Nonlinear Forced Oscillations of a Shallow Spherical Shell

Abstract

Axisymmetric forced oscillations of a shallow spherical shell subjected to harmonic excitation are investigated. Based on modal equations derived from the von Karman dynamic equations, a theoretical analysis is conducted of the harmonic oscillation as well as the subharmonic oscillation of order 1/2. The theoretical analysis reveals that in certain cases the response curve of the harmonic oscillation is of soft spring type, that the subharmonic oscillation of order 1/2 can occur, and that the characters of the subharmonic oscillation are greatly influenced by internal resonance. An experimental analysis is also conducted with use of a shallow spherical steel shell. The experimental analysis confirms the validity of the theoretical analysis.