回転するせっ頭円すい殻の不安定振動

抄録

An analysis is presented for the unstable vibration of a spinning truncated conical shell. For this purpose, the governing equations and the boundary conditions of the shell are derived by applying Hamilton's principle to the strain and kinetic energies of the shell. The frequency is treated as a complex value, and the variables in the equations can be written as a summation of the quasi-static components which are independent on time and the dynamic ones. The nonlinear equations governing the finite deformations caused by the spinning of the shell are solved by use of Picard's method of succesive approximation, and the linear equations on the vibration about the deformed state are solved by using the transfer matrix method. The method is applied to a spinning truncated conical shell clamped at the small edge, and the frequency parameters and the mode shapes of vibration are calculated numerically, and the behaviour of the shell on the unstable vibration are studied.