求解输流管道动态响应问题的一种有效方法

研究了两端铰支输流管道在脉动内流作用下的参数共振问题。根据数值分析中发现的参数共振响应特性,给出了第一和第二振型运动相互解耦的控制方程,并用谐波平衡法导出了参数共振响应曲线的近似解析解。算例表明,第一振型近似解与数值解吻合得很好,而第二振型解在共振点附近与数值解略有差距,但二者的整体走向完全相同。     

滚动轴承非线性轴承力及其对轴承系统振动特性的影响

滚动轴承在旋转机械中应用及其广泛,其振动特性对旋转机械的正常运行有很大影响。本文基于赫兹弹性接触理论和滚动轴承运动学,推导了滚动轴承在工作状态下产生的非线性轴承力,并在此基础上对滚动轴承系统的振动特性进行了分析。研究结果表明:滚动轴承的非线性轴承力会诱发变刚度振动。系统响应中存在多种周期(谐波、次谐波和超谐波)和非周期(拟周期和混沌)响应。通过频谱图、Po incaré图和分叉图,分析了滚动轴承系统在不同参数下的周期分叉特性。当非线性轴承力和不平衡力共同作用时,滚动轴承系统会产生组合振动,随着不平衡力的增大变刚度振动所对应频率的幅值逐渐降低。      

两端铰支输流管道在脉动内流作用下的稳定性和参数共振

 研究了两端铰支输流管道在脉动内流作用下的参数共振问题。用平均法导出了失稳判据和3 种参数共振区域的边界曲线方程,并据此讨论了系统参数对不稳定区域的影响。用数值方法分析了各种参数共振的响应曲线,其存在区域以及响应频率与脉动流频率之间的关系。研究结果发现,组合共振区域内发生两种不同的拟周期运动和组合周期运动, 而且第1 振型次谐波共振曲线延伸到组合共振区域。因此,在同一脉动频率下存在可发生多种不同运动(第1 振型次谐波振动、拟周期振动和组合周期振动等) 的参数区域。     

干摩擦对称黏滑响应的级数解及黏滑边界特性

针对航空发动机中的摩擦振动问题,给出了对称黏滑运动摩擦力的分段表达式.利用谐波平衡方法推导了具有偶数次黏着的黏滑运动的级数形式解析解,并基于该解析解给出了参数平面内的黏滑边界线方程.黏滑运动响应仅包含奇次谐波成分,在奇次分数倍频处存在超谐次共振.当频率比小于0.4时,黏滑边界线呈现凸凹交替特征,局部极小值位于各阶超谐次共振频率处.黏性阻尼增大能够缩小无黏着运动的参数范围,但在各阶超谐共振频率附近,黏性阻尼增大会扩大无黏着运动的参数区域.      

轴系非线性振动解析模型研究

针对高速柔性轴系振动中线性与非线性的耦合作用，定义了非线性尺度因子ε，构建了轴系振动耦合作用模型.该模型拓展了经典线性模型的研究思路，重点探讨轴系的非线性响应.应用多尺度法推导了转子非线性振动的通频解析解的Fourier级数形式，同时给出了非线性固有频率和基频近似频响方程（FRE）.通过实验验证了同尺度条件下（ε=1），通频解析解及基频近似频响方程的非线性特性，以及解析耦合振动模型与通频解析解的合理性和有效性.      

基于谐波平衡法的含Iwan模型干摩擦振子非线性振动

通过谐波平衡法,研究了由Iwan模型和1个质量块构成的干摩擦振子系统的自由振动和受迫振动问题.对于自由振动,推导了系统卸载和加载过程中各自对应的非线性运动方程;通过谐波平衡法,求得了各方程的1阶谐波解;为了得到方程正确的数值解,提出了确定零速度时刻的策略;数值算例结果表明:谐波平衡法与数值方法得到结果吻合较好,从而验证了谐波平衡法求解此类问题的有效性.对于系统微滑移下的受迫振动,采用谐波平衡法求得了系统的幅频关系.最后,对Iwan模型阻尼特性的研究发现,模型等效黏性阻尼比与其振幅存在非线性关系.      

圆锥齿轮行波共振应力响应仿真计算

文中叙述了圆锥齿轮行波振动和行波共振的概念。利用圆柱直齿轮齿间啮合力的形状函数,组织了对圆锥齿轮行波共振的仿真激励函数。算出了圆锥齿轮的二、三节径行波共振应力响应。算出的应力响应幅值与实测值比较一致。     

单圆盘转子非线性振动模型及机理

根据转子非线性振动的力学性质及大变形假设,结合工程实际构建了转子非线性振动具有Duffing方程形式的力学模型,推导了非线性系统的等效频率和频响方程,研究了刚度元件、阻尼元件与非线性元件对系统振动的影响.通过单圆盘转子非线性振动实验,验证了非线性振动模型结构与Duffing方程求解及频响方程的合理性与有效性,揭示了共振、突变、滞后等非线性现象的机理,为转子振动特性分析提供了一种新的研究方法.      

正三角形排列三圆柱绕流与涡致振动数值模拟

基于有限体积法求解二维粘性不可压缩N-S方程,对低雷诺数下正三角形排列等直径三圆柱的绕流与涡致振动进行数值模拟。圆柱振动简化为两自由度的质量-弹簧-阻尼模型,圆柱的动力响应通过Newmark-β方法求解。间距比在1.5~6.0之间变化,重点研究各圆柱的气动力和响应及相关的频率特性、尾流流动模式随间距比的变化。研究结果表明:三圆柱发生振荡时的气动力要远大于绕流结果,当间距比在3.5~4.0之间气动干扰最为强烈。当间距比大于3.0时,下游圆柱的横向和流向位移相位差出现周期性切换,导致升力系数均值出现波动,并且下游圆柱的质心运动轨迹为斜向上和斜向下椭圆形的叠加。三圆柱的最大横向位移幅值均能达到0.9D,下游圆柱的最大流向振幅达到1.1D,这说明组成多圆柱振荡系统单柱的横向位移远大于孤立圆柱发生涡激共振的最大位移,并且下游圆柱的流向振荡不可忽视。     

非平行边界层C型失稳的非线性演化(英文)

提出用抛物化稳定性方程(PSE)新方法,研究非平行边界层从层流向湍流转捩的C型失稳的演化过程,特别是非线性演化问题。研究了至关重要的初始条件,包括各扰动谐波的初始解、初始站均流变形的模拟、以及通过对线性 PSE 的求解获得 TS波和C型亚谐扰动的初始站值等。发展了高精度的数值方法,满足PSE的关键性正规化条件,实现非线性抛物化稳定性方程的有效求解和稳定推进。算例展示了Blasius边界层的C型失稳的非线性演化过程,与典型实验结果相吻合。     

Nonlinear resonance characteristics of a dual-rotor system with a local defect on the inner ring of the inter-shaft bearing

In this paper, the nonlinear resonance characteristics of a dual-rotor system are investigated with the consideration of a local defect on the inter-shaft bearing of the system. A simplified model of the dual-rotor system is proposed by considering that there is a local defect on the inner ring of inter-shaft bearing. The local defect is modelled as an inverted isosceles trapezoidal groove, which can make great influence on the inter-shaft bearing force due to the change of radial clearance of the inter-shaft bearing. The motion equations of the dual-rotor system are formulated by using the Lagrange equation. The Runge-Kutta method is employed to solve the motion equation. The amplitude-frequency response curve of the dual-rotor system is obtained, the abnormal resonance characteristics are analyzed. In addition, the influence of defect parameters, rotors and support parameters and inter-shaft bearing parameters on the amplitude-frequency characteristics of the system are discussed. The results show that there are two main resonance peaks and four abnormal resonance peaks on the amplitude-frequency response curve of the dual-rotor with a local defect on the inner ring of the inter-shaft bearing. Through analyzing the vibration response of the abnormal resonance peaks, it is found that the first two abnormal resonances are caused by the combined resonance, which are related to the inner ring fault and the rotational speed of high or low pressure rotors, and the last two resonances are caused by the induced resonance of the inner ring fault. At the same time, when the parameters of defect, rotors and support and inter-shaft bearing change, the resonance of the system also shows the corresponding change law.     

Natural and man-made noise in the Earth-ionosphere cavity at extremely low frequencies (Schumann resonances and man-made ‘interference’)

The equations for the Earth-ionosphere cavity resonance fields are given and some of the approximations used in their derivation are indicated. Typical electric and magnetic 5 to 20 Hz Schumann resonance field intensities are listed and compared with the level of other natural and man-made electromagnetic noise. Applications of Schumann resonances to thunderstorm location and measurement of global lightning activity are reviewed briefly. Ionospheric conductivity profiles appropriate for this frequency range are discussed and the importance of atmospheric conductivity below 60 km is pointed out.     

Nonlinear vibration response characteristics of a dual-rotor-bearing system with squeeze film damper

Rolling bearing and Squeeze Film Damper (SFD) are used in rotor support structures, and most researches on the nonlinear rotor-bearing system are focused on the simple rotor-bearing systems. This work emphasizes the comparative analysis of the influence of SFD on the nonlinear dynamic behavior of the dual-rotor system supported by rolling bearings. Firstly, a reduced dynamic model is established by combining the Finite Element (FE) method and the free-interface method of component mode synthesis. The proposed model is verified by comparing the natural characteristics obtained from an FE model with those from the experiment. Then, the steady-state vibration responses of the system with or without SFD are solved by the numerical integration method. The influences of the ball bearing clearance, unbalance, centralizing spring stiffness and oil film clearance of SFD on the nonlinear steady-state vibration responses of the dual-rotor system are analyzed. Results show that SFD can effectively suppress the amplitude jump of the dual rotor system sustaining two rotors unbalance excitations. As the ball bearing clearance or unbalance increases, the amplitude jump phenomenon becomes more obvious, the resonance hysteresis phenomenon strengthens or weakens, the resonant peaks shift to the left or the right, respectively. SFD with unreasonable parameters will aggravate the system vibration, the smaller the oil film clearance, the better the damping performance of the SFD, the larger the centralizing spring stiffness is, the larger resonance amplitudes are.     

考虑预应力和液体影响的圆柱壳颤振分析

 为了研究预应力和液体对圆柱壳颤振的影响,采用杂交元方法,建立了圆柱壳的气动弹性方程。由Sanders薄壳理论和经典有限元理论,从壳的精确解推导节点位移函数入手,并由一阶活塞理论得到结构的气动阻尼矩阵和刚度矩阵,最终推导出考虑预应力和内部液体影响的圆柱壳的混合有限元公式和气动弹性方程。通过特征值法验证了此种有限元方法的正确性,并重点研究了预应力和内部注有液体对圆柱壳稳定性的影响。计算结果表明:预应力和液体对圆柱壳的颤振特性有显著的影响。     

高速转动壳体行波振动实验研究

本文对轴对称薄壁壳结构的振动特性进行了试验研究。对一圆柱薄壳在静止状态和高速旋转状态下进行了模态试验。试验结果验证了轴对称薄壁壳在转动状态下,由于科氏力的影响,同一模态在转动坐标系中,存在不同频率的前后行波。为理论计算和发生在航空发动机中转动薄壁件振动设计,提供了可靠的试验依据。     

Analysis of nonlinear deformation and stability of oval cylindrical shells under combined loading by bending and torsion moments

A problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular cross-section contour is solved by the finite element method. The nonlinear system of algebraic equations to determine the nodal unknowns of finite elements is obtained with the use of the variational Lagrange principle. The system is solved by the method of successive loadings with the use of the Newton-Kantorovich method of linearization, the method of solving linear Craut’s equations and Sylvestor’s stability criterion. The nonlinear deformation and stability of shells with the oval and elliptical cross-sections under combined loading by bending and torsion moments are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity, shell ovality and ellipticity on the critical loads is clarified.     

一个非线性拟协调退化壳有限元

 根据非线性协调有限元列式方法,构造了几何非线性拟协调9结点四边形退化壳有限元。首先给出9结点四边形退化壳单元的几何描述和位移模式;接着讨论了非线性协调有限元列式方法;假设应力和应变;然后用所构造的壳单元,进行了方板、圆拱、球壳和圆柱壳的数值分析,并同精确解以及其他单元的解答进行了比较。结果表明本文壳单元是准确的和有效的。     

电动力绳系周期解求解及稳定性控制

电动力绳系姿态摆动动力学方程具有非线性特点,且姿态摆动状态直接影响着空间任务能否正常进行。首先,基于哑铃模型及偶极子地磁场模型假设,推导了在倾斜圆轨道上运行的电动力绳系姿态动力学方程。其次,给出了利用摄动法和不动点迭代法相互配合的数值方法求解该非线性方程周期解的过程及解的稳定性判断准则,并针对不稳定周期解提出了相应的稳定性控制策略。最后,通过数值仿真分析,得到了姿态摆动运动的周期解图像,验证了周期解求解算法的有效性,并对不稳定周期解实现了稳定性控制。