基本信息科学研究教育教学论文专著
基本信息



曹庆杰，男，汉族，博士，二级教授，博士生导师。长期从事非线性动力学理论及其应用研究，在 2006 年发现并提出了SD振子及其吸引子。在国内外学术期刊上发表论文 80 多篇，其中被 SCI 收录 50 多篇，EI 收录 20 多篇；主持并完成了多项国家级和国际合作研究项目。



联系方式
曹庆杰教授
手　机：**
E－mail：
q.j.cao@hit.edu.cn
邮　编：150001
通信地址：哈尔滨市南岗区西大直街92号137信箱


工作经历


时间工作经历
2010.03 - 至今哈尔滨工业大学 航天学院 教授 博士生导师
2007.04-2010.02石家庄铁道大学 数理系 教授 硕士生导师
2000.05-2007.03 Department of Engineering, Mechanical Engineering Division,

The University of Liverpool, Liverpool, Research Fellow

Department of Engineering, The University of Aberdeen, Aberdeen, Research Fellow
1994.08-1995.07

1999.08-2000.02

Department of Mathematical Sciences, Brunel University, Uxbridge

Visiting fellowship of Royal Society & Education Council Visiting fellowship of China

Department of Ship Science, University of Southampton, Southampton

Visiting fellowship of Royal Society & Education Council Visiting fellowship of China
1994.01-2007.03山东大学 数学院 教授 博士生导师
1988.09-1993.12天津大学 机械学院 博士 博士后
1978.02-1988.08山东曲阜师范大学 数学系 本科 硕士 助教 讲师


教育经历
1988年9月 - 1991年8月，天津大学, 机械学院，力学系，工学博士学位1985年9月 - 1988年8月, 山东曲阜师范大学， 数学系，硕士 1978年3月 - 1982年2月, 山东曲阜师范大学， 数学系，本科


主要任职
Editor Board Member of International Journal of Dynamics and Control.中国振动工程学会非线性振动专业委员会委员 （2009.05-）International journal of computer mathematics 编委 （2007.01 - 2009.12）第五 六届一般力学专业委员会委员 （1995 - 2003）山东省数学会副理事长 （1995 - 2003）山东省力学会常务副理事长 （1995 - 2003）


科研项目

项目名称1.基于零微重力地面仿真的零刚度系统动力学理论、实验与应用研究

项目来源国家自然基金委员会 重点项目

开始时间2018.01

结束时间2022.12

项目经费330万

担任角色负责
项目类别纵向项目
项目状态进行中


项目名称2.基于传动带摩擦构建的自激SD振子及其复杂动力学行为研究

项目来源国家自然基金委员会

开始时间2016.01

结束时间2019.12

项目经费80.6万

担任角色负责
项目类别纵向项目
项目状态进行中


项目名称3.一类几何非线性动力系统的理论、方法及应用研究

项目来源国家自然科学基金 面上项目

开始时间2014-01-01

结束时间2017-12-01

项目经费88万

担任角色负责
项目类别纵向项目
项目状态进行中


项目名称4.摩擦与碰撞联合作用下的SD振子的非线性动力学行为研究

项目来源国际自然科学基金 面上项目

开始时间2011-01-01

结束时间2013-12-01

项目经费48万元

担任角色负责
项目类别纵向项目
项目状态完成


项目名称5.SD振子及其吸引子的动力学行为研究

项目来源国家自然科学基金 面上项目

开始时间2009-01-01

结束时间2011-12-01

项目经费40万元

担任角色负责
项目类别纵向项目
项目状态完成


奖项成果

奖项名称1.滞后非线性系统分岔理论及车桥动力学行为分析

获奖时间2009

完成人杨绍普，曹庆杰等

所获奖项2009河北省自然科学一等奖



奖项名称2.非线性发展方程的孤立子研究

获奖时间1999

完成人曹庆杰

所获奖项1999年山东省教委自然科学三等奖



研究领域
主要研究方向: 非线性动力学与工程应用

载人航天动力学理论与方法；航天器结构设计理论方法；航空发动机整机动力学与控制；非线性动力学理论与应用；高余维非线性动力学理论与方法。


团队成员
梁廷伟: 博士, 高级工程师, 研究方向: 航天器动力学与控制

讲授课程
常微分方程定性与稳定性方法 作者：马知恩，周义仓；

简介:《常微分方程定性与稳定性方法（科学版）》是为应用数学专业的硕士生和高年级本科生所编写的一本教材。主要包括定性理论、稳定性理论和分支理论三个部分。内容着眼于应用的需要，取材精练，注意概念实质的揭示、定理思路的阐述、应用方法的介绍和实际例子的分析，并配合内容引入了计算机软件。章后附有习题。《常微分方程定性与稳定性方法（科学版）》可作为理工科专业研究生的教材和高年级本科生的选修课教材，也可供相关的科学技术人员参考。

Bifurcation and chaos in engineering作者：陈予恕

简介: 主要研究工程系统中的非线性动力学、分叉和混沌理论、控制理论及其应用，重点介绍近几年来国内外的最新进展，包括高维非线性系统的多脉冲全局分叉、时滞动力系统、非光滑动力系统等变非线性动力系统、C-L方法、规范形的计算、非线性随机优化控制、后绝对稳定性、网络结构与动力学、非线性色散波、非线性系统大范围运动动力学、碰撞振动系统、微转子系统、轴向运动弦线和梁的非线性动力学。

Nonlinear oscillations, dynamical systems, and bifurcations of vector fields (J. Guckenheimer & P. Holmes)

Introduction to applied nonlinear dynamical systems and chaos (Stephen Wiggins)










招生信息
面向全国招收有志从事非线性理论及工程应用的硕士生及博士生, 欢迎力学工程，数学，物理等学科优秀学生报考。

出版物

出版物名称非线性动力学与控制的若干理论及应用

作者杨绍普，曹庆杰，张伟

出版时间,完成时间2011-01-01

出版社科学出版社

简单介绍本书主要介绍非线性系统动力学行为与控制的研究进展，重点是近年来国内外的最新进展，包括强非线性与非光滑系统动力学、高维与无限维非线性系统动力学、载运工具系统的非线性动力学与控制、时滞非线性系统动力学与控制方法研究等。本书理论与应用兼顾，在介绍一些基本方法新进展的同时，也将各种方法用于解决机械系统中的许多实际问题，因此，本书可以引导读者尽快进入本领域的前沿，也将为该领域的研究提供有价值的参考。本书可供力学、机械、数学、物理 航空航天、土木工程等专业高年级大学生、研究生和教师使用。


论文期刊
Selected Publications Ning Han, Qingjie Cao*,A parametrically excited pendulum with irrational nonlinearity.International Journal of Non-Linear Mechanics,88,122-134, (2017)
Ning Han, Qingjie Cao*, Global bifurcations of a rotating pendulum with irrational nonlinearity,Communications in Nonlinear Science and Numerical Simulation, 36,434-445,(2016)
Ning Han, Qingjie Cao*,Multiple Bifurcations of a Cylindrical Dynamical System,Journal of Theoretical & Applied Mechanics,46(1),33-52,(2016)
Ning Han, Qingjie Cao*,Rotating Pendulum with Smooth and Discontinuous Dynamics,International Journal of Mechanical Sciences,(2016)
Zhixin Li, Qingjie Cao, Alain Leger.Complex dynamics of an archetypal self-excited SD oscillator driven by moving belt friction, Chinese Physics B, 25(1), 10502-10510, (2016).Zhixin Li, Qingjie Cao, Alain Leger.The equilibrium stability for a smooth and discontinuous oscillator with dry friction, Acta Mechanica Sinica, 32(2), 309-319, (2016)
Zhifeng Hao,Qingjie Cao,Marian Wiercigroch.Two-sided damping constraint control strategy for high-performance vibration isolation and end-stop impact protection,Nonlinear Dynamics,86(4), 2129-2144, (2016). Zhifeng Hao,Qingjie Cao,Marian Wiercigroch.Nonlinear dynamics of the quasi-zero-stiffness SD oscillator based upon local and global bifurcations,Nonlinear Dynamics,(2016).
Zhixin Li, Qingjie Cao, Alain Leger.Multiple stick-slip chaotic motion of an archetypal self-excited SD oscillator driven by moving belt friction, International Journal of Bifurcation and Chaos，(2016)Tao Yang,Qingjie Cao,Nonlinear transition dynamics in a time-delayed vibration isolator under combined harmonic and stochastic excitations,Journal of Statistical Mechanics: Theory and Experiment, (2016). Qiyi Dai, Qingjie Cao, Yushu Chen,Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method, Journal of Vibroengineering ,(2016 )
Zhifeng Hao, Qingjie Cao, The isolation characteristics of an archetypal dynamical model with stable-quasi-zero-stiffness. Journal sound and vibration, (2015)Yanwei Han, Qingjie Cao, Marian Wiercigroch, Chaotic thresholds for the piecewise linear discontinuous system with multiple well potentials International Journal of Non-Linear Mechanics, (2014)Qingjie Cao, Yanwei Han and Marian Wiercigroch, Multiple Buckling and Codimension-Three Bifurcation of a Nonlinear Oscillator,International journal of bifurcation and chaos, 24(1) **：1-17 （2014)Cao, Qingjie; Pastor, Javier; Piskarev, Sergey, Approximations of Parabolic equations at the vicinity of hyperbolic equilibrium point, Numerical Functional Analysis and Optimization 35 (10): 1287-1307, (2014)Zhang, Yongxiang; Luo, Guanwei; Cao, Qingjie, Wada basin dynamics of a shallow arch oscillator with more than 20 coexisting low-period periodic attractor, International Journal of Nonlinear Mechanics (58): 151-161, (2014)Zhifeng Hao, Qingjie Cao, A novel dynamical model for GVT nonlinear supporting system with stable-quasi-zero-stiffness. Journal of Theoretical and Applied Mechanics, 52(1), 199-213, (2014).Ning Han, Qingjie Cao, Tingwei Liang, A rotating disk linked by a pair of springs, Nonlinear Dynamics, (2014)Ning Han, Qingjie Cao^*, Marian Wiercigroch, Estimation of the chaotic thresholds for the recently proposed rotating pendulum, International journal of bifurcation and chaos, 23(4) **：1-22 （2013）.Zhixin Li, Qingjie Cao, Marian Wiercigroch, and Alain Leger. Analysis of the periodic solutions of a smooth and discontinuous oscillator, Acta Mechanica Sinica, 29(4), 575-582, (2013). Qingjie Cao^*, Yeping Xiong, Marian Wiercigroch, A novel model of dipteran flight mechanism, International journal of dynamics and control, 1,1-11（2013）.Yanwei Han, Qingjie Cao^*, Yushu Chen, Marian Wiercigroch, A novel smooth and discontinuous oscillator with strong irrational nonlinearities," Sci. China-Phys. Mech. Astron. 55, 1832-1843（2012）.Leger, Alain; Pratt, Elaine; Cao, Qingjie, A fully nonlinear oscillator with contact and friction, Nonlinear Dynamics, 70(1): 511-522, (2012 )Qingjie Cao^*, Dan Wang,Yushu Chen, Marian Wiercigroch, Irrational elliptic functions and the analytical solutions of SD oscillator, Journal of theoretical and applied mechanics, 50(3), 701-715 （2012）.Ruilan Tian, Xinwei Yang, Qingjie Cao, Yanwei Han, The study on the midspan deflection of a beam bridge under moving load s based on SD oscillator, International of bifurcation and chaos, 22(5), **:1-18（2012）.Qingjie Cao, Ning Han, Ruilan Tian, A rotating pendulum linked by an oblique spring, Chinese Physics Letters, 28(6) 60502:1-4（2011） .Qingjie Cao^*, Yeping Xiong, Marian Wiercigroch, Resonances of the SD oscillator due to the discontinuous phase, Journal of Applied Analysis and Computation, 1(2), 183-191（2011）.Qingjie Cao, Marian Wiercigroch, Ekaterina Pavlovskaia, Shaopu Yang, Bifurcations and the penetrating rate analysis of a model for percussive drilling, Acta Mechanica Sinica, 26(3): 467-475（2010）.Ruilan Tian , Qingjie Cao, Shaopu Yang, The codimension-two bifurcation for the recent proposed SD oscillator,Nonlinear Dynamics, 59. 19-27 (2010)Ruilan Tian, Qingjie Cao, Zhixin Li, Hopf Bifurcations for the Recently Proposed Smooth-and-Discontinuous Oscillator, Chinese Physics Letters, 27(7) 074701:1-4 (2010)Yongxin Lin, Yushu Chen, Qingjie Cao, Nonlinear and chaotic analysis of a financial complex system, Appl. Math. Mech. -Engl. Ed. 31(10), 1305–1316 (2010)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, 43 462-473 (2008)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, 366(1865): 635-652 (2008)Q. Cao, M. Wiercigroch, E E Pavlovskaia, C Grebogi and JMT Thompson, The SD oscillator and its attractors J. Phys.: Conf. Ser. 96, 012064 (6pp) doi:10.1088/1742-6596/96/1/012064 (2008)Q. Cao, M. Wiercigroch, E E Pavlovskaia, C Grebogi and JMT Thompson, SD Oscillator, SD attractor and its applications, Journal of Vibration Engineering, Vol.20, No.7:454-458 (2007)Q. Cao, M. Wiercigroch, E E Pavlovskaia, C Grebogi and JMT Thompson, An archetypal oscillator for smooth and discontinuous dynamics, Phys. Rev. E 74, 046218 (2006)Q. Cao, M. Wiercigroch, E E Pavlovskaia, C Grebogi and JMT Thompson, Advances in study on the SD oscillators, Science and Technology Review, Vol.25, No.23:33-37 (2007)Q. Cao, X. Lai, Some finite difference methods for a kind of GKdV equations, Communications in Numerical Methods in Engineering, 179-196,Vol.23, (2007)X. Lai, Q.Cao, Twizell, E.H, The global domain of attraction and the initial value problems of a kind of GKdV equations, Chaos Solitons & Fractals, Vol.23, No.5 1613–1628 (2005)Cao Q, Friswell MI, Ouyang H, Mottershead JE, Linear Eigenvalue Analysis of the Disc-Brake Squeal Problem,International Journal for Numerical Methods in Engineering, Vol.61.No.9: 1546-1563 (2004)Xu, L., M. W. Lu, Cao, Q, Analysis Of Dynamic Properties Of Forced Van Der Pol Equation With Ihb Method, MECHANICS IN ENGINEERING, Vol.25 No.1 P.50-53 (2003)Cao Q, Friswell MI, Ouyang H, Mottershead JE, James Sl, Car disc brake squeal: Theoretical and experimental study, MATER SCI FORUM 440-4: 269-276 (2003)Xu, L., M. W. Lu, Cao, Q, 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, 264(4): 873-882 ( 2003).Djidjeli K; Price WG;Twizell, E.H and Q.Cao, A Linearied impact pseudo-spectral method for some model equations: The regularized long wave equations, Communications in Numerical Method in Engineering, 19:847-863 ( 2003)Ouyang, H., Q.Cao, Mottershead, J. E., A methodology for the determination of dynamic instabilities in a car disc brake. Proc. Instn Mech. Engrs Vol217. J. Automobile Engineering, 867-875 ( 2003)Xu Lei, Lu Mingwan, Cao Qingjie, Nonlinear Dynamical Bifurcation Analysis of Van der Pol-Duffing Equation,Applied Mechanics, 4 130-134 (in Chinese) (2002)Xu, L., M. W. Lu, Cao, Q, "Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method, Physics Letters A 301(1-2): 65-73 (2002), .Cao Q; Xu L; Djidjeli K; Price WG; Twizell EH, Analysis of period-doubling and chaos of a non-symmetric oscillator with piecewise-linearity, CHAOS SOLITONS & FRACTALS , Vol. 12, No.10, pp 1917-1927 (2001)Qingjie Cao, Soliton, Bifurcation and Chaos for a class of Generalized Evolution Equations, Science Report of China, Vol.6 No.2: 181-183 (2000)Qingjie Cao, W. G. Price, K. Djidjeli, E.H. Twizell, Applications of the Six-points Scheme for GNLS equations,Applied Mathematics, JCU, 14B, Vol.14, No.1: 21-29 (1999)Q. Cao, W. G. Price, K. Djidjeli, E.H. Twizell, Periodic and chaotic behavior in a reduced form of the perturbed generalized KdV and KP equations, Physica D, 125 201-221 (1999)Q. Cao, W.G. Price, K. Djidjeli and E.H. Twizell, Computational methods for some non-linear wave equations, Journal of Engineering Mathematics, 35:323-338, (1999)Qingjie Cao, Tiande Zhang, Jiuping Li, Study of the Static and Global Bifurcations for Duffing Equation, Applied Mathematics and Mechanics, Vol.20, No.12. Pp: 1305- 1312 (1999)E.H. Twizell, A.B. Gumel, and Q. Cao, A Second-Order Scheme for the Brusselator Reaction-Diffusion System,Journal of Mathematical Chemistry, Vol.26, No.4 pp297-316 (1999)Qingjie Cao Zhang Tiande, W. G. Price, K. Djidjeli, E.H. Twizell, Applications of the Weighted Scheme for GNLS equations, Korea Journal of Computational and Applied Mathematics, Vol.12 , No.2:525-541 (1998)Qingjie Cao, W. G. Price, K. Djidjeli, E. H. Twizell, The properties of the soliton solutions of a class of generalized Schr？dinger equations, ACTA PHYSICA CHINA .No.11, 2166-2173 (1997)Qingjie Cao, W. G. Price, K. Djidjeli, E.H. Twizell, Soliton solutions of a class of generalized non-linear Schr？dinger equations, Applied Mathematics, JCU, 12B,389-398 (1997)Selected Conference Papers Qingjie Cao, Yanwei Han and Marian Wiercigroch, Multiple Bucklings and Co-dimension three with two parameters based upon the SD Oscillator, ENOC2014, 8th European Nonlinear Dynamics Conference, ,July 6 - 11, 2014, Vienna AustriaCao Qingjie, SD oscillator and the SD Isolators, ICDVC-2014, The Fourth International Conference on Dynamics, Vibration and Control, 22-25 August 2014, Shanghai, China.Cao Qingjie, SD oscillator and the Isolations, NCS 2014, The Fourth International Conference on Nonlinear Complexity, 4-8 August 2014, Xi’an, China.Qingjie Cao, Ning Han and Marian Wiercigroch, Nonlinear Dynamics of a Rotating SD Oscillator, SEMC 2013, The Fifth International Conference on Structural Engineering, Mechanics and Computation, 2-4 September 2013, Cape Town, South Africa.Qingjie Cao, Yeping Xiong and Marian Wiercigroch, Nonlinear Dynamics of the Recently Proposed Novel Model for Dipteran Flight Mechanism with Irrationality, International Conference On Nonlinear Dynamics in Engineering: Modelling, Analysis and Applications, The University of Aberdeen, 21-23 August 2013 Aberdeen , Scotland, UK.Qingjie Cao, Yushu Chen, (Invited) Some Nonlinear Dynamics Problems in Aero-engine and Gas Turbines, National Conference on Nonlinear Vibration and Control, 11 May 2013, Naning Guangxi China.Cao Qingjie, Geometrical Nonlinear Dynamics: Theory, Methodologies and the Applications, Main Land China, Hong Kong and Macau Symposium on Dynamical Systems and Vibration (SDSV 2012) 13 -19 December 2012 Hong Kong and Macuo.Cao Qingjie^*, Han Yanwei, Chen Yushu, Wiercigroch Marian, Sergey Piskarev, Two parameter codimension-three bifurcations of a novel nonlinear oscillator with strong irrational nonlinearities, ICTAM 2012, Beijing, China, 2012.08.19-24Q. Cao, Nonlinear Dynamics Analysis of the SD oscillatorwith virating base, IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design, Aberdeen, 27-30, July 2010, Aberdeen AB24 3UE,UKQ. Cao, Recent Advances of the SD oscillator, ICDVC-2010, The ThirdInternational Conference onDynamics, Vibration and Control12-14 May 2010Hangzhou, China.Q. Cao, Nonlinear Dynamics Analysis of the Rig-Coupled SD oscillator, The 4^th Internationa Conference on Recent Advances inApplied Dynamical Systems,16-20 June 2010, Jinhua, China.Q. Cao, SD oscillator: The theory and the experiments,The First Harbin International Conference in Nonlinear Dynamics, 11 May 2010, Harbin, China.Q. Cao, Invited Speaker, SD oscillator: the attractors and the complex dynamics,APM 2009，St. Petersburg 30 June-5 July 2009Q. Cao, The SD Oscillator and Its Attractors ,RANM2009，Kuala Lumpur 23-27 August 2009Q. 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, SD oscillator: the attractors and the complex dynamics,The 2nd Internationa Conference on Recent Advances in Applied Dynamical Systems, Jinhua, 2-4, June, 2007Q Cao, M I Friswell, H Ouyang, J E Mottershead and S James, Car Disc Brake Squeal: A New Theoretical Approach, 5th International Conference on Modern Practice in Stress and Vibration Analysis, 9 to 11 September 2003, University of Glassgow.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.H Ouyang, Q Cao, J E Mottershead, T Treyde, M P Cartmell, Modeling and simulation of the vibration and squeal of a car disc brake, Braking 2002, From the Driver to the Road, The Royal of Armouries, Leeds, UK, 10-12, July 2002.Cao_Q, Price_WG, Djidjeli_K, Twizell_EH, Chaotic behavior of a vibration system with the quartic no linearity, INTEGRATING DYNAMICS, CONDITION MONITORING AND CONTROL FOR THE 21ST CENTURY - DYMAC 99, 1999, Ch.87, pp.309-312, MANCHESTER, ENGLAND, 1-3 Sep 1999Cao_QJ, Wang_HL, Global bifurcation of the horizontal rotators, ICVE@#%98: PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON VIBRATION ENGINEERING, VOL I, 1998, Ch.97, pp.261-265 DALIAN, PEOPLES R CHINA, 6-9 Aug 1998Cao_QJ, Chen_YS, Zhang_TD, Price_WG, Djidjeli_K, Twizell_EH, Global bifurcations of the forced MKdV-Burgers equation, 3RD INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS, 1998, Ch.176, pp.593-596 SHANGHAI, P R CHINA, 17-20 Aug 1998CAO QJ, CHEN YS, Stochastic vibration and bifurcation with bilinear hysteresis under the excitation of the white noise, 2nd International Conference on Nonlinear Mechanics (ICNM II), AUG23-26,1993,PROCEEDINGS OF THE 2ND INTERNATIONAL CONFERENCE ON NONLINEAR MECHANICS , 471-474, 1993Invited Speakers/Seminars Q. Cao, SD oscillatorintroduction and the Advances and the Chanllenges in Science and Technology, Laboratoire de Mécanique et d’ Acoustique,French National Centre for Scientific Research, Marseille,1 March 2011, Q. Cao, SD oscillator: The Advances and the Chanllenges in Science and Technology, 27 September 2010, Beihang University, Beijing, 100081, China Q. Cao, SD oscillator: The Advances and the Chanllenges in Science and Technology, 24 September 2010, University of Southampton, Southampton SO17 1BJ, UK Q. Cao, New Development of the SD Oscillator and Its Attractors, Aberdeen University,Feburary 16, 2009, Aberdeen, UK Q. Cao, The New approach to the SD Oscillator, Aberdeen University, 18-Jan-2007, Aberdeen, UK Q. Cao, The Brief introduction to the SD Oscillator, Shandong University of Science Technology, 14-April-2007, Qingdao, China Q Cao, The advances of the study for SD oscillator and SD attractors, Department of Math, Shanghai Normal University, 2-10-2007. Q. Cao, Non-linear Vibration & Applications, School of Engineering and Physical Sciences, Aberdeen, AB24 3UE, 03 September 2003. Q. Cao, Soliton, Chaos and Bifurcations: the analysis and the numerical approach for Generalized KdV equations, Department of Mathematical Sciences, Brunel University, Uxbridge, Middlesex UB8 3PH, 18 August 1999. Cao Q, Modelling of the Car Disc Brake Squeal: A New Theoretical Approach, Jinan, Shandong University, 13 May 2004.