Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell

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dc.contributor.authorVoropay, Alexey
dc.contributor.authorPovaliaiev, Serhii
dc.contributor.authorSharapata, Andrey
dc.contributor.authorВоропай, Олексій Валерійович
dc.contributor.authorПоваляєв, Сергій Іванович
dc.contributor.authorШарапата, Андрій Сергійович
dc.date.accessioned2023-02-08T14:15:04Z
dc.date.available2023-02-08T14:15:04Z
dc.date.issued2022
dc.description.abstractProblem. Among the many problems of the solid mechanics, there is a whole class of problems that are related to inverse problems. In turn, among the inverse problems, many problems are ill-posed. Obtaining an exact analytical solution of such problems is related to certain mathematical difficulties and requires using special methods. Goal. The goal of the study is to obtain analytical solutions for inverse problems of the identification of non-stationary load and the control of nonstationary vibrations of a cylindrical shell with asymmetric boundary conditions. Methodology. In this investigation, a refined theory of medium-thickness shells was used. Fourier series expansion, the theory of integral equations and the Laplace transform were used to obtain the solution of the direct problem. Tikhonov’s regularization method was used to solve inverse problems. Results. As a result of the investigation, the solutions of two inverse problems of the solid mechanics were obtained. The first task is to identify a fixed and moving concentrated axisymmetric non-stationary force acting on a cylindrical shell, based on the displacement values at any point of the shell; identification of two fixed concentrated forces. The second task is to control vibrations at any point of the cylindrical shell by introducing an auxiliary concentrated force. Numerical results obtained demonstrate the fulfillment of the control criterion as a result of the action of the given and auxiliary force. Originality. Analytical solutions of the inverse problems of the solid mechanics for a cylindrical shell of medium thickness with asymmetric boundary support conditions are obtained. Practical value. The technique received allows effective identification of an unknown non-stationary load. It’s important for the rational design of reliable cylindrical shell structures. Its use also makes possible to create a theoretical basis to control the deflected mode parameters of cylindrical shell structural elements.uk_UK
dc.identifier.citationVoropay, A. Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell / A. Voropay, S. Povaliaiev, A. Sharapata // Автомобiльний транспорт : зб. наук. пр. / М-во освiти i науки України, ХНАДУ ; редкол.: А. В. Гнатов (гол. ред.) та iн. – Харкiв, 2022. –  Вип. 51. – С. 74–84.uk_UK
dc.identifier.issn2219-8342
dc.identifier.urihttps://dspace.khadi.kharkov.ua/handle/123456789/8589
dc.language.isoenuk_UK
dc.publisherХарківський національний автомобільно-дорожній університетuk_UK
dc.subjectcylindrical shelluk_UK
dc.subjectnon-stationary loaduk_UK
dc.subjectinverse problemuk_UK
dc.subjectregularization methoduk_UK
dc.subjectidentificationuk_UK
dc.subjectvibration controluk_UK
dc.subjectциліндрична оболонкаuk_UK
dc.subjectнестаціонарне навантаженняuk_UK
dc.subjectобернена задачаuk_UK
dc.subjectрегуляризаціяuk_UK
dc.subjectідентифікаціяuk_UK
dc.subjectуправління коливаннямиuk_UK
dc.subject.doi10.30977/AT.2219-8342.2022.51.0.08uk_UK
dc.subject.udc539.3uk_UK
dc.titleTwo inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shelluk_UK
dc.typeArticleuk_UK

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