Influence of discretely arranged longitudinal ribs on the stability and vibrations of open circular cylindrical shells

Abstract

Open cylindrical shells reinforced with quasiregular sets of longitudinal ribs and hinged at all edges are considered. The effect of the discrete arrangement and number of ribs on the critical stresses that cause instability under longitudinal compression and on the minimum natural frequencies of vibrations is examined. Numerical results are analyzed Keywords: open cylindrical shell, quasiregular arrangement of ribs, critical stress, minimum natural frequencies, minimum resonance frequencies, parametric resonance Introduction. The systematic research of the stability and vibrations of open circular cylindrical shells reinforced with quasiregular sets of longitudinal ribs was apparently initiated in [8], where the exact solutions were obtained for shells hinged at all edges. A set of ribs will be considered quasiregular if all the geometrical and mechanical characteristics of all ribs are equal, the ribs are equally spaced, and the distance from the extreme ribs to the longitudinal edges of the shell are equal to half the distance between ribs. The stability of closed shells reinforced with such sets of circular ribs was analyzed in [3] using an approximate problem formulation. Some other problems for open shells reinforced with either regular or quasiregular sets of ribs were solved in [2,[5][6][7][8]. Similar problems were also addressed in [9,10].In what follows, we will discuss how the discrete arrangement and number of ribs affect the stability of shells subjected to longitudinal compression and vibrations (natural vibrations and resonant states caused by longitudinal compressive stresses close to critical, the associated frequencies being called resonant).