标题：曹庆杰
哈尔滨工业大学曹庆杰
个人简介博士生导师
工作单位：哈尔滨工业大学航天学院　
成果：SD振子与SD吸引子高等教育经历理学博士学位,1991年10月,非线性随机动力系统的分叉与混沌研究,天津大学力学系,指导教师: 陈予恕. 
理学硕士学位,1988年8月,常微分方程稳定性研究,曲阜师范大学数学系,指导教师:赵素霞.
理学学士学位,1981年1月,数学,曲阜师范大学数学系.曾任学术简职山东数学会副理事长,1995-2003; 
山东力学会常务副理事长,1995-2003; 
中国非线性振动学会理事,1999-2003; 
中国一般力学学会理事,1995-2003. 
Member,Complex System Society,UK,2001-
石家庄铁道大学曹庆杰
个人简介姓名：曹庆杰[1]
性别：男
工作单位：石家庄铁道大学数理系
职位：教授.硕士导师.博士导师
最新成果：SD振子与SD吸引子教育经历理学博士学位,1991年10月,非线性随机动力系统的分叉与混沌研究,天津大学力学系,指导教师: 陈予恕.
理学硕士学位,1988年8月,常微分方程稳定性研究,曲阜师范大学数学系,指导教师:赵素霞.
理学学士学位,1981年1月,数学,曲阜师范大学数学系.研究与工作经历2007.4-今日,教授,石家庄铁道学院,数理系
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,国家留学基金资助学者, 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,硕士导师,博士导师,山东大学数学院;1991.10-1993.12, 博士后研究，天津大学力学系;
1981.2-1991.9, 助教，讲师，曲阜师范大学, 数学系教学工作常微分方程
微分方程稳定性
微分方程定性理论
非线性动力系统,分叉与混沌理论及其应用担任学术简职山东数学会副理事长,1995-2003;
山东力学会常务副理事长,1995-2003;
中国非线性振动学会理事,1999-2003;
中国一般力学学会理事,1995-2003.
Member,Complex System Society,UK,2001-
编委：International Journal of Computer Mathematics主持完成项目一类广义非线性发展方程的孤立子、分岔及浑沌特性研究，1999.1-2001.12, 国家自然科学基金,代码：A02010702, 批准号：19872041，11万元;
一类随机非线性动力系统分岔及浑沌特性研究，1994.1-1996.12, 国家自然科学基金，代码：A02010702, 批准号：19302015，4万元;
Bifurcations and Chaos in Non-linear Stochastic Vibration Systems, Royal Sciety, 1994-1995, \pounds 10,000;
广义发展方程孤立子理论及其应用研究,国家留学基金(回国), 96623712, 1996-1998, 3万元;
孤立子理论及其在船舶科学中的应用,国家留学基金, 98837129,1999.8-2000.1, 10万元;
非线性波动方程的孤立子理论及应用研究，1999.1-2001.12, 省自然科学基金, Y98A73016, 3万元;
广义非线性波动方程的孤立子的计算及应用研究,山东省青年人才基金,1996-1998,3万元;
大型非线性转子的混沌机理研究,天津市自然科学基金,Q94B203011,1994-1996,6万元。特邀学术报告Cao Q,SD振子及其吸引子的提出，研究现状与展望，上海师范大学非线性动力系统研究中心，2007年10月。
Cao Q,Modelling of the Car Disc Brake Squeal: 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, Soliton and 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.科研论文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-linear viscous damping 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 both stiffness and 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 Brake Colloquium and 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