Dynamic Stability Analysis of Flexible Bellows Subjected to Periodic Internal Fluid Pressure Excitation

This paper deals with theoretical stability analysis and experimental study of parametric vibrations of flexible bellows subjected to periodic internal fluid pressure excitation. The bellows is clamped at both ends rigidly, and is excited by the periodic internal fluid pressure. In the theoretical stability analysis, the bellows is treated as a Timoshenko’s beam including the effect of the internal fluid pressure excitation. And the Mathieus type equation is derived from the basic equation of the bellows subjected to periodic internal fluid pressure excitation. First, we theoretically examined the transverse natural frequencies of the bellows and the parametric instability regions. Second, we examine experimentally the natural frequencies of the bellows and the parametric instability regions to verify the results of the theoretical stability analysis. As a result, we found that the transverse natural frequencies of the bellows decrease with increasing the static internal fluid pressure and that primary and secondary parametric vibrations occur in the bellows due to the periodic internal fluid pressure excitation. And the theoretical results of the parametric instability boundaries agree well with the experimental results.