Abstract
This chapter is devoted to the study of propagation of magnetoelastic waves in isotropic and anisotropic electro-conductive media. The basic linearized equations, boundary conditions and relations of perfectly conducting media, describing magnetoelastic wave processes, are derived. Magnetoelastic plane waves in infinite media are investigated. The characteristic equation of bulk magnetoelastic waves is derived. The classification of fast and slow, as well as of quasi-longitudinal and quasi-transverse, magnetoelastic waves is given. It is shown in which cases, depending on the orientation of the external magnetic field, the medium is under plane-strain conditions. The condition of complete hyperbolicity, which ensures the possibility of propagation of magnetoelastic waves in any direction, is established. Investigation of the roots of the characteristic equation reveals the nature of propagation of fast and slow waves, depending on the physical and mechanical properties of the medium and the magnitude of the external magnetic field intensity. The changes in wave’s phase velocities depending on the direction of propagation characteristics of the elastic medium and magnetic field.
Keywords
- Magnetoelastic Waves
- Anisotropic Conductive Media
- Complete Hyperbolicity
- Basic Linearized Equations
- External Magnetic Field Intensity
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Sedov, L.I.: The mechanics of a continuous medium, vol.1,2, 492 p. Nauka, Moscow (1976)
Ambartsumyan, S.A., Baghdasaryan, G.Y.: Electrically conductive plates and shells in a magnetic field.M: Publishing House “Physics and Mathematics”, 288p (1996)
Baghdasaryan, G.Y.: Vibrations and stability of magnetoelastic systems, 440p. Publishing House. YSU, Yerevan (1999)
Guz, A.N., Mahort, F.G. Mechanics of connected fields in construction elements, vol. 3. Acousto-Electro-Magneto-Elasticity. Naukova dumka, Kiev, 288p (1988)
Novozhilov, V.V.: Fundamentals of the nonlinear theory of elasticity, 212p. Gostekhizdat, Moscow (1948)
Das, N.C., Bhattacharya, S.K.: Love waves in elastic media in presence of magnetic field. Geophys. Res. Bull. 16(2), 105–110 (1978)
Lehnitsky, S.G.: Theory of Elasticity of an Anisotropic Body. Nauka, Moscow, 416 pp (1977)
Novozhilov, V.V.: Theory of Elasticity, 370p. Sudpromgiz, Leningrad (1958)
Sirotin, Y.I., Shaskolskaya, M.P.: Fundamentals of Crystallophysics. Nauka, Moscow, 639p (1979)
Baghdasaryan, G.Y., Danoyan, Z.N.: Propagation of monochromatic magnetoelastic waves in ideally conducting media. In: Investigations on the Mechanics of a Solid Deformed Body. Ed. AN Arm.SSR, no. 2, pp. 42–50 (1983)
Baghdasaryan, G.Y., Danoyan, Z.N.: Equations of motion in displacements of ideally conducting elastic anisotropic media in the presence of a magnetic field. Mech., Interuniversity. Sat. Sci. Works, Yerevan 3, 32–42 (1984)
Danoyan, Z.N.: To the plane problem of propagation of magnetoelastic waves in ideally conducting isotropic media. Izv. AN Arm.SSR, Mechanics, T. 25(5):27–46 (1974)
Danoyan, Z.N.: On the propagation of magnetoelastic waves in ideally conducting isotropic media with cubic symmetry. In: Studies in Mech. Tv. Def. The bodies. Yerevan: Ed. AN Arm.SSR, pp. 104–109 (1981)
Danoyan, Z.N.: Propagation of plane magnetoelastic waves in anisotropic ideally conducting media. Izv. NAS of Armenia, Mech. 56(3), 37–48 (2003)
Kochin, N.E.: Vector calculus and the origin of the tensor calculus. Izd. AN SSSR, Moscow, 426 p (1961)
Dielesan, E., Royer, D.: Elastic waves in solids. Nauka, Moscow, 424p (1982)
Fedorov, F.I.: Theory of elastic waves in crystals. Nauka, Moscow, 386 pp (1965)
Grinchenko, V.T., Meleshko, V.V.: Harmonic oscillations and waves in elastic media. Naukova Dumka, Kiev, 283 p (1981)
Baghdasaryan, G.Y., Danoyan, Z.N.: Surface magnetoelastic Rayleigh waves. Mechanics, Rep. Interuniversity. Sat, Yerevan, №2, pp. 31–37 (1982)
Beetroot, V.A.: Elastic vibrations of an anisotropic body. Uch. App. Leningrad State University, issue 17, pp. 28–71 (1949)
Beetroot, V.A.: To the solution of dynamic problems of the plane theory of elasticity for an anisotropic body. PMM 25(5), 885–896 (1961)
Budaev, V.S.: Elastic waves in crystals and anisotropic media. PMTF (6), 143–153 (1974)
Osipov, I.O. Reflection and refraction of plane elastic waves on the boundary of two anisotropic media. Izv. ANSSSR, ser geofiz (5), 649–665 (1961)
Sveklo, B.A.: On the solution of dynamic problems of plane theory of elasticity for anisotropic body. AMM. 25(5), 885–896 (1961)
Kulikovskiy, A.G., Lyubimov, G.A.: Magnetic hydrodynamics. Physmatgiz, Moscow, 246p (1962)
Selezov, I.T., Selezova, L.V. Waves in magnetohydroelastic media. Nauk Dumka, Kiev, 164p (1975)
Osipov, I.O. To the method of functionally invariant solutions for problems of the dynamic theory of elasticity of anisotropic media. Izv. AN SSSR, sero geophys. (3), 391–396 (1963)
Osipov, I.O.: To the method of complex solutions of dynamical problems of the plane theory of elasticity of anisotropic media. Izv. RAS MTT. (4), 102–112 (1999)
Viktorov, I.A: Sound surface waves in solids. Nauka, Moscow, 286 p (1981)
Danoyan, Z.N.: To the method of functionally invariant solutions for the problem of magnetoelasticity of ideally conducting anisotropic media. Mechanics, Uche. Notes by YSU, №1, pp. 52–61 (1984)
Danoyan, Z.N.: Investigation of the roots of the characteristic equation of plane magnetoelastic waves for ideally conducting anisotropic media. Math. Methods Physicomechanical Fields 46(3), 116–120 (2003)
Danoyan, Z.N.: Plane magnetoelastic waves in an anisotropic perfectly conductive medium. Math. Methods Physical-mechanical Fields 46(3), 121–135 (2003)
Viktorov, I.A.: Physical basis for the application of ultrasonic waves of Rayleigh and Lamb in engineering. Nauka, Moscow, p. 168 (1966)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Baghdasaryan, G., Danoyan, Z. (2018). Some General Issues of Propagation of Magnetoelastic Waves in Electroconductive Isotropic and Anisotropic Media. In: Magnetoelastic Waves. Engineering Materials. Springer, Singapore. https://doi.org/10.1007/978-981-10-6762-4_2
Download citation
DOI: https://doi.org/10.1007/978-981-10-6762-4_2
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6761-7
Online ISBN: 978-981-10-6762-4
eBook Packages: EngineeringEngineering (R0)