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A semi-analytical method is proposed to analyze both axisymmetric and asymmetric vibrations of thin opened spherical shells with elastic boundary conditions and discontinuity in thickness. To establish the governing equation, the method is involved in dividing the shell into many narrow strips in meridional direction, and those strips are approximately treated as conical ones with uniform thickness. Flugge shell theory is used to describe the motions of strips and displacement functions are expanded as power series. Artificial springs are employed to restrain displacements at edges so that arbitrary boundary conditions can be analyzed. By assembling all continuity conditions of adjacent strips and boundary conditions, the governing equation is established. In numerical results discussion, many comparisons of frequency parameters of present method and those in literature are firstly presented and they illustrate high accuracy and wide application of present method. Furthermore, influences of elastic boundary conditions, open angle, ratio of thickness to radius and thickness discontinuity on natural frequencies of spherical shells are investigated. Results show that meridinoal and circumferential displacements have obvious effects on natural frequencies, and the influence of thickness discontinuity seriously depends on the location of discontinuity.

A semi-analytical method for vibration analysis of thin spherical shells with elastic boundary conditions