Edge and interfacial vibration of a thin elasic cylindrical panel

Abstract

Free vibrations of a thin elastic circular cylindrical panel localized near the rectilinear edge, propagating along the edge and decaying in its circumferential direction, are investigated in the framework of the two-dimensional equations in the Kircho↵-Love theory of shells. At first the panel is assumed to be infinite longitudinally and semi-infinite along its length of curvature (of course not realistically possible), followed by the assumption that the panel is then finite along its length of curvature and fixed and free conditions are imposed on the second resulting boundary. Using the comprehensive asymptotic analysis detailed in Kaplunov et al. (1998) “Dynamics of Thin Walled Elastic Bodies”, leading order asymptotic solutions are derived for three types of localized vibration, they are bending, extensional, and super-low frequency. Explicit representation of the exact solutions cannot be obtained due to the degree of complexity of the solving equations and relevant boundary conditions, however, computational methods are used to find exact numerical solutions and graphs. Parameters, particularly panel thickness, wavelength, poisson’s ratio, and circumferential panel length, are varied, and their e↵ects on vibration analyzed. This analysis is further extended to investigate localized vibration on the interface (perfect bond) of two cylindrical panels joined at their respective rectilinear edges, propagating along the interface and decaying in the circumferential direction away from the interface. An earlier, similar, localized vibration problem presented in Kaplunov et al. (1999) “Free Localized Vibrations of a Semi-Infinite Cylindrical Shell” and Kaplunov and Wilde (2002) “Free Interfacial Vibrations in Cylindrical Shells” is replicated for comparison with all cases. The asymptotics are similar, however in this problem the numerics highlight the stronger e↵ect of curvature on the decay of the super-low frequency vibrations, and to some extent on the leading order bending vibration.