Flow-Induced Vibration of Flexible Disk Subjected to Swirling Fluid Flow

Abstract

This paper deals with theoretical stability analysis and experimental study of flow-induced vibration of a flexible disk subjected to swirling fluid flow in a confined fluid. The flexible disk subjected to swirling fluid flow undergoes flow-induced vibration when the swirling fluid speed becomes high. The flow-induced vibration occurs due to the interaction between the out-of-plane motion of the flexible disk and swirling fluid flow generated around the disk. In this system, the swirling fluid flow is generated by a rigid disk rotating near the flexible disk. In the theoretical stability analysis, the basic equations of the swirling fluid flow around the flexible disk are based on the Navier-Stokes equations integrated over the gap width between the flexible disk and the rotating rigid disk. The structural equation of the flexible disk is based on the Kirchhoff-Love’s plate model. The equations of the fluid-structure coupling system are derived taking account of the moving boundary conditions of the flexible disk. The equations of the fluid-structure coupling motion are linearized for small out-of-plane motion of the flexible disk near the equilibrium state, and the solutions of the equations are obtained using the multi-modal expansion approximation and the Galerkin’s method. Modal frequencies and modal damping ratios of the system are obtained as a function of the rotational speed of the rotating rigid disk. As a result, it is clarified that unstable vibration occurs in the flexible disk due to the swirling fluid flow. And the critical rotational speed at which the unstable vibration occurs and vibration modes are clarified theoretically and experimentally.