张家忠
一直致力于力学(固体、流体力学及流-固耦合)方面的非线性动力系统的运动稳定性、分岔、混沌理论、数值方法及应用基础的研究。
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- 姓名:张家忠
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学术头衔:
博士生导师, 教育部“新世纪优秀人才支持计划”入选者
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学科领域:
力学
- 研究兴趣:一直致力于力学(固体、流体力学及流-固耦合)方面的非线性动力系统的运动稳定性、分岔、混沌理论、数值方法及应用基础的研究。
张家忠,教授、博士生导师。陕西省力学学会会员、中国流体工程学会风机专业委员会委员。入选2007年教育部“新世纪优秀人才支持计划”。
简历:1.1986、09-1993、05,于西安交通大学能源与动力学院流体机械及流体动力工程学科进行本科生、硕士研究生学习;2.1994、09-1997、12,在西安交通大学建筑工程与力学学院获得博士学位;3.1998、10-2001、02,应邀赴Eindhoven University of Technology进行博士后研究工作和学习;4.2001、03-现在,西安交通大学能源与动力工程学院,教师。
研究领域:一直致力于力学(固体、流体力学及流-固耦合)方面的非线性动力系统的运动稳定性、分岔、混沌理论、数值方法及应用基础的研究。目前的主要研究方向为:1)转子动力系统中的运动稳定性及分岔;透平机械中的流-固耦合或气弹问题、流动控制;2)无穷维非线性动力系统的降维方法研究;非线性偏微分耗散发展方程的多分枝解的跟踪问题及相应的数值方法;3)N-S方程、湍流中的奇异性、非线性行为(分岔、混沌)和建模, 以及通向湍流的途径、相应的数值分析方法;4)可变形飞行器的非线性气动弹性稳定性、增升减阻、气动加热、动态失速分析及数值方法;5)激波、等离子体的非线性动力学分析;高空、高超声速流动的低密度效应及数值方法;6)非线性连续动力系统中的惯性流形、分数微积分、多尺度分析、非光滑分析;7)薄壁结构的动力屈曲、多孔介质中的多尺度流动。
个人主页:http://jzzhang.gr.xjtu.edu.cn:8080/web/jzzhang
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张家忠, Jiazhong Zhang*, Sheng Ren, and Guanhua Mei
,-0001,():
-1年11月30日
Approximate Inertial Manifolds (AIMs) is approached by multilevel finite element method, which can be referred to as a Post-processed nonlinear Galerkin finite element method, and is applied to the model reduction for fluid dynamics, a typical kind of nonlinear continuous dynamic system from viewpoint of nonlinear dynamics. By this method, each unknown variable, namely, velocity and pressure, is divided into two components, that is the large eddy and small eddy components. The interaction between large eddy and small eddy components, which is negligible if standard Galerkin algorithm is used to approach the original governing equations, is considered essentially by AIMs, and consequently a coarse grid finite element space and a fine grid incremental finite element space are introduced to approach the two components. As an example, the flow field of incompressible flows around airfoil is simulated numerically and discussed, and velocity and pressure distributions of the flow field are obtained accurately. The results show that there exists less essential degrees-offreedom which can dominate the dynamic behaviors of the discretized system in comparison with the traditional methods, and large computing time can be saved by this efficient method. In a sense, the small eddy component can be captured by AIMs with fewer grids, and an accurate result can also be obtained.
Model reduction, Approximate Inertial manifolds, Nonlinear dynamics, Multilevel finite element method, Fluid Dynamics
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张家忠, Jiazhong Zhang, Wei Kang, Yan Liu
Journal of Computational and Nonlinear Dynamics JANUARY 2009, Vol.4 /011007-1,-0001,():
-1年11月30日
From the viewpoint of nonlinear dynamics, the stability and bifurcation of the rotor dynamical system supported in gas bearings are investigated. First, the dynamical model of gas bearing-Jeffcott rotor system is given, and the finite element method is used to approach the unsteady Reynolds equation in order to obtain gas film forces. Then, the method for stability analysis of the unbalance response of the rotor system is developed in combination with the Newmark-based direct integral method and Floquet theory. Finally, a numerical example is presented, and the complex behaviors of the nonlinear dynamical system are simulated numerically, including the trajectory of the journal and phase portrait. In particular, the stabilities of the system’s equilibrium position and unbalance responses are studied via the orbit diagram, phase space, Poincaré mapping, bifurcation diagram, and power spectrum. The results show that the numerical method for solving the unsteady Reynolds equation is efficient, and there exist a rich variety of nonlinear phenomena in the system. The half-speed whirl encountered in practice is the result from Hopf bifurcation of equilibrium, and the numerical method presented is available for the stability and bifurcation analysis of the complicated gas film-rotor dynamic system.
gas bearings, rotor dynamics, finite element method, stability, bifurcation, Floquet multiplier
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【期刊论文】Stability and bifurcation of doubly curved shallow panels under quasi-static uniform load
张家忠, Jiazhong Zhang a, Dick H. van Campen b
International Journal of Non-Linear Mechanics 38 (2003) 457-466,-0001,():
-1年11月30日
The focus of this paper is on the investigation of the mathematical nature of buckling from the point of view of bifurcation theory. For the doubly curved orthotropic panels subjected to quasi-static uniform load and with hinged boundary conditions, the solution to the non-linear partial di6erential equation is partitioned into two parts and projected onto the complete space spanned by the eigenfunctions of the linear operator of the governing equation. Furthermore, the fundamental branch, from which a new solution will emanate, is approximated by the 8rst single mode pair which is close to the real membrane state. Whereas the ensuing bifurcated branch is approximated by the other single mode pair, under the assumption that the coupling between modes can be neglected. The present analysis could give a deep insight into the mechanism of the instability of panel structures, and show that there exists a mode transition at the critical point and the snap-through, then results from saddle-node bifurcation on the bifurcated branch. As a conclusion, the buckling of the system studied can be stated as: a bifurcated branch emanates from the fundamental branch at a critical point, and a saddle-node bifurcation, behaving as jumping, then occurs on the ensuing bifurcated branch.
Bifurcation, Buckling, Stability, Shell, Non-linear analysis
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