Path integral solution of vibratory energy harvesting systems
- 50 Downloads
A transition Fokker-Planck-Kolmogorov (FPK) equation describes the procedure of the probability density evolution whereby the dynamic response and reliability evaluation of mechanical systems could be carried out. The transition FPK equation of vibratory energy harvesting systems is a four-dimensional nonlinear partial differential equation. Therefore, it is often very challenging to obtain an exact probability density. This paper aims to investigate the stochastic response of vibration energy harvesters (VEHs) under the Gaussian white noise excitation. The numerical path integration method is applied to different types of nonlinear VEHs. The probability density function (PDF) from the transition FPK equation of energy harvesting systems is calculated using the path integration method. The path integration process is introduced by using the Gauss-Legendre integration scheme, and the short-time transition PDF is formulated with the short-time Gaussian approximation. The stationary probability densities of the transition FPK equation for vibratory energy harvesters are determined. The procedure is applied to three different types of nonlinear VEHs under Gaussian white excitations. The approximately numerical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulation (MCS).
Key wordsnonlinear energy harvester path integration probability density function (PDF)
Chinese Library ClassificationO324 O316
2010 Mathematics Subject Classification70K50
Unable to display preview. Download preview PDF.
- WANG, H. R., XIE, J. M., XIE, X., HU, Y. T., and WANG, J. Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode. Applied Mathematics and Mechanics (English Edition), 35, 229–236 (2014) https://doi.org/10.1007/s10483-014-1786-6 MathSciNetCrossRefGoogle Scholar
- HAJHOSSEINI, M. and RAFEEYAN, M. Modeling and analysis of piezoelectric beam with periodically variable cross-sections for vibration energy harvesting. Applied Mathematics and Mechanics (English Edition), 37, 1053–1066 (2016) https://doi.org/10.1007/s10483-016-2117-8 MathSciNetCrossRefzbMATHGoogle Scholar
- YANG, Y. G. and XU, W. Stochastic analysis of monostable vibration energy harvesters with fractional derivative damping under Gaussian white noise excitation. Nonlinear Dynamics, 1–10 (2018)Google Scholar