Nonlinear vibration of structure composed of a thin annular plate and a shallow conical shell

Based on dimensionless governing equations of an elastic shell, the nonlinear vibration of a structure composed of a thin annular plate and a shallow conical shell under the actions of a uniform transverse load is studied in this paper. The shooting method is used to obtain the numerical solutions for the vibration problem with clamped edge boundary condition. The effects of transverse load, the ratio of the plate radius to the shell radius and cone's vertex angle on the natural frequencies of the structure are investigated and discussed. Finally, variations in the structural rigidity are discussed.