The Lowest Eigenfrequencies of an Immersed Thin Elastic Cylindrical Shell

Yücel, Hazel; Erbaş, Barış; Ege, Nihal; Kaplunov, Julius

Abstract

The plane strain time-harmonic motion of an immersed cylindrical elastic shell is considered. The revisit to this classical problem is motivated by modern technical applications, including the investigation of low-frequency band gaps arising at acoustic wave propagation through a periodic array of thin-walled cylinders. In this paper, the effect of the fluid is reduced to a mixed boundary condition along the outer face of the shell after the separation of the circumferential variable. The asymptotic analysis of the ordinary differential equations along a narrow interval results in approximate formulae for the lowest complex eigenfrequencies. It is demonstrated that their values are asymptotically smaller than the lowest eigenfrequencies of a shell with traction-free faces, and at leading order they do not depend on the shell density. At the same time, the fluid compressibility does not appear in the two-term asymptotic behaviour. Numerical examples for steel and aluminium shells immersed in water confirm that the imaginary parts of the sought-for frequencies are extremely small and may often be ignored in comparison with the contribution of structural damping.

Citation

Yücel, H., Erbaş, B., Ege, N., & Kaplunov, J. (2023). The Lowest Eigenfrequencies of an Immersed Thin Elastic Cylindrical Shell. In Advances in Linear and Nonlinear Continuum and Structural Mechanics (559-571). Springer. https://doi.org/10.1007/978-3-031-43210-1_31

• Online Publication Date: Dec 4, 2023
• Publication Date: 2023
• Deposit Date: Jan 31, 2024
• Publisher: Springer
• Pages: 559-571
• Series Title: Advanced Structured Materials
• Series ISSN: 1869-8441; 1869-8433
• Book Title: Advances in Linear and Nonlinear Continuum and Structural Mechanics
• Chapter Number: 30
• ISBN: 9783031432095
• DOI: https://doi.org/10.1007/978-3-031-43210-1_31
• Publisher URL: https://link.springer.com/chapter/10.1007/978-3-031-43210-1_31
• Additional Information: First Online: 4 December 2023