مقایسه حل عددی و تحلیلی معادلات حاکم بر ارتعاشات تیر پیزوالکتریک برداشت کننده انرژی تحت جریان گردابی

In this article, the effectiveness of the perturbation theory method in predicting the dynamic behavior of the energy harvesting beam under the effect of vortex shedding is investigated. For this purpose, a circular cylinder is attached to the end of a cantilever beam coated by a piezoelectric layer, and the fluid flow is passed on it parallel to the beam. Due to the interaction of the structure and fluid , the oscillating vortices is generated in the back of the cylinder, and the beam is oscillated perpendicular to the fluid flow. The aerodynamic drag is modeled by the modified Van der Pol oscillator equation. Hamilton's principle is also used to derive the equations of motion. After obtaining the free vibration mode shape, it is used as a comparison function in the assumed mode method and equations are discretized using Euler-Lagrange equation. The discretized equations are solved by both numerical and analytical methods of perturbation theory and the results are compared. The results show that the analytical method presented in this article can well predict the dynamics of energy harvesting.