Stability analysis of cylindrical shell in axial flow: A DQ-based approach and an instability prediction formula

A numerical approach in applying the differential quadrature method (DQM) to the stability of cylindrical shells subjected to axial flow is presented. Donnell–Mushtari shell equation and unsteady Bernoulli’s equation are respectively applied to model the shell motion and solve the fluid force. DQM discretizes the shell equation and its boundary conditions. Lagrange interpolation and trigonometric series are applied to solve the fluid force at the non-uniform grid points. Then the fluid–structure interaction equation based on DQM is established. The modal and fluid-induced instability analysis is carried out by eigenvalue analysis. The accuracy of the present method is verified via comparison with other theories and commercial software. The relationship between the shell frequencies and critical flow speeds is found, then a formula for predicting the critical flow speed with comprehensive accuracy validation is first derived. It can predict the critical flow speed using the shell’s frequencies in air and fluid but not through the traditional eigenvalue-based analysis. A brief theoretical explanation of this formula is given by the analysis of the principal mass and stiffness of the system. It may have great potential application for a vibrating structure with closed boundaries in axial flow.