تحلیل پایداری تیر دوسرگیردار متصل به یک جفت سیلندر دمبل شکل تحت تحریک جریان گردابی

In this article, the stability analysis of vortex induced vibration for a clamped-clamped beam with a pair of cylinders as a dumbbell-shaped attached to its middle part, has been studied. A piezoelectric layer is assumed on the beam with the purpose of collecting the electric current from the vibrations caused by the vortex induced vibration. The motion equations are written using Newton's second law and the aerodynamic force is modeled by the modified Van der Pol oscillator equation. The free vibration mode shapes are obtained using the Glerkin method, and the equations of motion are separated by the Glerkin method and stability analysis is performed on them. In this paper, a theoretical relationship is presented to predict the region where the linear system becomes unstable. The results show that the resulting relationship can predict the luck in domain well, and as a result, the complexities of numerical solution to find the luck in domain can be avoided.