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1.
为了研究动态风对覆冰输电线非线性舞动特征的影响,在原有稳定风作用下覆冰输电线舞动控制方程中添加周期激励载荷,并建立了新的受迫-自激振动控制方程,该控制方程也适用于描述相邻档导线对舞动档导线运动特征的影响。运用多尺度法分别对弱激励和强激励下的受迫-自激振动求解,得到主共振和谐波共振的幅频响应函数,分析了受迫-自激系统的主共振、超谐波和亚谐波共振。研究表明:弱激励下的主共振,当调谐参数大于0时,风速或激励幅值的增加会使得响应幅值出现跳跃、多值等不稳定的非线性动力学行为,并呈现硬弹簧特征;强激励下的自激系统,当激励频率接近固有频率的整数倍和分数倍时,更容易出现2次超谐波共振和1/2次亚谐波共振;当发生1/2次亚谐波共振时,随着激励幅值的增大,响应幅值也不断增大,共振峰值对应的调谐参数趋向于正轴方向,呈现硬弹簧特征,风速的增加会增强系统的非线性和硬弹簧特征。  相似文献   

2.
非线性转子动力学的稳定性和分岔   总被引:2,自引:0,他引:2  
大型高速转子的工作转速往往超过其第一阶临界转速,咽而需要考虑系统的非线性刚度和转轴材料的内阻尼对轴振动特性的影响。本文研究非线性围各阶共振点(临界转速)时的稳定性,并应用奇异性理论拱皋地转轴的定常运动(同步涡动)和自激振动(非同步涡动)周期响应的分岔。本文的结论不仅揭示了非线性转子丰富的动力学形为,对对大型高速转子的稳定性控制有一定参考价值。  相似文献   

3.
参激屈曲梁的倍周期分岔和混沌运动的实验研究   总被引:6,自引:0,他引:6  
季进臣  陈予恕 《实验力学》1997,12(2):248-259
本文对一端固定一端滑动承受轴向简谐载荷的屈曲梁的非线性响应进行了实验。研究了其基本参数共振和主参数共振两种情况,揭示了系统的倍周期分岔和混沌运动等复杂动力学行为。在某些情况下,混沌吸引子和周期吸引子共存,另一些则存在间歇混沌。给出了响应的时间历程、相图、频率谱和Poincare映射  相似文献   

4.
基于Winkler地基模型及Euler-Bernoulli梁理论,建立了弹性地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,并利用多尺度法求得该系统主共振的一阶近似解.分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响,然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响.结果表明:主共振幅频响应存在跳跃和滞后现象;阻尼对主共振响应有抑制作用;主共振显著增大系统稳态动力响应位移.  相似文献   

5.
本文用数值方法研究转子扭振-叶片弯曲振动等效系统的稳态和非稳态响应。叶片受气流周期激励力作用,与转轴通过平台干摩擦阻尼器相连,干摩擦力采用光滑模型计算。分析扭振和弯曲振动的固有频率具有1:1和1:3两种比值情况(内共振关系)的振动表明,系统不仅存在两个主共振,由于干摩擦力的非线性特点,还存在超谐和亚谐共振状况。由于阻尼器的引入,耦合系统的主共振频率点既可能升高(1:1情况),也可能降低(1:3情况),这是耦合系统中阻尼器的调频特点,在升速的非稳态响应中,主共振和超、亚谐共振幅值将会降低.而共振点一般会出现延迟现象,但也有某些共振点有所提前(1:3情况),因此存在内共振条件的干摩擦系统,具有丰富和复杂的振动现象。  相似文献   

6.
针对磁场环境中周期外载作用下轴向运动导电条形板的非线性振动及混沌运动问题进行研究。应用改进多尺度法对横向磁场中条形板的强非线性振动问题进行求解,得到超谐波共振下系统的分岔响应方程。根据奇异性理论对非线性动力学系统的普适开折进行分析,求得含两个开折参数的转迁集及对应区域的拓扑结构分岔图。通过数值算例,分别得到以磁感应强度、轴向拉力、激励力幅值和激励频率为分岔控制参数的分岔图和最大李雅普诺夫指数图,以及反映不同运动行为区域的动力学响应图形,讨论分岔参数对系统呈现的倍周期和混沌运动的影响。结果表明,可通过相应参数的改变实现对系统复杂动力学行为的控制。  相似文献   

7.
黏弹性传动带1:3内共振时的周期和混沌运动   总被引:14,自引:0,他引:14  
张伟  温洪波  姚明辉 《力学学报》2004,36(4):443-454
研究了参数激励作用下黏弹性传动带在1:3内共振时的周期解分岔和混沌动力学. 同时考虑传动带的线性外阻尼因素和材料内阻尼因素. 首先建立了具有线性外阻尼情况下的黏弹性传动带平面运动时的非线性动力学方程, 黏弹性材料的本构关系用Kelvin模型描述. 然后考虑黏弹性传动带的横向振动问题, 利用多尺度法和Galerkin离散法得到黏弹性传动带系统在1:3内共振时的平均方程. 最后利用数值模拟方法研究了黏弹性传动带系统的周期振动和混沌动力学, 得到了系统在不同参数下的混沌运动. 数值模拟结果说明黏弹性传动带系统存在周期分岔, 概周期运动及混沌运动.  相似文献   

8.
方孟孟  郭长青 《应用力学学报》2020,(2):653-660,I0013,I0014
首先建立了悬臂输流管道在基础激励与脉动内流联合作用下的运动方程;然后基于Galerkin法研究了该系统的非线性动力学行为,分析了系统运动状态随激励频率和相位差的变化,以及混沌百分比随频率比(基础激励频率与脉动频率之比)和相位差的变化。结果表明,无论以激励频率还是以相位差为分岔参数,系统都具有多种形式的动态响应,包括周期运动、概周期运动和混沌运动,但进入和脱离混沌的途径不同。相位差和频率比对系统的混沌百分比有重要影响:相位差为π/2时系统混沌百分比最大;频率比为1时系统混沌百分比最小,频率比较小或较大时系统混沌百分比与只有基础激励时接近。  相似文献   

9.
韩维  金栋平  胡海岩 《力学学报》2003,35(3):303-309
研究两自由度参数激励系统的非线性动力学与控制问题.利用Lagrange方程建立含反馈控制的参激捅及其驱动机构组成的系统动力学方程,以多尺度方法获得一阶近似控制方程.然后,对系统受一阶摸态参激主共振与一、二阶模态间3:1内共振联合作用下的幅额响应及其稳定性,以及反馈参数对系统稳态行为的影响作了详细分析.结果表明,响应的稳定域位置和大小取决于位移反馈,位移立方反馈改变了系统的非线性程度,速度反馈类似于阻尼,可使系统呈现自激振动特性.  相似文献   

10.
单自由度参数振动系统非线性响应的若干特征   总被引:6,自引:0,他引:6  
用数值积分方法,分析了无阻尼单自由度参数振动系统在给定的单频刚度激励和单频外载荷激振时的非线性动力学响应特性。研究表明了参数振动问题的主要特征:1)单频激励多频响应;2)多频响应中各谐波的分布具有特殊的规律;3)系统具有多频共振特性。  相似文献   

11.
An electromagnetic nonlinear energy harvester(NEH)based on a rotating system is proposed,of which the host system rotates at a constant speed and vibrates harmonically in the vertical direction.This kind of device exhibits several resonant phenomena due to the combinations of the rotating and the vibration frequencies of the host system as well as the cubic nonlinearity of the NEH.The governing equation of motion for the NEH is derived,and the dynamic responses and output power are investigated with the multiple scale method under the 1:1 primary and 2:1 superharmonic resonant conditions.The effects of system parameters including the nondimensional external frequency,the rotating speed,and the nonlinear stiffness on the responses of free vibration for the system are studied.The results of the primary resonance show that the responses exhibit not only the resonant characteristics but also the nonlinear dynamic characteristics such as the saddle-node(SN)bifurcation.The coexistence of multiple solutions and the varying trends of responses are verified with the direct numerical simulation.Moreover,the effects of system parameters on the average output power are investigated.The results of the analyses on the two resonant conditions indicate that the large power can be harvested in two resonant frequency bands.The effect of resonance on the output power is dominant for the 2:1 superharmonic resonance.Moreover,the results also show that introducing the nonlinearity can increase the value of the output power in large frequency bands and induce the occurence of new frequency bands to harvest the large power.The efficiency of the harvested power could be improved by the combined effects of the resonance as well as the nonlinearity of the NEH device.Suitable parameter conditions could help optimize the power harvesting in design.  相似文献   

12.
The nonlinear dynamics of a hybrid Rayleigh–Van der Pol–Duffing oscillator includes pure and impure quadratic damping are investigated. The multiple timescales method is used to study exhaustively various resonances states. It is noticed that the system presents nine resonances states. The frequency response curves of quintic, third and second superharmonic, and subharmonic resonances states are obtained. Bistability, hysteresis, and jump phenomenon are also obtained. It is pointed out that these resonance phenomena are strongly related to the nonlinear cubic and quadratic damping and to the external force. The numerical simulations are used to make bifurcation sequences displayed by the model for each type of oscillatory. It is noticed that the pure quadratic, impure cubic damping, and external excitation affect regular and chaotic states.  相似文献   

13.
An electromechanical integrated electrostatic harmonic actuator is promising for the miniaturization of electromechanical devices. As the dimensions of the actuator decrease, the effects of the van der Waals force become obvious. In this study, by considering the nonlinearity of electrostatic and van der Waals forces, nonlinear vibration equations of the flexible ring of an electrostatic harmonic actuator are deduced. Using these equations, the nonlinear free vibration and nonlinear forced response of the actuator are investigated. The effects of the van der Waals force on the nonlinear vibration of the flexible ring are analyzed. Results show that these effects of the van der Waals force are relatively obvious under some conditions and should be considered.  相似文献   

14.
范德华力对多壁纳米碳管力学性质的影响   总被引:2,自引:0,他引:2  
用分子动力学方法模拟了多壁纳米碳管在压缩、弯曲变形下力与变形的关系.通过与组成多壁碳管的各单壁碳管的比较分析,揭示了多壁纳米碳管层间范德华力对碳管力学性质的影响.采用Tersoff-Brenner势描述每一单壁纳米碳管内原子间作用,采用Lennard-Jones势描述碳管壁间范德华力.计算结果表明:多壁纳米碳管的比强度明显高于单壁纳米碳管.纳米碳管的半径虽然对杨氏模量影响不大,但对纳米碳管的曲屈行为影响却相当显著。  相似文献   

15.

This study presents an experimental method for identification of the backbone curves of cantilevers using the nonlinear dynamics of a van der Pol oscillator. The backbone curve characterizes the nonlinear stiffness and nonlinear inertia of the resonator, so it is important to identify this curve experimentally to realize high-sensitivity and high-accuracy sensing resonators. Unlike the conventional method based on the frequency response under external excitation, the proposed method based on self-excited oscillation enables direct backbone curve identification, because the effect of the viscous environment is eliminated under the linear velocity feedback condition. In this research, the method proposed for discrete systems is extended to give an identification method for continuum systems such as cantilever beams. The actuation is given with respect to both the linear and nonlinear feedbacks so that the system behaves as a van der Pol oscillator with a stable steady-state amplitude. By varying the nonlinear feedback gain, we can produce the self-excited oscillation experimentally with various steady-state amplitudes. Then, using the relationship between these steady-state amplitudes and the corresponding experimentally measured response frequencies, we can detect the backbone curve while varying the nonlinear feedback gain. The efficiency of the proposed method is determined by identifying the backbone curves of a macrocantilever with a tip mass and a macrocantilever subjected to atomic forces, which are representative sources of hardening and softening cubic nonlinearities, respectively.

  相似文献   

16.
This article explores enrichment to the method of Multiple Scales, in some cases extending its applicability to periodic solutions of harmonically forced, strongly nonlinear systems. The enrichment follows from an introduced homotopy parameter in the system governing equation, which transitions it from linear to nonlinear behavior as the value varies from zero to one. This same parameter serves as a perturbation quantity in both the asymptotic expansion and the multiple time scales assumed solution form. Two prototypical nonlinear systems are explored. The first considered is a classical forced Duffing oscillator for which periodic solutions near primary resonance are analyzed, and their stability is assessed, as the strengths of the cubic term, the forcing, and a system scaling factor are increased. The second is a classical forced van der Pol oscillator for which quasiperiodic and subharmonic solutions are analyzed. For both systems, comparisons are made between solutions generated using (a) the enriched Multiple Scales approach, (b) the conventional Multiple Scales approach, and (c) numerical simulations. For the Duffing system, important qualitative and quantitative differences are noted between solutions predicted by the enriched and conventional Multiple Scales. For the van der Pol system, increased solution flexibility is noted with the enriched Multiple Scales approach, including the ability to seek subharmonic (and superharmonic) solutions not necessarily close to the linear natural frequency. In both nonlinear systems, comparisons to numerical simulations show strong agreement with results from the enriched technique, and for the Duffing case in particular, even when the system is strongly nonlinear.  相似文献   

17.
A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube (DWNT) can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.  相似文献   

18.
Abdelkader developed a method for solving the van der Pol equation numerically. He observed that the orthogonal trajectories of the van der Pol equation satisfy a Riccati equation, the solution to which can be expressed in terms of Bessel functions. In the present paper, all nonlinear equations whose orthogonal trajectories satisfy Riccati or generalized Riccati equations are determined. Further on, another representation of the trajectories of the van der Pol equation is derived. This representation appears to be simpler than Abdelkader's.  相似文献   

19.
van der Pol型时滞系统的两参数余维一Hopf分岔及其稳定性   总被引:5,自引:0,他引:5  
研究具有三次非线性时滞项的van der Pol型时滞系统随两参数(时滞量和增益系数)余维一Hopf分岔,说明了线性化特性方程随两参数变化时的根的分布和Hopf分岔存在性;通过构造中心流形并且使用范式方法确定出Hopf分岔的方向以及周期解的稳定性;分析了时滞量对所论系统发生Hopf分岔的影响。  相似文献   

20.
近些年,很多学者致力于利用非线性增强振动响应减少的效果或者能量采集器的效率。因而非线性系统的响应值需要从理论计算方面更准确地预测。另外,根据学者已取得的研究成就,非线性能量汇(NES)中存在的立方刚度非线性可以将结构中宽频域的振动能量传递至非线性振子部分。文章将一种由NES和压电能量采集器组成的NES-piezo装置与两自由度主结构耦合连接,系统受谐和激励作用。文章采用谐波平衡法和复平均法分别推导了系统稳态响应,参照数值结果,对比两种近似解析方法在求解强非线性系统稳态响应时的异同。计算结果表明,系统体现较弱非线性时,二者计算结果差异很小;当系统体现强非线性时,复平均法不能准确地呈现系统高阶响应,提高阶数的谐波平衡法能更准确地表示系统响应值。基于谐波平衡法和数值算法,讨论NES-piezo装置对于系统宽频域减振的影响。与仅加入非线性能量汇情况对比,结果表明NES-piezo装置不会恶化宽频域减振效果,并且在第一阶共振频率附近,可以稍微提高结构减振效率。另外,计算结果也表明,采用恰当的NES-piezo装置可实现宽频域范围的结构减振和压电能量采集一体化。此项研究工作为研究不同情形强非线性系统的响应提供了理论方法的指导。另外,研究结果也为宽频域范围的结构减振和压电能量采集一体化提供了理论依据。  相似文献   

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