Abstract
On the basis of the linear bending shell theory, the axisymmetric free flexural vibrations of truncated conical shells clamped at one end and having an end-mass at the other are analyzed numerically, and the coupling between the end-mass and the mass of the shell is discussed in detail. Expanding the vibration mode into the cosine Fourier series, a family of characteristic equations for the natural circular frequencies are derived by the aid of the Rayleigh-Ritz method and solved by the use of the power method. The variation of circular frequencies and vibration modes of the shell with the end-mass, geometrical and completeness parameters are shown. And, for the cases where the mass of the shell can be ignored compared to the end-mass, the design charts for the natural circular frequency or axial spring constant of truncated conical shells are presented over a wide range of geometrical and completeness parameters.
