Effect of Bending on Vibrations of Spherical Shells

摘要: This paper is concerned with the vibration analysis of spherical shells, closed at one pole and open other, by means linear classical bending theory shells. Frequency equations are derived ha terms Legendre functions complex indices, for axisymmetric natural frequencies mode shapes deduced opening angles ranging from a shallow to shell. It found that all frequency spectrum consists two coupled infinite sets modes can be labeled as (or flexural) membrane modes. distinction made on basis comparison strain energies due stretching each mode. also practically independent thickness, whereas vary thickness. Previous analyses use have shown spaced within finite interval spectrum. in this set degenerate case modes, and, if theory, it applicable only when thickness shell zero. When employed, then extends infinity every value greater than