Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells
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Дата
2016
Автори
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
NTU "KhPI"
Анотація
An original method for investigation of geometrically nonlinear vibrations of functionally graded shallow
shells and plates with complex planform is presented. Shells under consideration are made from a composite of
ceramics and metal. Power law of volume fraction distribution of materials through thickness is chosen.
Mathematical statement is implemented in the framework of the refined geometrically nonlinear theory of the
shallow shells of the first order (Timoshenko type). The proposed approach combines the application of the Rfunctions
theory (RFM), variational Ritz method, procedure by Bubnov-Galerkin and Runge-Kutta method.
Due to use of this combined algorithm it is possible to reduce the initial nonlinear system of motion equations
with partial derivatives to a nonlinear system of ordinary differential equations. Investigation task of
functionally graded shallow shells with arbitrary planform and different types of boundary conditions is
carried out by the proposed method. Test problems and numerical results have been presented for one-mode
approximation in time. In future, the developed method may be extended to investigation of geometrically
nonlinear forced vibrations of functionally graded shallow shells with complex planform.
Опис
Ключові слова
functionally graded shallow shells, nonlinear vibrations, theory of the R-functions, method by Ritz
Бібліографічний опис
Shmatko T. Geometrically Nonlinear Vibrations of Functionally Graded Shallow Shells / T. Shmatko, A. Bhaskar // Nonlinear Dynamics–2016 (ND-KhPI2016) : proceedings of 5th International Conference, dedicated to the 90th anniversary of Academician V. L. Rvachev, September 27-30, 2016 = Нелінійна динаміка–2016 : тези доп. 5-ї Міжнар. конф., 27-30 вересня 2016 р. – Kharkov : NTU "KhPI", 2016. – P. 485-492.