Axially Symmetric Vibration of a Complete Conic Shell

We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with vertex. The procedure of construction of systems of basis functions for the approximation of displacements of the shell is based on the account of the formal...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2022-02, Vol.261 (2), p.319-336
Main Authors: Trotsenko, V. A., Trotsenko, Yu. V.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Basis functions
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical analysis
Vibration
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Summary:We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with vertex. The procedure of construction of systems of basis functions for the approximation of displacements of the shell is based on the account of the formal structure of the fundamental system of integrals of the original equations established as a result of the asymptotic integration of a singularly perturbed system of equations with regular singular point. We present examples of numerical analyses of specific conic shells illustrating the efficiency of the proposed algorithm for the solution of the problem.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-022-05753-8