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Free vibrations of thin, elastic, segmented shells of revolution reinforced with circumferential rings. (English) Zbl 0685.73035

Summary: The subject-matter of this paper is a method for calculation of frequencies and modes of free vibration of thin elastic, segmented shells of revolution reinforced with internal or external circumferential rings. The shape of the meridian and the change of thickness of the shell in the meridional direction may be arbitrary. Material and structural orthotropy of the shell have also been taken into account. The problem is posed in a variational form. The functional associated with Hamilton’s principle has been expanded into trigonometric series in the circumferential direction and finite-difference method has been applied along the meridian. In consequence, the problem has been converted into a generalized eigenvalue problem. Numerical examples, calculated with the program DYSAR based on an algorithm presented here, expose the possibilities of the method and the program itself. Analysis and comparison of these numerical results with the experimental data published in the literature confirm their correctness and accuracy, which turn out to be quite sufficient for practical applications even in the case of relatively small number of nodes of the finite difference net.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74H45 Vibrations in dynamical problems in solid mechanics
74K15 Membranes
74E10 Anisotropy in solid mechanics
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