Some new advance on the research of stochastic non-smooth systems

doi:10.1088/1674-1056/27/11/110503

中国物理B ›› 2018, Vol. 27 ›› Issue (11): 110503-110503.doi: 10.1088/1674-1056/27/11/110503

所属专题： SPECIAL TOPIC — 80th Anniversary of Northwestern Polytechnical University (NPU)

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Some new advance on the research of stochastic non-smooth systems

Wei Xu(徐伟), Liang Wang(王亮), Jinqian Feng(冯进钤), Yan Qiao(乔艳), Ping Han(韩平)

1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2 School of Science, Xi'an Polytechnical University, Xi'an 710048, China

收稿日期:2018-07-16 修回日期:2018-09-19 出版日期:2018-11-05 发布日期:2018-11-05
通讯作者: Liang Wang E-mail:liangwang1129@nwpu.edu.cn
基金资助:
Projected supported by the National Natural Science Foundation of China (Grant No. 11472212), the Natural Science Basic Research Plan in Shaanxi Province, China (Grant No. 2018JM1043), and the Fundamental Research Fund for the Central Universities, China (Grant No. 3102018ZY043).

Some new advance on the research of stochastic non-smooth systems

Wei Xu(徐伟)¹, Liang Wang(王亮)¹, Jinqian Feng(冯进钤)², Yan Qiao(乔艳)¹, Ping Han(韩平)¹

1 Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
2 School of Science, Xi'an Polytechnical University, Xi'an 710048, China

Received:2018-07-16 Revised:2018-09-19 Online:2018-11-05 Published:2018-11-05
Contact: Liang Wang E-mail:liangwang1129@nwpu.edu.cn
Supported by:
Projected supported by the National Natural Science Foundation of China (Grant No. 11472212), the Natural Science Basic Research Plan in Shaanxi Province, China (Grant No. 2018JM1043), and the Fundamental Research Fund for the Central Universities, China (Grant No. 3102018ZY043).

摘要/Abstract

摘要：

Due to the extensive applicability in real life, the non-smooth system with random factors attracted much attention in past two decades. A lot of methods and techniques have been proposed to research these systems by scholars. In this paper, we will summarize some new research advance on the stochastic non-smooth systems. The existing results about the stochastic vibro-impact system, the stochastic friction system, and the stochastic hysteretic system are introduced respectively. Some conclusions and outlook are given at the end.

关键词: non-smooth system, random factor, vibro-impact system, friction system, hysteretic system

Abstract:

Key words: non-smooth system, random factor, vibro-impact system, friction system, hysteretic system

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.45.-a (Nonlinear dynamics and chaos)

徐伟, 王亮, 冯进钤, 乔艳, 韩平. Some new advance on the research of stochastic non-smooth systems[J]. 中国物理B, 2018, 27(11): 110503-110503.

Wei Xu(徐伟), Liang Wang(王亮), Jinqian Feng(冯进钤), Yan Qiao(乔艳), Ping Han(韩平). Some new advance on the research of stochastic non-smooth systems[J]. Chin. Phys. B, 2018, 27(11): 110503-110503.

参考文献 119

[1]	Luo G W and Xie J H 2004 Periodic Motion and Bifurcation of Vibro-impact System (Beijing:Science Press) (in Chinese)
[2]	Jin D P and Hu H Y 2005 Impact Vibration and Control (Beijing:Science Press) (in Chinese)
[3]	Nayak P R 1972 J. Sound Vib. 22 297 doi: 10.1016/0022-460X(72)90168-X
[4]	Jing H S and Sheu K C 1990 J. Sound Vib. 141 363 doi: 10.1016/0022-460X(90)90632-A
[5]	Jing H S and Young M 1990 Earthq. Eng. Struct. D 19 789 doi: 10.1002/eqe.4290190602
[6]	Lin S Q and Bapat C N 1993 J. Sound Vib. 163 407 doi: 10.1006/jsvi.1993.1178
[7]	Feng Q and Pfeiffer F 1998 J. Sound Vib. 215 439 doi: 10.1006/jsvi.1998.1646
[8]	Feng Q and He H 2003 Eur. J. Mech. A/Solid 22 267 doi: 10.1016/S0997-7538(03)00015-9
[9]	Luo G W and Xie J H 2001 Physica D 148 183 doi: 10.1016/S0167-2789(00)00170-6
[10]	van de Wouw N, de Kraker A, van Campen D H and Nijmeijer H 2003 Int. J. Nonlin. Mech. 38 767 doi: 10.1016/S0020-7462(01)00132-9
[11]	Huang Z L, Liu Z H and Zhu W Q 2004 J. Sound Vib. 275 223 doi: 10.1016/j.jsv.2003.06.007
[12]	Dimentberg M F and Iourtchenko D V 2004 Nonlinear Dynam. 36 229 doi: 10.1023/B:NODY.0000045510.93602.ca
[13]	Namachchivaya N S and Park J H 2005 J. Appl. Mech. 72 862 doi: 10.1115/1.2041660
[14]	Feng J Q, Xu W, Rong H W and Wang R 2009 Int. J. Nonlin. Mech. 44 51 doi: 10.1016/j.ijnonlinmec.2008.08.013
[15]	Feng J Q, Xu W and Wang R 2008 J. Sound Vib. 309 730 doi: 10.1016/j.jsv.2007.07.070
[16]	Rong H W, Wang X D, Xu W and Fang T 2009 J. Sound Vib. 327 173 doi: 10.1016/j.jsv.2009.06.006
[17]	Li C, Xu W, Wang L and Li D X 2013 Chin. Phys. B 22 110205 doi: 10.1088/1674-1056/22/11/110205
[18]	Li C, Xu W, Feng J Q and Wang L 2013 Physica A 392 1269 doi: 10.1016/j.physa.2012.11.053
[19]	Gu X D and Zhu W Q 2014 J. Sound Vib. 333 2632 doi: 10.1016/j.jsv.2013.12.027
[20]	Wang D L, Xu W and Zhao X R 2016 Chaos 26 033103 doi: 10.1063/1.4942918
[21]	Zhao X R, Xu W, Yang Y G and Wang X Y 2016 Commun. Nonlinear Sci. 35 166 doi: 10.1016/j.cnsns.2015.11.008
[22]	Wang D L, Xu W, Gu X D and Yang Y G 2016 Nonlinear Dynam. 86 891 doi: 10.1007/s11071-016-2931-x
[23]	Yang G D, Xu W, Gu X D and Huang D M 2016 Chaos Solitons Fract. 87 125 doi: 10.1016/j.chaos.2016.03.017
[24]	Xiao Y W, Xu W and Wang L 2016 Chaos 26 033110 doi: 10.1063/1.4943753
[25]	Yang Y G, Xu W, Sun Y H and Xiao Y W 2017 Commun. Nonlinear Sci. 42 62 doi: 10.1016/j.cnsns.2016.05.004
[26]	Xiao Y W, Xu W and Yang Y G 2016 Nonlinear Dynam 85 1955 doi: 10.1007/s11071-016-2808-z
[27]	Yang G D, Xu W, Jia W T and He M J 2016 Commun. Nonlinear. Sci. 33 19 doi: 10.1016/j.cnsns.2015.08.003
[28]	Wang D L, Xu W, Gu X D and Pei H Q 2016 Int. J. Nonlin. Mech. 86 55 doi: 10.1016/j.ijnonlinmec.2016.08.001
[29]	Yang G D, Xu W, Feng J Q and Gu X D 2015 Nonlinear Dynam. 82 1797 doi: 10.1007/s11071-015-2278-8
[30]	Xu W, Yang G D and Yue X L 2016 Acta Phys. Sin. 65 210501(in Chinese)
[31]	Liu L, Xu W, Yue X L, Han Q 2017 Chaos Solitons Fract. 104 748 doi: 10.1016/j.chaos.2017.09.034
[32]	Liu D, Li M and Li J L 2018 Nonlinear Dynam. 91 1261 doi: 10.1007/s11071-017-3943-x
[33]	Xie X F, Li J L, Liu D and Guo R 2017 Acta Mech. 228 1153 doi: 10.1007/s00707-016-1761-8
[34]	Xu M, Wang Y, Jin X L, Huang Z L and Yu T X 2013 Int. J. Nonlin. Mech. 52 26 doi: 10.1016/j.ijnonlinmec.2012.12.010
[35]	Xu M, Wang Y, Jin X L and Huang Z L 2014 J. Sound Vib. 333 189 doi: 10.1016/j.jsv.2013.09.008
[36]	Xu M 2018 Appl. Math. Model. 54 284 doi: 10.1016/j.apm.2017.09.036
[37]	Feng J Q, Xu W and Wang R 2006 Acta Phys. Sin. 55 5733(in Chinese)
[38]	Li G J, Xu W, Wang L and Feng J Q 2008 Acta Phys. Sin. 57 2107(in Chinese)
[39]	Wang L, Xu W, Li G J and Li D X 2009 Chaos Solitons Fract. 41 2075 doi: 10.1016/j.chaos.2008.08.013
[40]	Wang L, Yue X L, Sun C Y and Xu W 2013 Nonlinear Dynam. 71 597 doi: 10.1007/s11071-012-0684-8
[41]	Wang L, Huang M, Xu W and Jin L M 2018 Nonlinear Dynam. 92 1147 doi: 10.1007/s11071-018-4114-4
[42]	Feng J Q and Xu W 2009 Appl. Math. Comput. 213 577
[43]	Xu W, Feng J Q and Rong H W 2009 Nonlinear Anal. Theor. 71 418 doi: 10.1016/j.na.2008.10.120
[44]	Kumar P, Narayanon S and Gupta S 2016 Nonlinear Dynam. 85 439 doi: 10.1007/s11071-016-2697-1
[45]	Huang D M, Xu W, Xie W X and Han Q 2015 Chin. Phys. B 24 040502 doi: 10.1088/1674-1056/24/4/040502
[46]	de Souza S L T, Caldas I L and Viana R L 2007 Chaos Soliton Fract. 32 74
[47]	Wang L, Xu W and Li Y 2008 Chin. Phys. B 17 2446 doi: 10.1088/1674-1056/17/7/018
[48]	Matias M A and Guemez 1994 Phys. Rev. Lett. 72 1455 doi: 10.1103/PhysRevLett.72.1455
[49]	Wang L, Xu W and Li Y 2008 Phys. Lett. A 372 530
[50]	Iourtchenko D V and Song L L 2006 Int. J. Nonlin. Mech. 41 447 doi: 10.1016/j.ijnonlinmec.2005.10.001
[51]	Lei H, Gan C B and Xie C Y 2010 J. Eng. Mech. 27 1
[52]	Gan C B and Lei H 2011 J. Sound Vib. 330 2174 doi: 10.1016/j.jsv.2010.09.025
[53]	Mo E and Naess A 2009 J. Comput. Nonlin. Dyn. 4 034501 doi: 10.1115/1.3124780
[54]	Zhu H T 2014 Int. J. Nonlin. Mech. 65 53 doi: 10.1016/j.ijnonlinmec.2014.05.003
[55]	Zhu H T 2015 Nonlinear Dynam. 82 1001 doi: 10.1007/s11071-015-2213-z
[56]	Kumar P, Narayanan S and Gupta S 2017 Int. J. Mech. Sci. 127 103 doi: 10.1016/j.ijmecsci.2016.12.009
[57]	Wang L, Ma S C, Sun C Y, Jia W T and Xu W 2018 J. Appl. Mech. 85 054502 doi: 10.1115/1.4039436
[58]	Hartog J P D 1930 Phil. Mag. 9 801 doi: 10.1080/14786443008565051
[59]	Ding W C, Zhang Y Q and Zhang Q S 2008 Eng. Mech. 25 10(in Chinese)
[60]	Ding Q and Zhai H M 2013 Adv. Mech. 1 112(in Chinese)
[61]	Brouwers J T H 1982 Ocean Eng. 3 235
[62]	Pollak E and Berezhkovskii A M 1993 J. Chem. Phys. 99 1344 doi: 10.1063/1.465379
[63]	Feng Q and Zhang X 2001 Appl. Math. Mech. 22 956
[64]	Feng Q 2003 Comput. Method Appl. M. 192 2339 doi: 10.1016/S0045-7825(03)00241-X
[65]	Feng Q 2008 Int. J. Appl. Math. 1 38
[66]	Qiao S, Beloiu D M and Ibrahim R A 2004 Nonlinear Dynam. 36 361 doi: 10.1023/B:NODY.0000045512.75470.f4
[67]	Gaus N and Proppe C 2011 Symposium on Nonlinear Stochastic Dynamics and Control (Dordrecht:Springer)
[68]	Wang Y, Jin X L and Huang Z L 2014 The 7th International Conference on Computational Stochastic Mechanics, Santorini
[69]	Sun J, Xu W and Lin Z 2018 Commun. Nonlinear Sci. 54 1 doi: 10.1016/j.cnsns.2017.05.014
[70]	Sun J, Xu W and Lin Z 2017 Appl. Math. Mech. 1 010
[71]	Sun J Q 1995 J. Sound Vib. 180 785 doi: 10.1006/jsvi.1995.0115
[72]	Baule A, Touchette H and Cohen E G D 2011 Nonlinearity 24 351 doi: 10.1088/0951-7715/24/2/001
[73]	Chen Y and Just W 2014 Phys. Rev. E 89 022103
[74]	Gennes P G 2005 J. Stat. Phys. 119 953 doi: 10.1007/s10955-005-4650-4
[75]	Tian Y P, Wang Y and Jin X L 2014 Smart Mater. Struct. 23 095001 doi: 10.1088/0964-1726/23/9/095001
[76]	Green P L, Worden K and Sims N D 2013 J. Sound Vib. 332 4696 doi: 10.1016/j.jsv.2013.04.024
[77]	Awrejcewicz J and Olejnik P 2005 Appl. Mech. Rev. 58 389 doi: 10.1115/1.2048687
[78]	Astrom K J and Wit C C 2008 IEEE Control Syst. Mag. 28 101
[79]	Berger E J 2002 Appl. Mech. Rev. 55 535 doi: 10.1115/1.1501080
[80]	Olsson H, Astrom K J and Wit C C 1998 Eur. J. Control 4 176 doi: 10.1016/S0947-3580(98)70113-X
[81]	Wang Y, Luan X L, Jin X L and Huang Z L 2016 Arch. Appl. Mech. 86 1827 doi: 10.1007/s00419-016-1147-3
[82]	Jin X L, Wang Y and Huang Z L 2018 Int. J. Nonlin. Mech. 104 1
[83]	Spencer B F, Dyke S J, Sain M K and Carlson J D 1997 ASCE J. Eng. Mech. 123 230 doi: 10.1061/(ASCE)0733-9399(1997)123:3(230)
[84]	Hughes D and Wen J T 1997 Smart Mater. Struct. 6 287 doi: 10.1088/0964-1726/6/3/007
[85]	Majima S, Kodama K and Hasegawa T 2001 IEEE T. Contr. Syst. T. 9 54 doi: 10.1109/87.896745
[86]	Yu Y H, Naganathan N and Dukkipati R 2002 Mech. Mach. Theory 37 49 doi: 10.1016/S0094-114X(01)00065-9
[87]	Krasnoselski M A and Pokrovskii A V 1989 Systems with Hysteresis (Berlin:Springer)
[88]	Caughey T K 1960 ASME J. Appl. Mech. 27 649 doi: 10.1115/1.3644077
[89]	Caughey T K 1971 Adv. Appl. Mech. 11 209 doi: 10.1016/S0065-2156(08)70343-0
[90]	Bouc R 1967 Proceedings of the 4th Conference on Non-linear Oscillation, Prague, Czechoslovakia
[91]	Lubarda V, Sumarac D and Krajcinovic D 1993 Eur. J. Mech. A-Solid 12 445
[92]	Mayergoyz I D 1991 Mathematical Models of Hysteresis (New York:Springer)
[93]	Noori M, Dimentberg M and Hou Z 1995 Probab. Eng. Mech. 10 161 doi: 10.1016/0266-8920(95)00013-O
[94]	Lin Y K and Cai G Q 1995 Probabilistic Structural Dynamics:Advanced Theory and Applications (New York:McGraw-Hill)
[95]	Ni Y Q, Ying Z G, Ko J M and Zhu W Q 2002 Int. J. Nonlin. Mech. 37 1407 doi: 10.1016/S0020-7462(02)00026-4
[96]	Ying Z G, Zhu W Q and Ni Y Q 2002 J. Sound Vib. 254 91 doi: 10.1006/jsvi.2002.4086
[97]	Jin X L, Wang Y and Huang Z L 2015 Soil Dyn. Earthq. Eng. 73 58 doi: 10.1016/j.soildyn.2015.02.015
[98]	Spanos Pol D, ASCE1 F, Cacciola P and Muscolino G 2004 J. Eng. Mech. 130 1257 doi: 10.1061/(ASCE)0733-9399(2004)130:11(1257)
[99]	Wang Y, Ying Z Q and Zhu W Q 2009 J. Sound Vib. 321 976 doi: 10.1016/j.jsv.2008.10.021
[100]	Xu M, Jin X L, Wang Y and Huang Z L 2014 Acta Mech. Solida Sin. 27 5
[101]	Zhu W Q and Lei Y 1988 Nonlinear Stochastic Dynamic Engineering Systems (Berlin:Springer)
[102]	Roberts J B 1988 Nonlinear Stochastic Dynamic Engineering Systems (Berlin:Springer)
[103]	Zeng Y and Li G 2013 Probab. Eng. Mech. 33 135 doi: 10.1016/j.probengmech.2013.03.005
[104]	Asano K and Iwan W D 1984 Earthq. Eng. Struct. D 12 229 doi: 10.1002/eqe.4290120207
[105]	Lutes L D 1970 J. Acoust. Soc. Am. 48 299 doi: 10.1121/1.1912128
[106]	Ni Y Q, Ying Z G and Ko J M 2002 ASME J. Appl. Mech. 69 171 doi: 10.1115/1.1428333
[107]	Ying Z G, Zhu W Q, Ni Y Q and Ko J M 2002 J. Sound Vib. 254 37 doi: 10.1006/jsvi.2001.4078
[108]	Liu J, Chen L C and Sun J Q 2017 Chin. J. Theor. Appl. Mech. 49 3(in Chinese)
[109]	Naess A and Moe V 1996 Int. J. Nonlin. Mech. 31 553 doi: 10.1016/0020-7462(96)00020-0
[110]	Luciano G M, Dimitris C L and Marcelo A S 2009 Int. J. Solids. Struct. 46 1269 doi: 10.1016/j.ijsolstr.2008.09.013
[111]	Rosario N M and Bernardo S 2005 J. Appl. Phys. 97 519
[112]	Li J and Chen J B 2006 Int. J. Numer. Meth. Eng. 65 882 doi: 10.1002/nme.1479
[113]	Yang J N and Wu J C 1995 J. Eng. Mech.-ASCE 121 1330 doi: 10.1061/(ASCE)0733-9399(1995)121:12(1330)
[114]	Yang J N, Agrawal A K and Chen S 1996 Earthq. Eng. Struct. Dyn. 25 1211 doi: 10.1002/(SICI)1096-9845(199611)25:11<1211::AID-EQE609>3.0.CO;2-3
[115]	Zhu W Q, Ying Z G and Ni Y Q 2000 J. Eng. Mech. 126 10
[116]	Wang Y, Ying Z G and Zhu W Q 2009 Probab. Eng. Mech. 24 255 doi: 10.1016/j.probengmech.2008.07.003
[117]	Li X P, Huan R H and Wei D M 2010 Probab. Eng. Mech. 25 245 doi: 10.1016/j.probengmech.2009.12.003
[118]	He W 2018 IEEE T. Contr. Syst. T. 26 2
[119]	Li J, Peng Y B and Chen J B 2011 Struct. Eng. Mech. 38 39 doi: 10.12989/sem.2011.38.1.039

Some new advance on the research of stochastic non-smooth systems

Some new advance on the research of stochastic non-smooth systems

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 119

相关文章 6

Metrics

本文评价

推荐阅读 0

[1]	Jian-Long Wang(王剑龙), Xiao-Lei Leng(冷小磊), and Xian-Bin Liu(刘先斌). Stationary response of colored noise excited vibro-impact system[J]. 中国物理B, 2021, 30(6): 60501-060501.
[2]	徐伟, 黄冬梅, 谢文贤. Multi-valued responses and dynamic stability of a nonlinear vibro-impact system with a unilateral non-zero offset barrier[J]. 中国物理B, 2016, 25(3): 30502-030502.
[3]	李超, 徐伟, 王亮, 李东喜. Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation[J]. 中国物理B, 2013, 22(11): 110205-110205.
[4]	苏敏邦, 戎海武. Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation[J]. 中国物理B, 2011, 20(6): 60501-060501.
[5]	李群宏, 谭洁燕. Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops[J]. 中国物理B, 2011, 20(4): 40505-040505.
[6]	王亮, 徐伟, 李颖. Dynamical behaviour of a controlled vibro-impact system[J]. 中国物理B, 2008, 17(7): 2446-2450.