The stability of finite length circular cross-section pipes conveying inviscid fluid

This paper is concerned with the linear stability of the system composed of a finite, thin elastic tube, replacing a section of an infinite rigid pipe, which conveys inviscid compressible fluid in uniform subsonic motion, by finding asymptotic forms for the fluid pressures. The analysis is based on linearized, potential flow theory, the Flugge-Kempner shell equation and Galerkin's method. Results are presented for the case of a simply-supported connection between the flexible and the rigid tube. For tubes of large length to radius ratio, the analysis demonstrates the connection between the finite length standing wave instability and the travelling wave instability of infinite tubes. The relationship between the “beam mode” and higher mode instabilities is made clear and discussed in some detail. The wide range of applicability of the asymptotic results is demonstrated by comparison with previously published numerical work. The small length to radius forms are also given and higher order terms are obtained in both limits.