The Correction of Finite Thickness to the Vibrational Spectra of a Spherical Elastic Shell

Abstract

The vibrational modes and corresponding eigenfrequencies in a spherical shell, such as C 60 , are obtained based on a continuum model. These modes are decomposed into the torsional and spheroidal modes (T-modes and S-modes), where S-modes are further decomposed into the upper and lower branches, a l and b l , respectively. The spectra dependence on shell thickness is taken into account to predict more accurate frequencies. The frequencies of T-modes decrease with shell thickness due to the purely transversal displacement. Moreover, the a l S-mode bears a similar fashion to the T-mode, but the frequency of the b l S-mode with a large l increases with shell thickness where the longitudinal displacement becomes predominant. The analytic expressions of corrections to vibrational frequencies are also derived up to third-order in the shell thickness. The differences between the present corrections and the previous results could be summarized as follows: (1) The leading correction to the frequency should be prop...