Tapered galloping energy harvester for power enhancement and vibration reduction

The cantilever beam was commonly designed with uniform cross-section for the galloping energy harvesters. To improve its performance, two tapered galloping energy harvesters are proposed in this work. In the first tapered design, the beam's thickness is linearly changed with constant width. In the second tapered design, both the beam's thickness and width are linearly varied. A generalized fluid-structure-electricity coupled distributed-parameter model is established by the Hamilton principle and Gauss law for the tapered galloping energy harvesters. By means of the properties of the Bessel function and the modal analysis method, the exact analytical modal shape of the tapered beam is derived. The effects of the tapered ratio on the beam mass, bending stiffness, electrical field, electromechanical coupling, and piezoelectric capacitance are accounted by the proposed theoretic model. Finite element analyses and wind tunnel experiments are performed, and the results show good agreement with the proposed beam modal shape, corresponding natural frequency and harvested power. The tapered ratio is tuned to realize the even distribution of the piezoelectric strain along the beam length. Compared with the uniform design, the tapered galloping energy harvester exhibits merits on up to 61% power enhancement and 44% vibration deduction.