陈立群
主要研究方向为轴向运动连续体振动分析和控制、混沌控制和同步化、航天器姿态动力学和控制、航天器姿态动力学和控制、复杂约束下连续体非线性振动。
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 姓名：陈立群
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基础力学
 研究兴趣：主要研究方向为轴向运动连续体振动分析和控制、混沌控制和同步化、航天器姿态动力学和控制、航天器姿态动力学和控制、复杂约束下连续体非线性振动。
陈立群，男，博士，上海大学力学系教授、力学学科点博士生导师。兼任“非线性动力学”丛书编委，期刊Cognitive Neurodynamics, 《应用数学和力学(中英文版)》、《力学进展》、《动力学与控制学报》、《力学与实践编委》。应邀为20余种国际期刊审稿。中国力学学会动力学与控制专业委员会委员，中国振动工程学会非线性振动专业委员，American Academy of Mechanics的Professional Member, Centre for Chaos and Complex Networks的Associate Member。曾出访University of Toronto, University of California at San Diego和City University of Hong Kong担任Visiting Professor, Research Fellow, Research Associate或Visiting Scholar。
主要研究方向为轴向运动连续体振动分析和控制、混沌控制和同步化、航天器姿态动力学和控制、航天器姿态动力学和控制、复杂约束下连续体非线性振动。研究工作受到国家自然科学基金(主持10672092, 10472060, 10172056；参加10082003, 19782003, 19727027)、上海市自然科学基金(04ZR14058)、上海市教育委员会科研项目(07ZZ07)、上海市高校科技发展基金(2000A12)、上海市科技发展基金(98SHB1417)、中国博士后科学基金资助。所发表论文被SCI收录120余篇，被EI收录近90篇；根据SCI检索被他人引用近300次，单篇最高他引20余次。出版教材和专著《理论力学》、《振动力学》、《非线性振动》和《非线性动力学》。指导博士生16人，已获得博士学位8人。
4次获上海市科学技术进步奖二的奖(第一完成人，2005年；第一完成人，2004年；第四完成人，2002年；第二完成人，2000年)，获教育部科技进步奖二等奖(第二完成人，2005年)，获中国高校科学技术奖一等奖(第三完成人，2000年)。2005年被国家人事部表彰为“全国优秀博士后”。2004年获“宝钢优秀教师奖”。博士学位论文被上海市教委和上海市学位办评为“2000年上海市优秀博士论文”。

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陈立群， BY LIQUN CHEN，
Proc. R. Soc. A (2005) 461, 27012720 Published online 25 July 2005，0001，（）：
1年11月30日
The steadystate transverse responses and the stability of an axially accelerating viscoelastic string are investigated. The governing equation is derived from the Eulerian equation of motion of a continuum, which leads to the Mote model for transverse motion. The Kirchhoff model is derived from the Mote model by replacing the tension with the averaged tension over the string. The method of multiple scales is applied to the two models in the case of principal parametric resonance. Closedform expressions of the amplitudes and the existence conditions of steadystate periodical responses are presented. The Lyapunov linearized stability theory is employed to demonstrate that the first (second) nontrivial steadystate response is always stable (unstable). Numerical calculations show that the two models are qualitatively the same, but quantitatively different. Numerical results are also presented to highlight the effects of the mean axial speed, the axialspeed fluctuation amplitude, and the viscoelastic parameters.
nonlinear parametric vibration， method of multiple scales， stability， axially moving string， viscoelasticity

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陈立群， LiQun Chen， XiaoDong Yang
L. Q. Chen, X. D. Yang. Journal of Sound and Vibration 284 (2005) 879891，0001，（）：
1年11月30日
Stability in transverse parametric vibration of axially accelerating viscoelastic beams is investigated. The governing equation is derived from Newton’s second law, the Kelvin constitution relation, and the geometrical relation. When the axial speed is a constant mean speed with small harmonic variations, the governing equation can be regarded as a continuous gyroscopic system under small periodically parametric excitations and a damping term. The method of multiple scales is applied directly to the governing equation without discretization. The stability conditions are obtained for combination and principal parametric resonance. Numerical examples are presented for beams with simple supports and fixed supports, respectively, to demonstrate the effect of viscoelasticity on the stability boundaries in both cases.

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陈立群， LiQun Chen ， XiaoDong Yang
L. Q. Chen, X. D. Yang. International Journal of Solids and Structures 42 (2005) 3750，0001，（）：
1年11月30日
Principal parametric resonance in transverse vibration is investigated for viscoelastic beams moving with axial pulsating speed. A nonlinear partialdifferential equation governing the transverse vibration is derived from the dynamical, constitutive, and geometrical relations. Under certain assumption, the partialdifferential reduces to an integropartialdifferential equation for transverse vibration of axially accelerating viscoelastic nonlinear beams. The method of multiple scales is applied to two equations to calculate the steadystate response. Closed form solutions for the amplitude of the vibration are derived from the solvability condition of eliminating secular terms. The stability of straight equilibrium and nontrivial steadystate response are analyzed by use of the Lyapunov linearized stability theory. Numerical examples are presented to highlight the effects of speed pulsation, viscoelascity, and nonlinearity and to compare results obtained from two equations.
Axially accelerating beam， Principal parametric resonance， Nonlinearity， Viscoelascity

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陈立群， L.Q. Chen， J. W. Zu， J. Wu
Acta Mechanica 162, 143155 (2003)，0001，（）：
1年11月30日
The steadystate transverse vibration of a parametrically excited axially moving string with geometric nonlinearity is investigated in this paper. The Boltzmann superposition principle is employed to characterize the material property of the string. The method of multiple scales is applied directly to the governing equation, which is a nonlinear partialdifferentialintegral equation. The solvability condition of eliminating the secular terms is established. Closed form solutions for the amplitude and the existence conditions of nontrivial steadystate response of the summation resonance are obtained. Some numerical examples showing effects of the viscoelastic parameter, the amplitude of excitation, the frequency of excitation, and the transport speed are presented.

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【期刊论文】The energetics and the stability of axially moving Kirchhoff strings (L)
陈立群， LiQun Chena， WeiJia Zhao
L. Q. Chen and W. J. Zhao: Letters to the Editor J. Acoust. Soc. Am., Vol. 117, No. 1, January 2005，0001，（）：
1年11月30日
The energetics and the stability of free transverse vibration of an axially moving string are investigated based on the Kirchhoff nonlinear model. The model is derived in a physically meaningful manner. The timerate of the total mechanical energy associated with the vibration is calculated to show that the energy is not conserved. It is proved that there exists a conserved quantity that remains a constant during the nonlinear vibration. The conserved quantity is applied to verify the Lyapunov stability of the axially moving Kirchhoff string.

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【期刊论文】The energetics and the stability of axially moving strings undergoing planar motion
陈立群， LiQun Chen
L. Q. Chen. International Journal of Engineering Science 44 (2006) 13461352，0001，（）：
1年11月30日
Free coupled planer vibration of an axially moving string is investigated from the point of view of energetics. The timerate of the total mechanical energy associated with the vibration is calculated for axially accelerating strings with ends moving in a prescribed way. The result shows that the energy is not conserved for a string moving in a constant axial speed and constrained by two fixed ends. For such a string, it is proved that there exists a conserved quantity that remains a constant during the coupled planar vibration. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration.
Axially moving string， Planar vibration， Energetics， Conserved quantity， Stability

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陈立群， LiQun Chen， ， WeiJia Zhao， Jean W.Zu
L. Q. Chen et al. Journal of Sound and Vibration 278 (2004) 861871，0001，（）：
1年11月30日
This paper deals with the transverse vibration of an initially stressed movingviscoe lastic string obeying a fractional differentiation constitutive law. The governing equation is derived from Newtonian second law of motion, and reduced to a set of nonlinear differential–integral equations based on Galerkin’s truncation. A numerical approach is proposed to solve numerically the differential–integral equation through developing an approximate expression of the fractional derivatives involved. Some numerical examples are presented to highlight the effects of viscoelastic parameters and frequencies of parametric excitations on the transient responses of the axially movingstring .

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陈立群， LiQun Chen， ， XiaoDong Yang
L. Q. Chen, X. D. Yang Chaos, Solitons and Fractals 27 (2006) 748757，0001，（）：
1年11月30日
This paper investigates bifurcation and chaos in transverse motion of axially accelerating viscoelastic beams. The Kelvin model is used to describe the viscoelastic property of the beam material, and the Lagrangian strain is used to account for geometric nonlinearity due to small but finite stretching of the beam. The transverse motion is governed by a nonlinear partialdifferential equation. The Galerkin method is applied to truncate the partialdifferential equation into a set of ordinary differential equations. When the Galerkin truncation is based on the eigenfunctions of a linear nontranslating beam subjected to the same boundary constraints, a computation technique is proposed by regrouping nonlinear terms. The scheme can be easily implemented in practical computations. When the transport speed is assumed to be a constant mean speed with small harmonic variations, the Poincare′ map is numerically calculated based on 4term Galerkin truncation to identify dynamical behaviors. The bifurcation diagrams are present for varying one of the following parameter: the axial speed fluctuation amplitude, the mean axial speed and the beam viscosity coefficient, while other parameters are unchanged.

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陈立群， LIQUN CHEN， JEAN W. ZU， JUN WU ， XIAODONG YANG
Journal of Engineering Mathematics 48: 171182, 2004.，0001，（）：
1年11月30日
Twotoone parametric resonance in transverse vibration of an axially accelerating viscoelastic string with geometric nonlinearity is investigated. The transport speed is assumed to be a constant mean speed with small harmonic variations. The nonlinear partial differential equation that governs transverse vibration of the string is derived from Newton’s second law. The method of multiple scales is applied directly to the equation, and the solvability condition of eliminating secular terms is established. Closedform solutions for the amplitude of the vibration and the existence conditions of nontrivial steadystate response in twotoone parametric resonance are obtained. Some numerical examples showing effects of the mean transport speed, the amplitude and the frequency of speed variation are presented. Lyapunov’s linearized stability theory is employed to analyze the stability of the trivial and nontrivial solutions for twotoone parametric resonance. Some numerical examples highlighting the effects of the related parameters on the stability conditions are presented.
axially accelerating string,， geometric nonlinearity,， method of multiple scales,， stability,， viscoelasticity

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【期刊论文】Vibration and stability of an axially moving viscoelastic beam with hybrid supports
陈立群， LiQun Chen， ， XiaoDong Yang
L. Q. Chen, X. D. Yang. European Journal of Mechanics A/Solids 25 (2006) 9961008，0001，（）：
1年11月30日
Vibration and stability are investigated for an axially moving beam constrained by simple supports with torsion springs. A scheme is proposed to derive natural frequencies and modal functions from given boundary conditions of an elastic beam moving at a constant speed. For a beam constituted by the Kelvin model, effects of viscoelasticity on the free vibration are analyzed via the method of multiple scales and demonstrated via numerical simulations. When the axial speed is characterized as a simple harmonic variation about the constant mean speed, the instability conditions are presented for axially accelerating viscoelastic beams in parametric resonance. Numerical examples show the effects of the constraint stiffness, the mean axial speed, and the viscoelasticity.
Axially moving beam， Vibration frequency， Dynamic stability， Method of multiple scales， Viscoelasticity

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