Nonlinear dynamic analysis for a cantilever beam with a tip mass piezoelectric harvester under parametric and direct excitations with multi-scale method
XIA Guanghui, WANG Jianguo
School of Civil and Hydraulic Engineering, Hefei University of Technology, Hefei 230009, China
Abstract：Here, considering geometric nonlinearity, damping nonlinearity and axial inextensibility of beams, the electro-mechanical coupled nonlinear dynamic equation of a cantilever beam with a tip mass piezoelectric energy harvester under parametric and direct excitations was established by using Hamilton variational principle. In fact, the piezoelectric energy harvester is a piezoelectric bimorph cantilever beam structure. Using Galerkin method, the electro-mechanical coupled nonlinear dynamic equation was reduced to an electro-mechanical coupled nonlinear Mathieu-Duffing equation. In order to study the first-order resonance response of the energy harvester, the multi-scale method was used to obtain the analytical expressions for beam deflection, output voltage and output power of the energy harvester. These analytical expressions were used to study influences of impedance, damping coefficient and tip mass under parametric and direct excitations on performances of the piezoelectric energy harvester.
夏光辉,王建国. 参数和直接激励下附加端部质量块悬臂梁压电俘能器的多尺度法非线性分析[J]. 振动与冲击, 2020, 39(19): 69-77.
XIA Guanghui, WANG Jianguo. Nonlinear dynamic analysis for a cantilever beam with a tip mass piezoelectric harvester under parametric and direct excitations with multi-scale method. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(19): 69-77.
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