Two inverse non-stationary problems of axially symmetric deformation of a finite-length elastic cylindrical shell
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Дата
2022
Назва журналу
Номер ISSN
Назва тому
Видавець
Харківський національний автомобільно-дорожній університет
Анотація
Problem. 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.
Опис
Ключові слова
cylindrical shell, non-stationary load, inverse problem, regularization method, identification, vibration control, циліндрична оболонка, нестаціонарне навантаження, обернена задача, регуляризація, ідентифікація, управління коливаннями
Бібліографічний опис
Voropay, 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.