An analytical framework for the design and comparative analysis of galloping energy harvesters under quasi-steady aerodynamics

This paper presents a generalized formulation, analysis, and optimization of energy harvesters subjected to galloping and base excitations. The harvester consists of a cantilever beam with a bluff body attached at the free end. A nondimensional lumped-parameter model which accounts for the combined loading and different electro-mechanical transduction mechanisms is presented. The aerodynamic loading is modeled using the quasi-steady assumption with polynomial approximation. A nonlinear analysis is carried out and an approximate analytical solution is obtained. A dimensional analysis is performed to identify the important parameters that affect the system's response. The analysis of the response is divided into two parts. The first treats a harvester subjected to only galloping excitations. It is shown that, for a given shape of the bluff body and under quasi-steady flow conditions, the harvester's dimensionless response can be described by a single universal curve irrespective to the geometric, mechanical, and electrical design parameters of the harvester. In the second part, a harvester under concurrent galloping and base excitations is analyzed. It is shown that, the total output power depends on three dimensionless loading parameters; wind speed, base excitation amplitude, and excitation frequency. The response curves of the harvester are generated in terms of the loading parameters. These curves can serve as a complete design guide for scaling and optimizing the performance of galloping-based harvesters.

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