Path integral solution of vibratory energy harvesting systems

doi:10.1007/s10483-019-2467-8

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (4): 579-590.doi: https://doi.org/10.1007/s10483-019-2467-8

• 论文 • 上一篇

Path integral solution of vibratory energy harvesting systems

Wenan JIANG¹, Peng SUN¹, Gangling ZHAO², Liqun CHEN³

1. Department of Engineering Mechanics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu Province, China;
2. School of Electronic and Electrical Engineering, Shangqiu Normal University, Shangqiu 476000, Henan Province, China;
3. Department of Mechanics, Shanghai University, Shanghai 200072, China

收稿日期:2018-05-02 修回日期:2018-09-16 出版日期:2019-04-01 发布日期:2019-04-01
通讯作者: Wenan JIANG E-mail:wenajiang@just.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11702119 and 51779111) and the Natural Science Foundation of Jiangsu Province of China (Nos. BK20170565 and BK20170581)

Path integral solution of vibratory energy harvesting systems

Wenan JIANG¹, Peng SUN¹, Gangling ZHAO², Liqun CHEN³

1. Department of Engineering Mechanics, Jiangsu University of Science and Technology, Zhenjiang 212003, Jiangsu Province, China;
2. School of Electronic and Electrical Engineering, Shangqiu Normal University, Shangqiu 476000, Henan Province, China;
3. Department of Mechanics, Shanghai University, Shanghai 200072, China

Received:2018-05-02 Revised:2018-09-16 Online:2019-04-01 Published:2019-04-01
Contact: Wenan JIANG E-mail:wenajiang@just.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11702119 and 51779111) and the Natural Science Foundation of Jiangsu Province of China (Nos. BK20170565 and BK20170581)

摘要/Abstract

摘要：

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 GaussLegendre 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).

关键词: elastoplasticity, principle of virtual work, mathematical programming, FEM, nonlinear energy harvester, probability density function (PDF), path integration

Abstract:

Key words: elastoplasticity, principle of virtual work, mathematical programming, FEM, probability density function (PDF), path integration, nonlinear energy harvester

中图分类号:

70K50

Wenan JIANG, Peng SUN, Gangling ZHAO, Liqun CHEN. Path integral solution of vibratory energy harvesting systems[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(4): 579-590.

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Path integral solution of vibratory energy harvesting systems

Path integral solution of vibratory energy harvesting systems

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