直撞式霍普金森压杆二次加载技术

利用传统分离式霍普金森压杆（split Hopkinson pressure bar, SHPB）实验技术来实现试件在较低应变率下的大变形时,需要使用超长的压杆系统,杆件的加工和实验空间限制了该技术的推广应用。鉴于此,提出一种直撞式霍普金森压杆二次加载实验技术,利用透射杆中的应力波在其末端的准刚性壁反射实现对试件的二次加载,并分析了准刚性质量块尺寸对二次加载的影响规律;采用二点波分离方法对叠加的应力波进行了有效分离和计算,在总长4 m的压杆系统中实现了1.2 ms的长历时加载,并可以准确获得试件的加载应变率曲线和应力应变关系。建立了直撞式霍普金森压杆二次加载有限元模型,数值仿真结果表明,该实验技术能有效地实现试件的二次加载,与超长SHPB系统获得的仿真结果相比较,两者的试件应力应变关系完全一致。利用该技术对1100铝合金材料进行动态压缩实验,实现了其在10² s⁻¹量级应变率下的大变形动态力学性能测试。

     

参数激励耦合系统的复杂动力学行为分析

分析了耦合van der Pol振子参数共振条件下的复杂动力学行为．基于平均方程，得到了参数平面上的转迁集，这些转迁集将参数平面划分为不同的区域，在各个不同的区域对应于系统不同的解．随着参数的变化，从平衡点分岔出两类不同的周期解，根据不同的分岔特性，这两类周期解失稳后，将产生概周期解或3—D环面解，它们都会随参数的变化进一步导致混吨．发现在系统的混沌区域中，其混吨吸引子随参数的变化会突然发生变化，分解为两个对称的混吨吸引子．值得注意的是，系统首先是由于2—D环面解破裂产生混吨，该混吨吸引子破裂后演变为新的混吨吸引子，却由倒倍周期分岔走向3—D环面解，也即存在两条通向混沌的道路：倍周期分岔和环面破裂，而这两种道路产生的混吨吸引子在一定参数条件下会相互转换．     

两自由度耦合van der Pol振子的拟主振动解

本文运用非线性系统的模态方法研究了两自由度耦合van der Pol振子。从退化系统稳定的主振动解出发,得到了原系统的拟主振动解,并给出了系统周期运动的条件,讨论了系统周期解、概周期解的分叉。     

双频内共振系统的Normal Form及其简化

讨论双频内共振系统的 Normal Form及其降维问题.利用发展的 Normal Form直接方法,导出了任意双频内共振系统 Normal Form的一般形式.指出 Poincare共振项分为内共振项和非内共振性两类,并定义了内共振项的阶.提出了一种普遍适用的降维变换,并证明了该变换可将任意双频内共振系统的 Normal Form方程降到3维.应用举例表明,该变换不仅适用于半单问题,也适于非半单问题（即强:1:1内共振系统）.     

有初内力的板的内共振

本文利用非线性时空有限方法和样条有限元技术对具有初内力的板的非线性频响特性进行了分析，计算了在不同初始内力下方板的大振幅自由振动、有阻尼强迫振动和矩形板的内共振。     

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.     

NONLINEAR VIBRATION OF THE COUPLED STRUCTURE OF SUSPENDED-CABLE-STAYED BEAM-1:2 INTERNAL RESONANCE

Through the Galerkin method the nonlinear ordinary differential equations （ODEs） in time are obtained from the nonlinear partial differential equations （PDEs） to describe the mo- tion of the coupled structure of a suspended-cable-stayed beam. In the PDEs, the curvature of main cables and the deformation of cable stays are taken into account. The dynamics of the struc- ture is investigated based on the ODEs when the structure is subjected to a harmonic excitation in the presence of both high-frequency principle resonance and 1：2 internal resonance. It is found that there are typical jumps and saturation phenomena of the vibration amplitude in the struc- ture. And the structure may present quasi-periodic vibration or chaos, if the stiffness of the cable stays membrane and frequency of external excitation are disturbed.     

多自由度内共振系统非线性模态的分岔特性

利用多尺度法构造了一个立方非线性1:3内共振系统的内共振非线性模态(NonlinearNormal Modes associated with internal resonance)．研究表明,内共振非线性系统除存在单模态运动外还存在耦合模态运动．耦合内共振模态具有分岔特性．利用奇异性理论对模态分岔方程进行分析发现此类系统的模态存在叉形点分岔和滞后点分岔这两种典型的分岔模式．     

内共振条件下直线运动梁的动力稳定性

基于Kane方程,建立起了包含有耦合的三次几何及惯性非线性项大范围直线运动梁动力学控制方程．利用多尺度法并结合笛卡尔坐标变换,对所得方程进行一次近似展开,着重对满足一、二阶模态间3:1内共振现象的两端铰支梁参激振动平凡解稳定性进行了详尽的分析,得出了稳定性边界的解析表达式．采用中心流形定理对调制微分方程组进行降维处理,分析了相应Hopf分岔类型并通过数值计算发现了稳定的极限环存在．     

FORCED VIBRATIONS WITH INTERNAL RESONANCE OF A PIPE CONVEYING FLUID UNDER EXTERNAL PERIODIC EXCITATION

Applying the multidimensional Lindstedt-Poincaré (MDLP) method, we study the forced vibrations with internal resonance of a clamped-clamped pipe conveying fluid under external periodic excitation. The frequency-amplitude response curves of the first-mode resonance with internal resonance are obtained and its characteristics are discussed; moreover, the motions of the first two modes are also analyzed in detail. The present results reveal rich and complex dynamic behaviors caused by internal resonance and that some of the internal resonances are decided by the excitation amplitude. The MDLP method is also proved to be a simple and efficient technique to deal with nonlinear dynamics.