Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

doi:10.1007/s10483-019-2543-5

Applied Mathematics and Mechanics (English Edition) ›› 2019, Vol. 40 ›› Issue (12): 1759-1776.doi: https://doi.org/10.1007/s10483-019-2543-5

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Lincong CHEN¹, Haisheng ZHU¹, J. Q. SUN²

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian Province, China;
2. School of Engineering, University of California, Merced, CA 95343, U.S.A.

收稿日期:2019-02-06 修回日期:2019-05-31 出版日期:2019-12-03 发布日期:2019-11-20
通讯作者: Lincong CHEN E-mail:lincongchen@hqu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11672111, 11332008, 11572215, and 11602089), the Program for New Century Excellent Talents in Fujian Province University, the Natural Science Foundation of Fujian Province of China (No. 2019J01049), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University (Nos. ZQNYX307 and ZQNYX505)

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Lincong CHEN¹, Haisheng ZHU¹, J. Q. SUN²

1. College of Civil Engineering, Huaqiao University, Xiamen 361021, Fujian Province, China;
2. School of Engineering, University of California, Merced, CA 95343, U.S.A.

Received:2019-02-06 Revised:2019-05-31 Online:2019-12-03 Published:2019-11-20
Contact: Lincong CHEN E-mail:lincongchen@hqu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11672111, 11332008, 11572215, and 11602089), the Program for New Century Excellent Talents in Fujian Province University, the Natural Science Foundation of Fujian Province of China (No. 2019J01049), and the Promotion Program for Young and Middle-Aged Teacher in Science and Technology Research of Huaqiao University (Nos. ZQNYX307 and ZQNYX505)

摘要/Abstract

摘要： The vibroimpact systems with bilateral barriers are often encountered in practice. However, the dynamics of the vibroimpact system with bilateral barriers is full of challenges. Few closed-form solutions were obtained. In this paper, we propose a novel method for random vibration analysis of single-degree-of-freedom (SDOF) vibroimpact systems with bilateral barriers under Gaussian white noise excitations. A periodic approximate transformation is employed to convert the equations of the motion to a continuous form. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form stationary probability density function (PDF) of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow. Finally, the versatility of the proposed approach is demonstrated by its application to two typical examples. Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

关键词: bilateral barrier, vibroimpact system, weighted residue method, iterative, random vibration

Abstract: The vibroimpact systems with bilateral barriers are often encountered in practice. However, the dynamics of the vibroimpact system with bilateral barriers is full of challenges. Few closed-form solutions were obtained. In this paper, we propose a novel method for random vibration analysis of single-degree-of-freedom (SDOF) vibroimpact systems with bilateral barriers under Gaussian white noise excitations. A periodic approximate transformation is employed to convert the equations of the motion to a continuous form. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form stationary probability density function (PDF) of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow. Finally, the versatility of the proposed approach is demonstrated by its application to two typical examples. Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

Key words: bilateral barrier, vibroimpact system, weighted residue method, iterative, random vibration

中图分类号:

Lincong CHEN, Haisheng ZHU, J. Q. SUN. Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(12): 1759-1776.

参考文献 39

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Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

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