Parametric Instability of Curved Girders

Abstract

The parametric instability of a curved girder subjected to equal and opposite periodic moments at the ends is examined. It is shown that the relationship of the frequencies at which parametric resonance occurs differs from the frequency relationship of ordinary resonance. For small values of the applied couples at the ends, the parametric resonant frequency is twice the natural frequency. The method presented can also be used to determine the natural frequencies and static buckling moment for a curved girder. Special analytical solutions and numerical results are obtained and presented in nondimensional forms.