個人簡介
博士生導師
工作單位：哈爾濱工業大學航天學院
成果：SD振子與SD吸引子
高等教育經歷
理學博士學位,1991年10月,非線性隨機動力系統的分叉與混沌研究,天津大學力學系,指導教師: 陳予恕.
理學碩士學位,1988年8月,常微分方程穩定性研究,曲阜師範大學數學系,指導教師:趙素霞.
理學學士學位,1981年1月,數學,曲阜師範大學數學系.
曾任學術簡職
山東數學會副理事長,1995-2003;
山東力學會常務副理事長,1995-2003;
中國非線性振動學會理事,1999-2003;
中國一般力學學會理事,1995-2003.
Member,Complex System Society,UK,2001-
石家莊人物
姓名：曹慶傑
性別：男
工作單位：石家莊鐵道大學數理系
職位：教授.碩士導師.博士導師
最新成果：SD振子與SD吸引子
教育經歷
理學博士學位,1991年10月,非線性隨機動力系統的分叉與混沌研究,天津大學力學系,指導教師: 陳予恕.
理學碩士學位,1988年8月,常微分方程穩定性研究,曲阜師範大學數學系,指導教師:趙素霞.
理學學士學位,1981年1月,數學,曲阜師範大學數學系.
研究與工作經歷
2007.4-今日,教授,石家莊鐵道學院,數理系
2003.10- Research Fellow, Discontinuous system modelling in engineering systems, Department of Engineering, Aberdeen University, Aberdeen, AB24 3UE,UK;
2000.4-2003-8,Research Fellow, Modelling a frictional system, Department of Engineering, Liverpool University, Liverpool, L69 3GH,UK;
1999.8-2000.2,國家留學基金資助學者, Department of Ship Science, Southampton University, Southampton, SO17 1BJ,UK;
1994.8-1995.7,Royal Society Visiting Research Fellow, Department of Mathematics, Brunel University, Uxbridge, Middlesex, London, UB8 3PH,UK;
1994.1－2007.3,教授,碩士導師,博士導師,山東大學數學院;1991.10-1993.12, 博士後研究，天津大學力學系;
1981.2-1991.9, 助教，講師，曲阜師範大學, 數學系
教學工作
常微分方程
微分方程穩定性
微分方程定性理論
非線性動力系統,分叉與混沌理論及其套用
擔任學術簡職
山東數學會副理事長,1995-2003;
山東力學會常務副理事長,1995-2003;
中國非線性振動學會理事,1999-2003;
中國一般力學學會理事,1995-2003.
Member,Complex System Society,UK,2001-
編委：International Journal of Computer Mathematics
主持完成項目
一類廣義非線性發展方程的孤立子、分岔及渾沌特性研究，1999.1-2001.12, 國家自然科學基金,代碼：A02010702, 批准號：19872041，11萬元;
一類隨機非線性動力系統分岔及渾沌特性研究，1994.1-1996.12, 國家自然科學基金，代碼：A02010702, 批准號：19302015，4萬元;
Bifurcations and Chaos in Non-linear Stochastic Vibration Systems, Royal Sciety, 1994-1995, \pounds 10,000;
廣義發展方程孤立子理論及其套用研究,國家留學基金(回國), 96623712, 1996-1998, 3萬元;
孤立子理論及其在船舶科學中的套用,國家留學基金, 98837129,1999.8-2000.1, 10萬元;
非線性波動方程的孤立子理論及套用研究，1999.1-2001.12, 省自然科學基金, Y98A73016, 3萬元;
廣義非線性波動方程的孤立子的計算及套用研究,山東省青年人才基金,1996-1998,3萬元;
大型非線性轉子的混沌機理研究,天津市自然科學基金,Q94B203011,1994-1996,6萬元。
特邀學術報告
Cao Q,SD振子及其吸引子的提出，研究現狀與展望，上海師範大學非線性動力系統研究中心，2007年10月。
Cao Q,Modelling of the Car Disc Brakesqueal: A New Theoretical Approach, Jinan, Shandong University,13 May 2004.
Cao Q,Non-linear Dynamics and Applications:Disc-Brake Squeal Problem: Modelling and Analysis,Aberdeen, 03 September 2003.
Cao Q,Modelling of the Car Disc Brake Squeal: A New Theoretical Approach, Liverpool,13 May 2002.
Cao Q,Periodic motion,Solitonand Chaos in nonlinear evolution equations,Brunel University, 10 October 1999.
Cao Q,The computation methods in soliton and chaos of a class of nonlinear evolution equations, National Computational Mathematics Conference,Yantai,China,10-11 August 1999.
科研論文
Q. Cao，M. Wiercigroch， E E Pavlovskaia， C Grebogi and JMT Thompson， The limit case response of the archetypal oscillator for smooth and discontinuous dynamics， International Journal of nonlinear Mechanics ( 2008 In Press， proven).
Q. Cao，M. Wiercigroch，E.E Pavlovskaia，C. Grebogi，and J.M.T. Thompson，Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics， Phil. Trans. R. Soc. A, 2008, Vol. 366, No.1865: 635-652;
Q. Cao，M. Wiercigroch，E E Pavlovskaia，C Grebogi and JMT Thompson， An archetypal oscillator for smooth and discontinuous dynamics， Phys. Rev. E , 2006, Vol. 74, No.4:046218
Q. Cao，M. Wiercigroch，E E Pavlovskaia， C Grebogi and JMT Thompson， Advances in study on the SD oscillators ，Science and Technology Review，2007，Vol.25,No.23:33-37
Q. Cao，M. Wiercigroch，E E Pavlovskaia， C Grebogi and JMT Thompson，SD Oscillator，SD attractor and its applications，Journal of Vibration Engineering，2007，Vol.20, No.7:454-458
Q. Cao，M. Wiercigroch，E E Pavlovskaia， C Grebogi and JMT Thompson，SD oscillator from smooth to discontinuous dynamics，CACAM-2007，21st Canadian Congress of Applied Mechanics， Ryerson University Toronto， Canada， June 3-7， 2007.
Q. Cao，M. Wiercigroch，E E Pavlovskaia C Grebogi and JMT Thompson，The SD oscillator and its attractors J.Phys.: Conf.Ser.96,2008, 012064 (6pp) doi:10.1088/1742-6596/96/1/012064
Q. Cao，M. Wiercigroch，E. E. Pavlovskaia， Local bifurcations analysis for the model of impact percussive drilling system，International Conference on Advances in nonlinear Mechanics，Aberdeen ，July 29-August 1，2005.
X. Lai，Q. Cao，Some finite difference methods for a kind of GKdV equations，Communications in Numerical Methods in Engineering，2007，Vol.23，No.3:179-196
Q.Cao，X. Lai，Twizell，E.H，The global domain of attraction and the initial value problems of a kind of GKdV equations，CHAOS SOLITONS FRACTALS，2005 Vol.23, No.5:1613-1628
L. Xu，M.W.Lu, Q. Cao，Nonliner vibrations of dynamial systems with general form of piecewise-linearviscousdamping by incremental harmonic balance method，Physics Letters A，2002 Vol 301,No.1-2:65-73.
L. Xu，M.W.Lu, Q. Cao，Incremental Harmonic Balance Computation Scheme for a Class of Piecewise-linear Circuit Systems, Chinese Journal of Computation Physics, 2003, Vol.20, No.2:107-110
L. Xu，M.W.Lu, Q. Cao，Analysis Of Dynamic Properties Of Forced Van Der Pol Equation With Ihb Method， Mechanics And Engineering，2003 Vol.25,No.1: 50-53
L. Xu，M.W.Lu, Q. Cao，Bifurcation and chaos of a harmonically excited oscillator with bothstiffnessand viscous damping piecewise linearities by incremental harmonic balance method，Journal of Sound and Vibration 2003 Vol.264,No.4: 873-882.
L. Xu，M.W.Lu, Q. Cao，Nonlinear Dynamical Bifurcation Analysis of Van der Pol-Duffing Equation, Chinese Journal of Applied Mechanics, 2002,Vol.19, No.04:130-133
Q. Cao，M.I. Friswell，H. Ouyang，J.E. Mottershead，Linear Eigenvalue Analysis of the Disc-Brake Squeal Problem，International Journal for Numerical Methods in Engineering，2004 Vol.61.No.9: 1546-1563
Q. Cao，M.I. Friswell，H. Ouyang，J.E. Mottershead，S. James， Car disc brake squeal: Theoretical and experimental study，Mater Science Forum 2003, 440-4:269-276
Q. Cao，H. Ouyang，J. E. Mottershead，A methodology for the determination of dynamic instabilities in a car disc brake. Proc.Instn Mech. Engrs Vol217. J.Automobile Engineering，2003，867-875
Q. Cao，Ouyang H and Abu Bakar A R，Interface pressure distributions through structural modifications. Proc. of the 21st Annual SAE Brakecolloquiumand Exhibition，SAE Paper 2003-01-3332，161-166
Q. Cao，H Ouyang，J E Mottershead，D J Brookfield and S. James，Stick-slip vibration in a disc brake system，Braking 2002，From the Driver to the Road，The Royal of Armouries，Leeds，UK，10-12，July 2002:101-108
Q. Cao，Ouyang Huajiang，Vibration and squeal of a car disc brake:Modelling and Experimental Vibration， National Solid Mechanics Conference，Dalian 2002，2002.8.19-21.
Cao Q; Xu L; Djidjeli K; Price WG; Twizell EH， Analysis of period-doubling and chaos of a non-symmetric oscillator with piecewise-Linearity， Source:Chaos Solitons Fractals 2001， Vol 12，No. 10，pp 1917-1927
Twizell E.H，Gumel A.B，Q. Cao, A second-order scheme for the "Brusselator" reaction-diffusion system， Journal Of Mathematical Chemistry，1999，Vol.26，No.4，pp.297-316
Q. Cao，Soliton，Bifurcation and Chaos for a Class of Generalised Evolution Equations，Chinese Science Abstracts (Research paper)，2000，Vol.6.，No.2:181-182
Q. Cao，W. G.Price，K. Djidjeli，E.H. Twizell，Applications of the，Six-points Scheme for GNLS equations， Applied Mathematics，JCU，14B，1999，Vol.14.，No.1:21-29
Q. Cao，W. G. Price，K.Djidjeli and E.H. Twizell，Chaotic Behavior of a vibration System in the Presence of Quartic Nonlinearity, Proceeding of the International Conference on the Integration of Dynamics，Monitoring and Control，Manchester United Kingdom，1-3 September 1999，330-335.
Q. Cao，W. G. Price，K. Djidjeli，E.H.Twizell，Periodic and chaotic behaviour in a reduced form of the perturbed generalised KdV and KP equations，Physica D，125 (1999)201-221
Q. Cao，W.G. Price，K. Djidjeli and E.H. Twizell，Computational methods for some nonlinear wave equations，Journal of Engineering Mathematics，35:323-338， 1999.
Q. Cao，T. Zhang，J. Li，Study of the Static and Global Bifurcations for Duffing Equation，Applied Mathematics and Mechanics，Vol.20，No.12.1999，pp:1308-1316.
Q. Cao，T. Zhang，J. Li， Study Of Soliton Solutions Of A Class Of Generalized Nonlinear Schrdinger Equations In N Space, ACTA Physica Sinica, 1997, Vol.46,No.11:2166-2173.
T. Zhang, Q. Cao，G.W. Price, K. Djidjeli,E.H. Twizell, Source: Korean Journal of Computational Applied Mathematics, 1998, Vol.5,No.3:525-541
