Nonlinear dynamic analysis for a cantilever beam with a tip mass piezoelectric harvester under parametric and direct excitations with multi-scale method

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (19) : 69-77.

XIA Guanghui, WANG Jianguo

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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.

Key words

parametric excitation / direct excitation / tip mass / piezoelectric energy harvesting / geometric nonlinearity / damping nonlinearity / multi-scale method

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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[J]. Journal of Vibration and Shock, 2020, 39(19): 69-77

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