受简谐激励弹簧测力机构的主参数共振研究

应用拉格朗日方程得到有阻尼弹簧测力机构在简谐激励作用下的非线性运动微分方程Duffing-Mathieu方程;根据非线性振动的多尺度法求得系统满足主参数共振情况的一次近似解,并对其进行数值计算.分析激力、谐调值、阻尼等对系统主参数共振响应曲线的影响.随着阻尼的减小和参数激励幅值的增大,系统幅频响应曲线的峰值和共振区增大.其他参数相同时, 硬刚度力幅响应曲线与软刚度力幅响应曲线关于谐调值反对称.     

Winkler地基上四边自由矩形薄板的亚谐共振与奇异性分析

研究Winkler地基上四边自由矩形薄板的亚谐共振问题.按照弹性力学理论建立Winkler地基上四边自由受简谐激励作用矩形薄板的动力学方程.利用Galerkin方法将其转化为非线性振动方程.应用非线性振动的多尺度法求得系统满足1/3次亚谐共振情况时的一次近似解,并进行数值计算.分析激励、阻尼等对系统响应曲线的影响.应用奇异性理论对1/3次亚谐共振幅频响应方程进行奇异性分析,得到选取不同分岔参数时开折参数平面的转迁集和分岔图.     

Winkler地基上材料非线性矩形薄板1/3次亚谐共振

为研究Winkler地基上材料非线性矩形薄板受简谐激励的非线性振动,应用弹性力学理论建立其动力学方程,并由Galerkin方法将其转化为非线性振动方程。应用非线性振动的多尺度法求得系统1/3次亚谐共振的近似解,并进行数值计算。分析激励、几何参数、阻尼系数、非线性参数对共振响应曲线的影响。     

温度场中非线性弹性地基上矩形薄板主共振

为了研究温度场中非线性地基上矩形薄板受简谐激励的主共振稳定性问题,应用弹性力学理论建立其动力学方程,应用Galerkin方法将其转化为非线性振动方程.利用非线性振动的多尺度分析方法求得系统主共振的近似解,并进行数值计算.分析温度、地基系数、阻尼、几何参数、激励等对系统主共振的影响.幅频响应曲线存在跳跃现象.随着阻尼、板厚、地积系数的增加,主共振振幅减小;随着激励幅值的增加,主共振振幅增大.随着温度系数-T1的增加,共振曲线的振幅增大;随着温度系数-T0的增加,共振曲线的振幅减小.     

温度场中输电线在谐扰力作用下的3次超谐共振

研究输电线在温度场中谐扰力作用下的3次超谐共振问题,应用动力学方法建立温度场中受谐扰力作用输电线的非线性振动.根据非线性振动的多尺度解法,得到系统满足3次超谐共振情况的近似解,并对其进行数值计算.分析温差变化、外部激励、谐调值、阻尼等对系统的影响.得到系统失稳的临界温度,指出幅频响应曲线存在跳跃现象.     

黏弹性传动带系统1/2次亚谐-主参数共振分析

基于参数激励作用下黏弹性传动带横向振动运动方程,应用多尺度法得到1/2次亚谐-主参数共振的近似解。分析了黏弹性参数、调谐参数、轴向速度等参数对稳态响应幅值和存在区域的影响,揭示了黏弹性带的动力学现象。     

电阻电感非线性RLC电路弹簧耦合系统3次超谐共振

研究电阻和电感非线性RLC(resistance-inductance-capacitance)电路弹簧耦合系统的非线性振动,应用拉格朗日-麦克斯韦方程,建立受简谐激励的具有电阻和电感非线性RLC电路弹簧耦合系统的数学模型.根据非线性振动的多尺度法,得到系统满足3次超谐共振条件的一次近似解以及对应的定常解.对其进行数值计算,分析系统不同参数对响应曲线的影响.增大激励电压、极板面积和非线性电阻系数,响应曲线振幅和共振区变大.增大极板间距、线性电感系数和线性电阻系数,响应曲线振幅和共振区变小.系统的固有频率随极板间距增大而增大,随极板面积和线性电感系数的增大而减小.     

皮带驱动机构的1/3次亚谐共振分析

应用拉格朗日方程,得到皮带驱动机构的非线性振动微分方程,根据非线性振动的多尺度解法,得到系统满足1/3次亚谐共振情况的一次近似解以及对应的定常解,并对其进行数值计算,分析带的长度和横截面积、外激力、谐调值、系统阻尼等对系统的影响,揭示一些新的动力学现象.     

螺栓连接悬臂梁超谐响应特性试验研究

针对光电设备中广泛采用的螺栓连接形式,采用单螺栓连接悬臂梁模型,对螺栓连接引起的结构振动特性的改变进行实验。利用激振器和振动信号采集设备,结合快速傅立叶分析方法指出螺栓连接模型在一定条件下有超谐共振响应现象。模型的谐振频率随着扭矩的增大呈先增大后减小的现象。结构在相同扭矩下,第一阶谐振频率随着激励幅值的增大而减小,结构呈渐软非线性。给定1/2和1/3倍谐振频率下的正弦激励,系统能量随着激励幅值的增大而趋向于固有频率处。结构在低预紧扭矩下,非线性项中二次项对结构响应起主要作用;在较高预紧下,非线性项中三次非线性项对结构响应起主要作用。该实验结果对开展后续连接结构的非线性振动特性的研究有一定的理论和指导意义。     

齿轮传动系统的参数稳定性及振动特性分析

考虑齿轮时变啮合刚度与齿侧间隙,建立齿轮副系统动力学模型。利用Floquet理论推导了参数激励作用下齿轮系统的近似解析解,得到了系统的稳定性边界曲线。采用Newmark-β数值求解法对齿轮系统进行动力学仿真,研究了时变刚度、齿侧间隙、啮合阻尼对齿轮传动系统动力学特性的影响。研究结果表明:当参数激励的频率等于派生系统自由振动周期的2/n倍时,系统可能产生参数共振,随着参数激励频率的增加不稳定区域逐渐增大;齿侧间隙的存在则导致齿轮系统产生多值解和幅值跳跃等典型的非线性动力学特征;随着外部激励幅值和阻尼比增大及内部激励幅值的减小,齿轮系统的非线性振动特征逐渐减弱。     

转矩分流式齿轮传动系统的非线性动力学特性

为研究转矩分流式齿轮传动系统的非线性动力学特性,建立系统的非线性动力学模型,考虑了齿侧间隙、时变刚度、综合传动误差、阻尼和外激励等参数。使用PNF(Poincaré-Newton-Floquet)方法对系统的动力学微分方程进行求解发现,在不同的参数条件下系统会出现4种动态响应：简谐响应、次谐波响应、拟周期响应及混沌响应。4种状态下的时间历程、相图、Poincaré映射图、快速傅里叶变换(Fast Fourier transform,FFT)频谱图表明该系统有很强的非线性特性,应使用非线性理论进行更深入的研究。     

充液飞行器多频运动模式下燃料晃动的全局分岔行为

建立充液飞行器多频运动模式下液体燃料晃动方程,利用Melnikov方法对其全局动力学行为进行分析,得到系统不同参数下异宿分岔和次谐分岔的阈值,确定混沌运动产生的机理.同时,通过对系统模型的非线性系数与充液深度之间关系的分析,发现系统存在一“充液转换点”,使得系统的全局动力学行为发生巨大改变,需引起重视.     

非线性弹性转子系统动力特性分析

以线性项和立方项之和来表示转轴材料的物理非线性因素，建立了具有非线性弹性轴的转子系统的动力学方程，利用多尺度法对系统的非共振、主共振、超谐共振和亚谐共振等非线性动力学响应进行了分析，为具有此类特性的转子系统安全运行提供了一定的参考。     

Nonlinear saturation controller for vibration supersession of a nonlinear composite beam

In this paper, a study for nonlinear saturation controller (NSC) is presented that used to suppress the vibration amplitude of a structural dynamic model simulating nonlinear composite beam at simultaneous sub-harmonic and internal resonance excitation. The absorber exploits the saturation phenomenon that is known to occur in dynamical systems with quadratic non-linearities of the feedback gain and a two-to-one internal resonance. The analytical solution for the system and the nonlinear saturation controller are obtained using method of multiple time scales perturbation up to the second order approximation. All possible resonance cases were extracted at this approximation order and studied numerically. The stability of the system at the worst resonance case (Ω = 2ω _s and ω _s = 2ω _c ) is investigated using both frequency response equations and phase-plane trajectories. The effects of different parameters on the system and the controller are studied numerically. The effect of some types of controller on the system is investigated numerically. The simulation results are achieved using Matlab and Maple programs.     

Investigation of oscillation modes based on numerical solutions of nonlinear models

A single-frequency approximation according to the Prony method for numerical solution of a nonlinear model estimates the central fundamental frequency that determines the period of oscillations, i.e., the minimal time scale of this numerical solution. Then, subharmonic modes of this numerical solution can be identified in the time slots multiple to the oscillation period. Numerical solutions of a bistable oscillator model are considered as an example of spectral identification of a sub-harmonic oscillation mode according to the Prony method.     

螺栓松动损伤的亚谐波共振识别方法

螺栓松动将导致结构完整性的破坏,螺栓连接状态的实时有效监测和评估具有重大意义。提出了一种基于亚谐波共振分析的螺栓松动识别方法。针对螺栓连接结构简化的单自由度非线性模型,采用多尺度方法分析了亚谐波共振现象,定性模拟了螺栓松动损伤亚谐波激励条件。以铝梁螺栓搭接结构为实验对象,利用粘贴在铝梁表面的压电作动/传感单元,采用不同频率的激励信号作用在作动片上,传感片接收响应信号,对其进行频谱分析,通过提取响应频谱中的亚谐波成分进行螺栓松动损伤识别。仿真与实验结果表明,亚谐波产生所需激励频率在两倍固有频率附近,使用亚谐波检测方法能有效识别螺栓松动。     

一种新的转子碰摩故障诊断特征的研究

建立Jeffcott碰摩转子的弯扭耦合振动非线性微分方程，通过数值仿真手段，着重分析转子碰摩故障的扭振时频域特点及其非线性振动特性，并描述动静间隙对碰摩转子扭振非线性特性的影响。研究表明，转子碰摩激起丰富的扭振频谱信息，主要包括N/2X、N/3X等分频成分以及1X、2X等倍频成分，且分频幅值往往比倍频大许多。在一定转速范围内，周期运动与复杂的非线性运动交替出现。而动静间隙对转子扭振特性影响明显，动静间隙越小，转子动静碰摩越严重，频谱成分越丰富，运动形式更趋复杂，相应的各复杂运动区的范围也越宽。文中揭示的扭振特征为转子碰摩的状态识别与诊断提供了一种新方法。     

Determination of temperature and wear during braking

A model of the braking process has been proposed. We have obtained the contact temperature, the value of wear and the sliding speed for general experimental dependencies of the coefficient of friction and that of wear on the temperature. The problem has been reduced to a system of nonlinear integral equations of the Volterra type by means of the Laplace integral transform with respect to time. In case when the coefficient of friction is constant and for a linear dependence of the wear coefficient on the temperature we succeeded in obtaining the solution of the system of the integral equations in a closed form. In this way we have obtained simple engineering formulae for the computation of the contact temperature and wear. The results of the computations are presented in diagrams.     

Comparisons of gear dynamic responses with rectangular mesh stiffness and its approximate form

The mesh stiffness is close to rectangular stiffness, and the first harmonic approximate term of rectangular stiffness is generally adopted in the nonlinear gear dynamic analysis. The differences between the rectangular stiffness and its approximate form are analyzed in detail. The frequency response and dynamic factor are calculated by a numerical method, to illustrate the dynamic characteristics of the gear nonlinear system with different mesh stiffness forms. The results show that: The trends of frequency response of gear dynamic system with rectangular stiffness and its approximate form are identical. The jump phenomena are detected in both cases. Without the effect of static transmission error, the dynamic factor with rectangular mesh stiffness is larger than that with approximate mesh stiffness. Under design power and speed condition, the result with approximate mesh stiffness function may deduce reasonless suggestions for a designer. The static transmission error will enlarge the vibration amplitude and dynamic factor when the approximate mesh stiffness is adopted, but the effects on the response of gear system with rectangular mesh stiffness are fractional. The mesh stiffness may excite the odd subharmonic resonance, and the static transmission error may excite the even sub-harmonic resonance respectively.