Nonlinear free vibrations of multilayer shallow shells with a symmetric structure and with a complicated form of the plan

We propose a method to study free nonlinear vibrations of multilayer shallow shells with a complicated form of the plan. The mathematical statement of the problem is realized in the frame of a refined firstorder theory of the Tymoshenko type. A distinctive specific feature of the work is the applica...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2009-10, Vol.162 (1), p.85-98
Main Author: Kurpa, L. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We propose a method to study free nonlinear vibrations of multilayer shallow shells with a complicated form of the plan. The mathematical statement of the problem is realized in the frame of a refined firstorder theory of the Tymoshenko type. A distinctive specific feature of the work is the application of the theory of R -functions and variational methods to the determination of eigenfunctions used as the basis in the construction of the required solution of a nonlinear problem. The proposed method is tested, and some new problems are solved. As a result, we constructed the amplitude–frequency dependences for spherical shells with a complicated form of the plan.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-009-9622-9