|
|
|
Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems |
| Wen-Wei Ye(叶文伟)1,2, Lin-Cong Chen(陈林聪)1,2,†, Zi Yuan(原子)1,2, Jia-Min Qian(钱佳敏)1,2, and Jian-Qiao Sun(孙建桥)3 |
1 College of Civil Engineering, Huaqiao University, Xiamen 361021, China;
2 Key Laboratory for Intelligent Infrastructure and Monitoring of Fujian Province, Huaqiao University, Xiamen 361021, China;
3 Department of Mechanical Engineering School of Engineering, University of California Merced, CA 95343, USA |
|
|
|
|
Abstract The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom (DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker-Plank-Kolmogorov (FPK) equation is obtained by using radial basis function (RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations (MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.
|
Received: 14 October 2022
Revised: 06 December 2022
Accepted manuscript online: 27 December 2022
|
|
PACS:
|
05.10.-a
|
(Computational methods in statistical physics and nonlinear dynamics)
|
| |
05.10.Gg
|
(Stochastic analysis methods)
|
| |
05.10.Ln
|
(Monte Carlo methods)
|
| |
05.40.-a
|
(Fluctuation phenomena, random processes, noise, and Brownian motion)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 12072118), the Natural Science Funds for Distinguished Young Scholar of the Fujian Province, China (Grant No. 2021J06024), and the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005). |
Corresponding Authors:
Lin-Cong Chen
E-mail: lincongchen@hqu.edu.cn
|
Cite this article:
Wen-Wei Ye(叶文伟), Lin-Cong Chen(陈林聪), Zi Yuan(原子), Jia-Min Qian(钱佳敏), and Jian-Qiao Sun(孙建桥) Semi-analytical steady-state response prediction for multi-dimensional quasi-Hamiltonian systems 2023 Chin. Phys. B 32 060506
|
[1] Xu W, Wang L, Feng J Q, Qian Y and Han P2018 Chin. Phys. B 27 110503
[2] Ghany H A2014 Chin. Phys. Lett. 31 60503
[3] Zhu W Q, Cai G Q and Lin Y K1992 IUTAM Symposium, 1991, Turin, Italy, p. 543
[4] Zhu W Q2006 Appl. Mech. Rev. 59 230
[5] Huang Z L and Jin X L2009 Sci. China Ser. E-Technol. Sci. 52 2424
[6] Zhu W Q and Huang Z L2001 Int. J. Nonlinear Mech. 36 39
[7] Ying Z G and Zhu W Q2000 Int. J. Nonlinear Mech. 35 837
[8] Huang Z L and Zhu W Q2000 J. Sound Vib. 230 709
[9] Zhu W Q and Yang Y Q1996 J. Appl. Mech. 63 493
[10] Zhu W Q and Deng M L2004 J. Sound Vib. 274 1110
[11] Zhu W Q, Huang Z L and Suzuki Y2001 Int. J. Nonlinear Mech. 36 773
[12] Jia W T and Zhu W Q2014 Nonlinear Dynam. 76 1271
[13] Zeng Y and Zhu W Q2010 J. Appl. Mech. 78 021002
[14] Deng M L and Zhu W Q2007 J. Sound Vib. 305 783
[15] Huang Z L and Zhu W Q2004 Probabilist. Eng. Mech. 19 219
[16] Wang J L, Leng X L and Liu X B2021 Chin. Phys. B 30 60501
[17] Sun J Q, Xiong F R, Schütze O and Hernández C2018 Cell mapping methods (Singapore: Springer)
[18] Er G K2000 Int. J. Nonlinear Mech. 35 69
[19] Guo S S, Er G K and Lam C C2014 Nonlinear Dynam. 77 597
[20] Zhang H, Xu Y, Liu Q, Wang X L and Li Y G2022 Nonlinear Dynam. 108 4029
[21] Zhang Y an Yuen K V2022 Int. J. Nonlinear Mech. 147 104202
[22] Xu Y, Zhang H, Li Y G, Zhou K, Liu Q and Kurths J2020 Chaos 30 13133
[23] Zio E2013 Monte carlo simulation: The method (London: Springer) pp. 19-58
[24] Hirvijoki E, Kurki-Suonio T, äkäslompolo S, Varje J, Koskela T and Miettunen J2015 J. Plasma Phys. 81 435810301
[25] Chen L C and Sun J Q2020 Appl. Math. Mech. 41 967
[26] Li J Y, Wang Y, Jin X L and Huang Z L2021 Nonlinear Dynam. 105 1297
[27] Yang J N, Liu J G and Guo Q2018 Acta Phys. Sin. 67 048901 (in Chinese)
[28] Wang X Y, Wang Y, Qin X M, Li R and Eustace J2018 Chin. Phys. B 27 100504
[29] Jin L, Wang X J, Zhang Y and You J W2018 Chin. Phys. B 27 98901
[30] Luo S L, Gong K, Tang C S and Zhou J2017 Acta Phys. Sin. 66 188902 (in Chinese)
[31] Sun J C2016 Chin. Phys. Lett. 33 100503
[32] Fang P J, Zhang D M and He M H2015 Chin. Phys. Lett. 32 88901
[33] Gao S G, Dong H R, Sun X B and Ning B2015 Chin. Phys. B 24 10501
[34] Chen H, Kong L and Leng W J2011 Appl. Soft Comput. 11 855
[35] Mai-Duy N and Tanner R I2005 Int. J. Numer. Meth. Eng. 63 1636
[36] Li J Y, Luo S W, Qi Y J and Huang Y P2003 Neural Netw. 16 729
[37] Wang X, Jiang J, Hong L and Sun J Q2022 J. Vib. Acoust. 144 051014
[38] Wang X, Jiang J, Hong L and Sun J Q2022 Int. J. Dynam. Control 10 1385
[39] Er G K2011 Ann. Phys. 523 247
[40] Nelles O2020 Nonlinear system identification, 2nd edn. (Cham: Springer Nature) pp. 831-891
[41] Chen J B and Li J2008 Int. J. Numer. Meth. Eng. 74 1988
[42] Zhu W Q, Huang Z L and Yang Y Q1997 J. Appl. Mech. 64 975 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
