Dynamic Stability Analysis of Periodic Loaded Rotating Conical Shells using Floquet Exponent Method

Abstract

The dynamic stability/parametric stability characteristics of rotating truncated conical shells under periodic axial loads is investigated. The partial differential equations of rotating conical shells are transformed into Mathieu-Hill ordinary differential equations based on Haar wavelet discretization method. In general, Bolotin method can be used to analyze the stability of parametrically excited systems. This method is a boundary tracing method, and the stability boundary can be easily obtained. However, Bolotin method is not suitable for analyzing the stability of gyroscopic system under parametric excitation, because this method is not satisfied with the hypothesis of the Floquet multiplier for gyroscopic system. In this article, Floquet exponent method, which is widely used in parametric excitation system, is used to analyze the parametric stability of rotating conical shells. The correctness of the proposed model and stability analysis method is verified by comparing with the results of the other literature. The results show that due to the rotational effect, only the combination instability zone exists in the rotating shell, but no principal instability zone is found. When the circumferential wave number is 1 and other wave numbers are compared, it is found that the rotational speed has different effects on the stability under the two circumferential wave numbers. Communicated by Francesco Tornabene.