Abstract Summary
A semi-infinite thin shell is considered within the framework of 2D Koiter-Sanders theory. The focus is on the frequency domain near the lowest cut-off frequencies, being of order of the relative shell thickness, with the values tending to zero at a thin shell limit. Within this domain, the dynamic behaviour of the shell is strongly affected by its curvature and cannot be interpreted in terms of plate bending and plate extension even at a rough approximation. The solution is sought for as the composition of slowly decaying semi-membrane modes and a boundary layer in the form of a simple edge effect, e.g. see [1, 2] and references therein. In contrast to previous considerations in [3], a sophisticated iterative asymptotic process of satisfying the edge boundary conditions is not implemented this time. Instead, the dispersion relation for the sought for edge wave presented in the form the fourth-order determinant is subject to straightforward analysis using a symbolic algebra package. Numerical results are presented for several types of boundary conditions at the edge, including the case of a free edge. The effect of anisotropy is also addressed. References [1] Kaplunov, J., Manevitch, L. I., & Smirnov, V. V. (2016). Vibrations of an elastic cylindrical shell near the lowest cut-off frequency. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2189), 20150753. [2] Kaplunov, J., & Nobili, A. (2017). A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell. Journal of Sound and Vibration, 401, 23-35. [3] Kaplunov, J. D., Kossovich, L. Y., & Wilde, M. V. (2000). Free localized vibrations of a semi-infinite cylindrical shell. The Journal of the Acoustical Society of America, 107(3), 1383-1393.
