:	9783031603075$q(electronic bk.)

Magnetoelastic vibrations and stability of magnetically active plates and shells
Baghdasaryan, Gevorg Y.

Magnetoelastic vibrations and stability of magnetically active plates and shells[electronic resource] /by Gevorg Y. Baghdasaryan, Marine A. Mikilyan. - Cham :Springer Nature Switzerland :2024. - xiii, 273 p. :ill., digital ;24 cm.

Basic equations and relations of magnetoelasticity of magnetically active deformable bodies -- Vibrations and stability of soft ferromagnetic plates in magnetic field -- Effects of magnetoelastic interactions in soft magnetic cylindrical shells -- Interaction of superconducting cylindrical shell with magnetic fields -- Issues of magnetoelastic interactions in spherical shells -- Effects of magnetoelastic interactions in magnetostrictive rectangular plates -- Vibrations and stability of magnetostrictive rectangular plates in a magnetic field -- Aeromagnetic-elastic interactions in dielectrical plate.

This book introduces the reader to methods of mathematical modeling and solving non-stationary (dynamic) problems of the theory of magnetoelasticity, as well as to give an idea of the wealth of physical effects caused by the interaction of electromagnetic and mechanical phenomena in magnetically active elastic thin bodies. The studies are mainly limited to a model of isotropic body under the assumption of small deformations. In the first chapter of the book, based on the basic connected nonlinear equations and relations of mechanics and quasi-static electrodynamics of continuum media, a system of equations of magnetoelasticity, surface conditions, and governing equations describing the behavior of disturbances in a magnetoactive medium interacting with an external magnetic field is obtained. On this basis, in Chapters 2 and 3, using the main equations and relations of magnetoelastic vibrations and stability of magnetically soft, thin plates and shells are obtained. By solving specific applied problems, a number of qualitative and quantitative results were identified, caused by the interaction of mechanical and magnetic phenomena in ferromagnetic thin bodies. An approximate formula is obtained to determine magnetohydrodynamic pressure on the oscillating surfaces of plate flowing by supersonic flow of perfectly conducting gas in the presence of magnetic field. This formula is the generalization of well-known formula obtained on the basis of the classical piston theory of gas dynamics in the case of magneto-gas-dynamic flow. On this basis, it became possible to solve complex problems of zero magnetoelasticity. In the 4th and 5th chapters magnetoelastic processes in superconducting thin shells located in stationary and non-stationary magnetic fields are studied. Two-dimensional equations and corresponding conditions are obtained, which characterize vibrations and stability of superconducting cylindrical and spherical shells under the influence of the given magnetic field. By solving specific problems, the possibility of loss of both static and dynamic stability of thin superconducting bodies under the influence of external magnetic field has been established. The sixth chapter is devoted to mathematical modeling and investigation of issues of dynamics of magnetostrictive plates in magnetic fields (stationary and non-stationary) of several orientations. To study the processes of magnetoelastic interaction in the plate under consideration with complex physical properties of its material, the main postulates of the classical theories and methods were used. The influence of plate in-homogeneity on the processes under consideration was also studied.

ISBN: 9783031603075$q(electronic bk.)

Standard No.: 10.1007/978-3-031-60307-5doiSubjects--Topical Terms:

969797
Magnetostriction
--Mathematical models.

LC Class. No.: QC754.2.M36 / B34 2024

Dewey Class. No.: 538.3

Magnetoelastic vibrations and stability of magnetically active plates and shells
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505 0 $a Basic equations and relations of magnetoelasticity of magnetically active deformable bodies -- Vibrations and stability of soft ferromagnetic plates in magnetic field -- Effects of magnetoelastic interactions in soft magnetic cylindrical shells -- Interaction of superconducting cylindrical shell with magnetic fields -- Issues of magnetoelastic interactions in spherical shells -- Effects of magnetoelastic interactions in magnetostrictive rectangular plates -- Vibrations and stability of magnetostrictive rectangular plates in a magnetic field -- Aeromagnetic-elastic interactions in dielectrical plate.
520 $a This book introduces the reader to methods of mathematical modeling and solving non-stationary (dynamic) problems of the theory of magnetoelasticity, as well as to give an idea of the wealth of physical effects caused by the interaction of electromagnetic and mechanical phenomena in magnetically active elastic thin bodies. The studies are mainly limited to a model of isotropic body under the assumption of small deformations. In the first chapter of the book, based on the basic connected nonlinear equations and relations of mechanics and quasi-static electrodynamics of continuum media, a system of equations of magnetoelasticity, surface conditions, and governing equations describing the behavior of disturbances in a magnetoactive medium interacting with an external magnetic field is obtained. On this basis, in Chapters 2 and 3, using the main equations and relations of magnetoelastic vibrations and stability of magnetically soft, thin plates and shells are obtained. By solving specific applied problems, a number of qualitative and quantitative results were identified, caused by the interaction of mechanical and magnetic phenomena in ferromagnetic thin bodies. An approximate formula is obtained to determine magnetohydrodynamic pressure on the oscillating surfaces of plate flowing by supersonic flow of perfectly conducting gas in the presence of magnetic field. This formula is the generalization of well-known formula obtained on the basis of the classical piston theory of gas dynamics in the case of magneto-gas-dynamic flow. On this basis, it became possible to solve complex problems of zero magnetoelasticity. In the 4th and 5th chapters magnetoelastic processes in superconducting thin shells located in stationary and non-stationary magnetic fields are studied. Two-dimensional equations and corresponding conditions are obtained, which characterize vibrations and stability of superconducting cylindrical and spherical shells under the influence of the given magnetic field. By solving specific problems, the possibility of loss of both static and dynamic stability of thin superconducting bodies under the influence of external magnetic field has been established. The sixth chapter is devoted to mathematical modeling and investigation of issues of dynamics of magnetostrictive plates in magnetic fields (stationary and non-stationary) of several orientations. To study the processes of magnetoelastic interaction in the plate under consideration with complex physical properties of its material, the main postulates of the classical theories and methods were used. The influence of plate in-homogeneity on the processes under consideration was also studied.
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