In-plane Parametric Vibrations of Curved Bellows Subjected to Dynamic Internal Fluid Pressure Excitation

Abstract

This paper deals with a theoretical study of in-plane parametric vibrations of a curved bellows subjected to oscillating internal fluid pressure excitation. In the theoretical analysis, the curved bellows is modeled as a combination of beam models including the effect of the internal fluid and fluid pressure by the finite element method. Mathieu's type equation is derived from the basic equation of the bellows. The natural frequencies of the curved bellows and the parametric instability boundaries are examined. As a result, the curved bellows have two types of parametric vibrations, longitudinal and transverse vibrations. The longitudinal parametric instability boundaries become broader with increasing the curved ratio of the bellows. On the other hand, the transverse parametric instability boundaries become narrower.