Dynamic stability of flexible bellows subjected to periodic internal fluid pressure excitation

This paper deals with the theoretical stability analysis and experimental study of flexible bellows subjected to periodic internal fluid pressure excitation. The bellows studied in this paper are fixed at both ends rigidly, and art excited by the periodic internal fluid pressure. In the theoretical stability analysis, the basic equation of the bellows subjected to periodic internal fluid pressure excitation is derived as a Mathieu's equation. Natural frequencies of the bellows are examined and stability maps tire presented for parametric instability, computed by Bolotin's method. It is found that the transverse natural frequencies of the bellows decrease with increasing the static internal fluid pressure and buckling occurs due to high internal fluid pressure. It is also found that primary and secondary parametric vibrations occur to the bellows in transverse direction due to the periodic internal fluid pressure excitation. Parametric instability regions are clarified and the theoretical calculations of the parametric instability boundaries are in good agreement with the experimental ones. Moreover, effects of damping and static internal fluid pressure on the parametric instability regions are examined theoretically.