Concerning the problem of vibrational process localization on coatings with defects
UDC
539.3Abstract
We described earlier, that both in dynamic and in static mixed boundary value problems can occur the localization of processes, which are described by the considered boundary problem. At the same time some new phenomena, which were not investigated earlier, are revealed. Block element approach is a useful tool for the investigation of phenomena of localization processes because the wording of the conditions of localization is based on the integral method of factorization, which is included in the algorithm of block elements building. The conditions of vibration localization process by the example of the mixed boundary problem concerning the vibration of coatings with defects are listed below. The investigation is based on the block element approach and also on “natural viruses” theory developed earlier in the study. The connection between the integral equations of the considered boundary value problem with the same ones in the specified theory is found.
Keywords:
localization, anomaly natural process, natural virus, boundary-value problemsFunding information
Отдельные фрагменты работы выполнены при поддержке грантов РФФИ (12-01-00330, 12-01-00332, 13-01-96502, 13-01-96505, 13-01-96508, 14-08-00404, 13-01-12003-м), гранта Президента РФ (НШ-1245.2014.1), программ отделения ЭММПУ и Президиума РАН (проект 43), выполняемых Южным научным центром РАН.
References
- Бабешко В.А., Ритцер Д., Евдокимова О.В., Бабешко О.М. О локализации энергии природных процессов и природные вирусы // ДАН. 2013. Т. 448, № 4. С. 406-409. [Babeshko V.A., Rittser D., Evdokimova O.V., Babeshko O.M. O lokalizatsii energii prirodnykh protsessov i prirodnye virusy [On the localization energy of natural processes and natural viruses]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2013, vol. 448, no. 4, pp. 406-409. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. О "вирусной" теории некоторых аномальных природных явлений // ДАН. 2012. Т. 447. № 1. С. 33-37. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. O "virusnoy" teorii nekotorykh anomal'nykh prirodnykh yavleniy [About "viral" theory some anomalous natural phenomena]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2012, vol. 447, no. 1, pp. 33-37. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. "Вирусная теория" некоторых природных аномалий // ДАН. 2012. Т. 447. № 6. С. 624-628. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. "Virusnaya teoriya" nekotorykh prirodnykh anomaliy [A "viral theory" some natural anomalies]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2012, vol. 447, no. 6, pp. 624-628. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. О локализации, резонансах и некоторых аномальных явлениях // Экологический вестник научных центров Черноморского экономического сотрудничества. 2014. № 1. С. 5-10. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. O lokalizatsii, rezonansakh i nekotorykh anomal'nykh yavleniyakh [About localization, resonances and some abnormal phenomena]. Ekologicheskiy vestnik nauchnykh tsentrov Chernomorskogo ekonomicheskogo sotrudnichestva [Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation], 2014, no. 1, pp. 5-10. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. О скрытых дефектах в наноструктурах, телах с покрытиями и сейсмологии // ДАН. 2014. Т. 457. № 1. С. 45-49. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. O skrytykh defektakh v nanostrukturakh, telakh s pokrytiyami i seysmologii [Hidden defects in nanostructures, bodies, coatings and seismology]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2014, vol. 457, no. 1, pp. 45-49. (In Russian)]
- Бабешко В.А., Ритцер Д., Евдокимова О.В., Бабешко О.М., Федоренко А.Г. К теории прогноза сейсмичности на основе механической концепции, топологический подход // ДАН. 2013. Т. 450. № 2. С. 166-170. [Babeshko V.A., Rittser D., Evdokimova O.V., Babeshko O.M., Fedorenko A.G. K teorii prognoza seysmichnosti na osnove mekhanicheskoy kontseptsii, topologicheskiy podkhod [To the theory of prediction of seismicity based on mechanical concepts topological approach]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2013, vol. 450, no. 2, pp. 166-170. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М., Федоренко А.Г., Шестопалов В.Л. К проблеме покрытий с трещинами в сейсмологии и наноматериалах // Механика твердого тела. 2013. № 5. С. 39-45. [Babeshko V.A., Evdokimova O.V., Babeshko O.M., Fedorenko A.G., Shestopalov V.L. K probleme pokrytiy s treshchinami v seysmologii i nanomaterialakh [The problem surfaces with cracks in seismology and nanomaterials]. Mekhanika tverdogo tela [Rigid Body Mechanics], 2013, no. 5, pp. 39-45. (In Russian)]
- Бабешко В.А. Павлова А.В., Ратнер С.В., Вильямс Р. К решению задачи о вибрации упругого тела, содержащего систему внутренних полостей трещин // ДАН. 2002. Т. 382, № 5. С. 625-628. [Babeshko V.A. Pavlova A.V., Ratner S.V., Vil'yams R. K resheniyu zadachi o vibratsii uprugogo tela, soderzhashchego sistemu vnutrennikh polostey treshchin [To the solution of the problem of vibration of the elastic body containing a system of internal cavities cracks]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2002, vol. 382, no. 5, pp. 625-628. (In Russian)]
- Бабешко В.А., Бабешко О.М. Метод факторизации в краевых задачах в неограниченных областях // ДАН. 2003. Т. 392. № 6. C. 767-770. [Babeshko V.A., Babeshko O.M. Metod faktorizatsii v kraevykh zadachakh v neogranichennykh oblastyakh [Method of factorization in boundary-value problems in unbounded domains]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2003, vol. 392, no. 6, pp. 767-770. (In Russian)]
- Бабешко В.А., Бабешко О.М. Формулы факторизации некоторых мероморфных матриц-функций // ДАН. 2004. Т. 399, № 1. С. 163-167. [Babeshko V.A., Babeshko O.M. Formuly faktorizatsii nekotorykh meromorfnykh matrits-funktsiy [Formula factorization of some meromorphic matrix functions]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2004, vol. 399, no. 1, pp. 163-167. (In Russian)]
- Бабешко В.А., Бабешко О.М. Метод факторизации решения некоторых краевых задач // ДАН. 2003. Т. 389. № 2. С. 184-188. [Babeshko V.A., Babeshko O.M. Metod faktorizatsii resheniya nekotorykh kraevykh zadach [Method factorization solution of some boundary value problems]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2003, vol. 389, no. 2, pp. 184-188. (In Russian)]
- Бабешко В.А., Евдокимова О.В., Бабешко О.М. Об автоморфизме и псевдодифференциальных уравнениях в методе блочного элемента // ДАН. 2011. Т. 438. № 5. С. 623-625. [Babeshko V.A., Evdokimova O.V., Babeshko O.M. Ob avtomorfizme i psevdodifferentsial'nykh uravneniyakh v metode blochnogo elementa [About the automorphism and pseudodifferential equations in method block element]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2011, vol. 438, no. 5, pp. 623-625. (In Russian)]
- Бабешко В.А., Бабешко О.М, Евдокимова О.В. К проблеме исследования материалов с покрытиями // ДАН. 2006. Т. 410. № 1. С. 49-52. [Babeshko V.A., Babeshko O.M, Evdokimova O.V. K probleme issledovaniya materialov s pokrytiyami [The problem of research materials and coatings]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2006, vol. 410, no. 1, pp. 49-52. (In Russian)]
- Бабешко В.А., Бабешко О.М, Евдокимова О.В. К проблеме оценки состояния материалов с покрытиями // ДАН. 2006. Т. 409. № 4. С. 481-485. [Babeshko V.A., Babeshko O.M, Evdokimova O.V. K probleme otsenki sostoyaniya materialov s pokrytiyami [The problem of assessing the condition of materials and coatings]. Doklady Akademii nauk [Reports of the Academy of Sciences], 2006, vol. 409, no. 4, pp. 481-485. (In Russian)]
- Бабешко В.А. Белянкова Т.И., Калинчук В.В. Метод фиктивного поглощения в задачах теории упругости для неоднородного полупространства // Прикладная математика и механика. 2002. Т. 66. Вып. 2. С. 276-284. [Babeshko V.A. Belyankova T.I., Kalinchuk V.V. Metod fiktivnogo pogloshcheniya v zadachakh teorii uprugosti dlya neodnorodnogo poluprostranstva [Method bogus absorption problems of elasticity theory for inhomogeneous half-space]. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics], 2002, vol. 66, iss. 2, pp. 276-284. (In Russian)]
- Ворович И.И., Бабешко В.А. Динамические смешанные задачи теории упругости для неклассических областей. М.: Наука, 1979. 320 с. [Vorovich I.I., Babeshko V.A. Dinamicheskie smeshannye zadachi teorii uprugosti dlya neklassicheskikh oblastey [Dynamic mixed problems of elasticity theory for non-classical fields]. Moscow, Nauka Publ., 1979, 320 p. (In Russian)]
- Бабешко В.А. О системах интегральных уравнений динамических контактных задач // Доклады АН СССР. 1975. Т. 220. № 6. С. 1293-1296. [Babeshko V.A. O sistemakh integral'nykh uravneniy dinamicheskikh kontaktnykh zadach [About systems of integral equations of dynamic contact problems]. Doklady AN SSSR [Reports of the USSR Academy of Sciences], 1975, vol. 220, no. 6, pp. 1293-1296. (In Russian)]
- Бабешко В.А. Статические и динамические контактные задачи со сцеплением // Прикладная математика и механика. 1975. Т. 39. Вып. 3. С. 505-512. [Babeshko V.A. Staticheskie i dinamicheskie kontaktnye zadachi so stsepleniem [Static and dynamic contact problems with adhesion]. Prikladnaya matematika i mekhanika [Applied mathematics and mechanics], 1975, vol. 39, iss. 3, pp. 505-512. (In Russian)]
- Бабешко В.А. Факторизация одного класса матриц-функций и ее приложения // Доклады АН СССР. 1975. Т. 223. № 5. С. 1094-1097. [Babeshko V.A. Faktorizatsiya odnogo klassa matrits-funktsiy i ee prilozheniya [Factorization of a class of matrix functions and its applications]. Doklady AN SSSR [Reports of the USSR Academy of Sciences], 1975, vol. 223, no. 5, pp. 1094-1097. (In Russian)]
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Dates
Submitted
December 7, 2014
Accepted
December 14, 2014
Published
December 22, 2014
How to Cite
[1]
Babeshko, V.A., Babeshko, O.M., Gladskoi, I.B., Grishchenko, D.V., Lozovoy, V.V., Pluzhnik, A.V., Shestopalov, V.L., Concerning the problem of vibrational process localization on coatings with defects. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2014, № 4, pp. 13–20.
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Copyright (c) 2014 Бабешко В.А., Бабешко О.М., Гладской И.Б., Грищенко Д.В., Лозовой В.В., Плужник А.В., Шестопалов В.Л.
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