Investigation of electromagnetic excitation method of volumetric ultrasonic waves in the metal half-space. Part 2. Formulation of the problems of determination of kinematic characteristics not interact-ing longitudinal and transverse (shear) ultrasonic w
Main Article Content
Abstract
Given the wording of boundary problems of dynamic theory of elasticity, the solutions of which determine by the kinematic and dynamic characteristics are not interacting longitudinal and transverse waves that are excited by a system of surface and volumetric forces. Given methods of determining the potentials of force field which are specified in the volume of elastic half-space. Made quantitative estimate of the scalar and vector potentials of the Joule forces field, which are created in axially magnetized conductive ferromagnet by variable magnetic field of the coil ring. It is shown that scalar and vector potentials offset fields of material particles, which are formed by longitudinal and shear waves, should be sought in the form of sums of series in even and odd spherical harmonics, respectively.
References 12, figures 5, tabl 1.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
References
Aki K., Richards P. (1983), «Quantitative seismology» Vol.1. – Moscow, Mir, P. 520. (Rus)
Grinchenko V.T., Meleshko V. V. (1981), “Harmonic oscillations and waves in elastic bodies”. Kyiv, Naukova dumka. P. 283. (Rus)
Kravtsov A.V., Kuznetsov S.V., Sekerzh-Zenkovich S.Y. (2011), “Finite-element models in the problem of the lamb”. Izvestiya ran. Mekh. No.6. - pp. 166 - 175. (Rus)
A. G. Gorbashova, O. N. Petrischev, M. I. Romanyuk. (2013), “Study transfer characteristics ultrasonic tracts with electromagnetic excitation and registration of Rayleigh waves in ferromagnets. Part 2”. Electronics and communications. No 3. pp. 56 – 64. (Rus)
Kamke E. (1976) “Handbook on ordinary differential equations”. Мoscow, Nauka. P. 576 . (Rus)
Koshlyakov N. S., Gliner E. B., Smirnov M. M. (1970), “Equations of mathematical physics”. M.: Vysshaya shkola, P. 710. (Rus)
Loytsyanskiy L. G. (1970) “Mechanics of fluid and gas”. Мoscow, Nauka. P. 904 . (Rus)
Mikheeva A.N, Petryschev O.N. (2014), “Investigation of electromagnetic excitation method of volumetric ultrasonic waves in the metal half-space. Part 1. Calculation of the magnetic field and the force field, which are generated in a magnetized annular inductor conductive ferromagnet” . Electronics and communications. Vol. 19, No 2(79). pp. 59 – 74. (Rus)
Nikiforov A. F., Uvarov V. B. (1974), «Fundamentals of the theory of special functions». Мoscow, Nauka. P. 304 . (Rus)
Novatskiy V. (1975), “Theory of elasticity”. Мoscow, Mir. P. 875 . (Rus)
Smirnov V. I. .(1974) “Course of higher mathematics”. Vol. 3. Part 2.. Мoscow, Nauka. P. 672 . (Rus)
M. Abramowitz, I. Stegun (1979), “Handbook of Mathematical Functions with formulas, graphs and mathematical tables”. Мoscow, Nauka. P. 832 . (Rus)