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

This paper deals with the theoretical stability analysis of in-plane parametric vibrations of a curved bellows subjected to periodic internal fluid pressure excitation. The curved bellows studied in this paper are fixed at both ends rigidly, and are excited by the periodic internal fluid pressure. In the theoretical stability analysis, the governing equation of the curved bellows subjected to periodic internal fluid pressure excitation is derived as a Mathieu’s equation by using finite element method (FEM). Natural frequencies of the curved bellows are examined and stability maps are presented for in-plane parametric instability. It is found that the natural frequencies of the curved bellows decrease with increasing the static internal fluid pressure and buckling occurs due to high internal fluid pressure. It is also found that two types of parametric vibrations, longitudinal and transverse vibrations, occur to the curved bellows in-plane direction due to the periodic internal fluid pressure excitation. Moreover, effects of axis curvature on the parametric instability regions are examined theoretically.

Download Full-text

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

Journal of Pressure Vessel Technology ◽

10.1115/1.1687380 ◽

2004 ◽

Vol 126 (2) ◽

pp. 188-193 ◽

Cited By ~ 3

Author(s):

Masahiro Watanabe ◽

Nobuyuki Kobayashi ◽

Yuichi Wada

Keyword(s):

Stability Analysis ◽

Natural Frequencies ◽

Theoretical Calculations ◽

Parametric Instability ◽

Fluid Pressure ◽

Internal Fluid ◽

Mathieu’S Equation ◽

Stability Maps ◽

Instability Regions ◽

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 are 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 are 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.

Download Full-text