Parametric instability analysis of multi-segment conical shells under periodic spin speed

This study is the first to investigate the parametric instability of multi-segment conical shells (MSCSs) under periodic spin speed. The artificial spring simulates the general boundary constraints and the constraints between shell segments. Based on Donnell’s shell theory and the Lagrange equation, the dynamic equations for MSCSs under periodic spin speed are formulated. Parametric instability analysis is conducted based on Floquet theory. The effects of circumferential wave number, boundary conditions, spin speed, and cone angle on the stability of single-segment conical shells under periodic spin speed are examined. As the spin speed increases, the instability region shifts towards higher frequencies, and its area substantially increases. Additionally, the effects of cone angle and geometric configurations on the stability of MSCSs are investigated. The results indicate that for variable cone-angle MSCSs, reducing the cone angle of the second segment can improve stability. For stepped MSCSs, a configuration with thickened ends effectively reduces the instability region area and improves structural stability. For MSCSs with thickened both ends, the step position has a minimal effect on the area and starting point of the instability region, and the differences in instability region areas among various step thickness ratios are also negligible.