Abstract
This paper is concerned with the natural vibrations of a spherical shell with variable thickness in the meridional direction. The governing equations of motion are based upon the classical small deflection theory of thin shells postulated by Love for the case of shell vibrations. In this paper, it is shown that the eight solutions of these equations for the asymmetrical vibrations can be obtained analytically by the method of series solution. As a practical example, four solutions required in the case of a hemispherical shell with a free edge are derived. Last, to demonstrate the utility of the present method, the numerical results are compared with the experimental data.
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