Vibration of functionally graded shallow shells with complex shape

dc.contributor.authorAwrejcewicz, Janpl
dc.contributor.authorKurpa, Lidiyaen
dc.contributor.authorShmatko, T.en
dc.date.accessioned2018-07-20T12:03:51Z
dc.date.available2018-07-20T12:03:51Z
dc.date.issued2015
dc.description.abstractThe method for studying the geometrically nonlinear vibrations of functionally graded shallow shells with a complex planform is proposed. Сomposite shallow shells made from a mixture of ceramic and metal are considered. In order to take into account varying of the volume fraction of ceramic the power law is accepted. Formulation of the problem is carried out using the refined geometrically nonlinear theory of shallow shells of the first order (Timoshenko’s type). The R-functions theory, variational Ritz’s method, procedure by Bubnov Galerkin and Runge-Kytta method are used in the developed approach. A distinctive feature of the proposed approach is the method of reducing the initial nonlinear system of equations of motion for partial derivatives to a nonlinear system of ordinary differential equations. According to the developed approach first it is necessary to solve linear vibration problem. Further to solve elasticity problems for inhomogeneous differential equations with right hand side, containing eigen functions. Obtained solutions of these problems are applied for representation of unknown functions of the nonlinear problem. Application of the theory of R-functions on every step allows us to extend the proposed approach to the shell with arbitrary shape of plan and different kinds of boundary condition. The proposed method is validated by investigation of test problems for shallow shells with rectangular and elliptical planform and applied to new vibration problems for shallow shells with complex planform.en
dc.identifier.citationAwrejcewicz J. Vibration of functionally graded shallow shells with complex shape / J. Awrejcewicz, L. Kurpa, T. Shmatko // Dynamical Systems. Mathematical and Numerical Approaches (DSTA–2015) : [proc. of the 13th conf., December 7-10, 2015, Lodz, Poland]. – Lodz : DABM, 2015. – P. 57-68.en
dc.identifier.urihttps://repository.kpi.kharkov.ua/handle/KhPI-Press/37081
dc.language.isoen
dc.publisherDepartment of Automation, Biomechanics and Mechatronicsen
dc.subjectcomposite materialsen
dc.subjectfunctionally graded materialsen
dc.subjectfinite element methoden
dc.titleVibration of functionally graded shallow shells with complex shapeen
dc.typeThesisen

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