A parametric frequency domain approach to analysis and design of critical design parameters of nonlinear energy harvesting systems: Parametric output spectrum and power generation functions. (1st December 2022) - Li, Meng; Jing, Xingjian
Graphical abstract: Highlights: It is for the first time to provide explicit expressions for power generations with respect to structural parameters of a nonlinear energy harvesting system. Vibration output response and power generation functions are established into unique linear and nonlinear characteristic output spectrum (lnCOS) functions. The lnCOS functions are directly related to critical design parameters and such advantages cannot be achieved in a traditional way. This paper presents an efficient approach to the analysis and design of nonlinear systems with respect to design parameters. Abstract: Nonlinear energy harvesting systems have been extensively studied which usually involve quite a few critical design parameters to determine. However, a straightforward parametric design method for such a purpose is still far from developed. Traditional methods with harmonic balance or numerical simulation usually cannot reveal a straightforward relationship between the energy harvesting performance and system parameters, and in most cases face relatively large computational costs during parametric studies. To this aim, a novel Volterra series-based frequency domain method is established in this study with respect to a typical nonlinear harvesting system. A concise parametric characteristic approach, namely the linear and nonlinear characteristic output spectrum (lnCOS) method, is thus proposed to achieve parametric characteristic expression for the nonlinear output frequency response and power generation function (PGF) of the system, referred to as the lnCOS function and the Parametric-PGF respectively. Compared with the harmonic balance method, the vibration responses/power generation can be obtained in a more straightforward way without solving complex algebraic equations, and the lnCOS method directly links the power outputs to critical system parameters in a concise parametric way. It is for the first time to provide explicit expressions for vibration responses and power generations with respect to structural parameters of a nonlinear energy harvesting system, which cannot be achieved in a traditional way. Based on the obtained explicit expressions of the lnCOS function/Parametric-PGF, the sensitivity analysis of vibration response and power generation with respect to structural parameters can be directly performed. Our work provides an efficient way to characterize both the linear and nonlinear effects on a nonlinear energy harvesting system and demonstrates an efficient approach to the analysis and design of nonlinear energy harvesting systems.