多间隙二级齿轮非线性振动分岔特性研究

采用集中质量法,建立了多间隙二级齿轮系统的五自由度非线性振动模型.模型考虑了各齿轮副间变刚度、齿侧间隙、支承间隙以及传动误差等非线性因素,推导出系统量纲振动微分方程,并利用分岔图、Poincaré截面图,全面地分析了系统转速、阻尼比对系统分岔特性的影响.结果发现系统在各种非线性因素的综合影响下,表现出丰富复杂的分岔特性.系统随着参数的变化先后出现短周期运动、长周期运动、拟周期运动及混沌运动.在不同阻尼比下,系统随着转速的逐渐减小,由稳定的周期1运动,倍化分岔变为稳定的周期2运动,再经过Hopf分岔变为拟周期运动,通过激变又变为稳定的周期1运动,最终通过Hopf分岔-锁相进入混沌.随着转速的逐渐增大,系统随阻尼比变化的混沌运动范围减小,出现稳定的周期1运动、长周期和拟周期运动,并且长周期和拟周期运动范围逐渐变小而稳定的周期1运动的范围逐渐变大.     

路面方向扰动下重型汽车的横向稳定性及分岔、混沌运动

针对三轴重型汽车建立了二自由度非线性人-车-路闭环模型,考虑驾驶员控制和路面方向扰动,推导了系统动力学方程．在运用Hopf分岔理论进行分析的基础上,以临界车速为评价指标,通过数值模拟研究了轴距、预瞄距离、载重量、驾驶员控制时滞和轮胎侧偏刚度对转向稳定性的影响,并确定了转向系统的数值稳定范围．另外,还通过分岔图、时程曲线、相轨线、功率谱、Poincaré图和Lyapunov指数研究了不同车速下汽车的非线性动力学响应．结果表明,随着车速的增加汽车可能发生周期运动、拟周期运动及混沌运动,汽车的横向稳定性与车辆和驾驶员参数密切相关.     

多自由度强非线性颤振分析的增量谐波平衡法

对多个自由度上含有强非线性项系统的颤振问题,推广应用增量谐波平衡法进行分析．考虑带有强非线性立方平移和俯仰刚度项的二元机翼颤振方程,首先将方程用矩阵形式表示,然后把振动过程分解成为振动瞬态的持续增量过程,再采用振幅作为控制参数应用谐波平衡法,以这种推广的增量谐波平衡法求得方程解的表达式,并由此分析系统的分岔现象、极限环颤振现象和谐波项数的取值问题,最后用龙格-库塔数值方法进行验算,结果表明:分析多个自由度的强非线性颤振,增量谐波平衡法是精确有效的．     

一类弹性储液箱同液体耦合晃动问题的分岔行为分析

建立了弹性圆柱型储液箱同液体耦合系统在外激励下的非线性振动方程组．采用多尺度法、奇异性理论研究此非线性振动系统共振解的分岔行为,通过对其分岔行为的分析和讨论,得到了这一系统的多种转迁集和分岔图,建立了系统参数与其拓扑分岔解的联系,并且分析了不同参数下系统的分岔特性,为实现储液器参数的优化控制提供了理论依据．     

离散时间二型模糊双线性时滞系统的可达集估计与耗散性

文章研究了一类带有时变时滞和外部干扰的非线性系统的可达集估计与耗散控制问题.首先,考虑非线性系统的不确定参数,将非线性系统建模为区间二型模糊双线性时滞系统.其次,通过构造Lyapunov-Krasovskii泛函,提出区间二型模糊状态反馈控制准则,并利用反互凸组合引理界定二、三重时滞差分交叉项,得到保守性较小的区间二型模糊双线性闭环系统的可达集估计条件及系统严格耗散稳定性充分性条件.定理的条件可以保证系统的所有状态都收敛在一个椭圆内,并通过序列线性规划矩阵方法得到模糊控制器.最后,给出数值算例和仿真结果验证所得结论的有效性和正确性.     

离散区间二型模糊双线性时滞系统的稳定控制

本文研究了带有常时滞的离散时间二型模糊双线性系统的状态反馈控制问题。首先,考虑隶属函数的不确定性,将非线性系统建模为区间二型模糊双线性系统。其次,基于Lyapunov稳定性理论,提出了区间二型模糊状态反馈控制准则,以保证区间二型模糊双线性闭环系统的稳定性。控制器的设计可以通过序列线性规划矩阵方法求解得到。最后,通过数值仿真例子验证所得结果的有效性和正确性。     

非线性颤振系统中既是超临界又是亚临界的Hopf分岔点研究

研究了二元机翼非线性颤振系统的Hopf分岔．应用中心流形定理将系统降维,并利用复数正规形方法得到了以气流速度为分岔参数的分岔方程．研究发现,分岔方程中一个系数不含分岔参数的一次幂,故使得分岔具有超临界和亚临界双重性质．用等效线性化法和增量谐波平衡法验证了所得结果．     

超声速流中含间隙和立方非线性二元机翼的动力学分析

研究超声速流中含间隙和立方非线性二元机翼的气动弹性响应．首先由二阶活塞理论得到了双楔机翼的气动力和气动力矩．然后由平均法得到了气动弹性方程的极限环响应,并用Floquet理论分析了极限环的稳定性．结果表明,间隙系统在超临界Hopf分岔的条件下也存在Fold分岔和幅值的跳跃现象．而后,数值解与平均法的结果进行了对比,两者吻合得很好．最后,详细研究了间隙参数对气动弹性响应的影响．     

磁场中旋转运动圆环板主共振分岔及混沌研究

研究了磁场中旋转运动圆环板的磁弹性主共振及分岔、混沌问题.通过Hamilton(哈密顿)原理推得磁场中旋转运动圆环板的横向振动方程,并采用Bessel(贝塞尔)函数作为振型函数进行Galerkin(伽辽金)积分,得到磁场中旋转运动圆环板的无量纲非线性振动常微分方程.利用多尺度法展开,得到静态分岔方程、对应的转迁集与分岔图,以及物理参数作为分岔控制参数时的分岔图.利用Mel’nikov(梅利尼科夫)方法,对系统混沌特性进行研究,得到外边夹支内边自由边界条件下异宿轨破裂的条件;通过数值计算,得到外激振力幅值作为分岔控制参数时系统的分岔图与指定参数条件下系统响应图.结果表明,磁场扼制多值现象的产生;激振频率、转速、磁感应强度越小,激振力幅值越大,系统的异宿轨越容易发生破裂,从而引发混沌或概周期运动.     

两自由度非对称三次系统非线性模态的奇异性质

利用非线性模态子空间的不变性和摄动技术,研究两自由度非对称三次系统在奇异条件下系统的性质.重点考虑子系统之间线性耦合退化时的奇异性质.对于非共振情形,所得到的解析结果表明,系统出现单模态运动以及振动局部化现象,这种现象的强弱不但与非线性耦合刚度有关,而且与非对称参数有关.并解析地得到了参数的门槛值;对于1:1共振情形,模态随非线性耦合刚度和非对称参数的变化会出现分岔,得到了参数分岔集以及模态的分岔曲线.     

Grazing bifurcation in aeroelastic systems with freeplay nonlinearity

A nonlinear analysis is performed to characterize the effects of a nonsmooth freeplay nonlinearity on the response of an aeroelastic system. This system consists of a plunging and pitching rigid airfoil supported by a linear spring in the plunge degree of freedom and a nonlinear spring in the pitch degree of freedom. The nonsmooth freeplay nonlinearity is associated with the pitch degree of freedom. The aerodynamic loads are modeled using the unsteady formulation. Linear analysis is first performed to determine the coupled damping and frequencies and the associated linear flutter speed. Then, a nonlinear analysis is performed to determine the effects of the size of the freeplay gap on the response of the aeroelastic system. To this end, two different sizes are considered. The results show that, for both considered freeplay gaps, there are two different transitions or sudden jumps in the system’s response when varying the freestream velocity (below linear flutter speed) with the appearance and disappearance of quadratic nonlinearity induced by discontinuity. It is demonstrated that these sudden transitions are associated with a tangential contact between the trajectory and the freeplay boundaries (grazing bifurcation). At the first transition, it is demonstrated that increasing the freestream velocity is accompanied by the appearance of a superharmonic frequency of order 2 of the main oscillating frequency. At the second transition, the results show that an increase in the freestream velocity is followed by the disappearance of the superharmonic frequency of order 2 and a return to a simple periodic response (main oscillating frequency).     

High-order sliding mode controller with backstepping design for aeroelastic systems

A nonlinear system for controlling flutter in an aeroelastic system is proposed. The dynamic model describes the plunge and pitch motion of a wing. Interacting nonlinear forces such as structural and aerodynamic forces cause destabilizing phenomena such as flutter and limit cycle oscillation on the wing. Aeroelastic models have a wing section with only a single trailing-edge control surface for suppressing limit cycle oscillation. When modeling a single control surface, the controller design can achieve trajectory control of either plunge displacement or pitch angle, but not both, and internal dynamics describe the residual motion in closed-loop systems. Internal dynamics of aeroelasticity depend on model parameters such as freestream velocity and spring constant. Since single control surfaces have limited effectiveness, this study used leading- and trailing-edge control surfaces to improve control of limit-cycle oscillation. Moreover, two control surfaces were used to provide sufficient flexibility to shape both the plunge and the pitch responses. In this study, high order sliding mode control (HOSMC) with backstepping design achieved system stability and eliminated limit cycle phenomenon. Compared to the conventional sliding mode control design, the proposed control law not only preserves system robustness, but also avoids chatter phenomenon. Simulation results show that the proposed controller effectively regulate the response to origin in state space even under saturated controller input.     

An effective computer modelling approach to the study of aeroelastic characteristics of an aircraft composite wing with high aspect ratio

Static aeroelastic and flutter characteristics of an aircraft composite wing with high aspect ratio were analysed by an effective Computational Fluid Dynamics and Computational Structure Dynamics coupled method. Effects of stiffness distribution on aeroelastic characteristics were considered. Honeycomb core sandwich composite was considered to be equivalent to an orthotropic material by stiffness and inertance equivalent method to allow highly efficient numerical simulation, which was used for analysis of bending and torsional stiffness distribution. The results showed that the redistributed aerodynamic load leads to a decrease of pressure difference between the upper and lower airfoils. The flutter speed of the composite wing is near 0.64 Ma. Both bending and torsional stiffness increases with a small increase of beam size. Stiffness of the wing root has a major influence generally on the static aeroelastic characteristics. Both the lift coefficient and the loss percent decrease with a small increase of beam size. Effects of stiffness distribution on frequency are not obvious. Flutter speed remains close to the initial value when the beam size is changed.     

Analysis of effect of random perturbation on dynamic response of gear transmission system

In order to investigate the effects of random perturbation of a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness, the random dynamic model of a single pair of three-degree-of-freedom spur gear transmission system is established. With gear meshing frequency changing, the dynamic characteristics of the gear transmission system were analyzed by bifurcation diagram, phase diagram, time course diagram and Poincaré map of the system. The effects of random perturbation caused by a low-frequency excitation caused by torque fluctuations, gear damping ratio, gear backlash, meshing frequency and meshing stiffness were comparative analyzed. Numerical simulation shows that the gear transmission system with nonlinear clearance exists rich period-doubling bifurcation phenomenon. With the increasing of the gear meshing frequency, gear transmission system will be from the chaotic motion to periodic motion by inverse period-doubling bifurcation. The effect of the meshing frequency random perturbation on the gear transmission system movement is largest. On the contrary, the effect of the meshing stiffness random perturbation on the system is minimum.     

大型水平轴风力机叶片气动弹性计算

给出了一种考虑几何非线性的大型风力机静、 动气动弹性一体化计算方法．采用涡尾迹方法进行风力机气动载荷计算．建立风力机风轮的三维壳模型．沿周向平均风力机叶片载荷并加载到结构模型进行非线性静气动弹性分析．基于动力学小扰动假设, 在静平衡构型下进行动力学线性化, 计算风轮固有振动特性．继而结合非定常涡尾迹方法计算风力机动气动弹性响应．计算了NH 1500叶片考虑几何非线性的静气动弹性位移和动气动弹性响应．结果表明,大型风力机叶片几何非线性较为明显地减小静气动弹性位移,同时降低动气动弹性的响应幅值．大型风力机气动弹性响应计算需要考虑几何非线性     

Aeroelastic analysis of large horizontal wind turbine baldes?

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear ?nite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aero-dynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities signi?cantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

赤潮藻类非线性动力学模型的分岔及稳定性研究

选取两种常见赤潮藻类和一种浮游动物,考虑生态环境的富营养化及赤潮藻类与浮游动物的相互作用,建立了多种群赤潮藻类的非线性动力学模型．首次运用现代非线性动力学理论,对模型的稳定性及分岔行为进行了研究．得到了发生Hopf分岔时的分岔参数值,判断了极限环的稳定性,并发现了该模型通过准周期分岔产生混沌．     

The new airfoil model NACA0015, modal analysis and flutter properties

The experimental airfoil model NACA0015 was used to study aeroelastic phenomena during self-excited profile vibration. It provides data for control of aeroelastic calculation programs at subsonic speeds of the stream. The model movability is two-dimensional with two-degree of freedom dynamic system, one in pitch and the second in plunge, and is proposed to be a dynamic system having two near corresponding eigenfrequencies. To quantitatively evaluate flow field using interferometry, a special test section design and profile was constructed. It utilized a large visual field for the optical system together with the option of changing support stiffness for both degrees of freedom. In this paper experimental results from the range of Reynolds numbers Re = (2.63–2.83) 10⁵ are published. The identified eigenvalues and eigenmodes for zero flow velocity are compared with measured flutter properties (frequency, modes and time evolutions) of the airfoil.     

Delay-induced Bogdanov–Takens bifurcation in a Leslie–Gower predator–prey model with nonmonotonic functional response

This work is concerned with the dynamics of a Leslie–Gower predator–prey model with nonmonotonic functional response near the Bogdanov–Takens bifurcation point. By analyzing the characteristic equation associated with the nonhyperbolic equilibrium, the critical value of the delay inducing the Bogdanov–Takens bifurcation is obtained. In this case, the dynamics near this nonhyperbolic equilibrium can be reduced to the study of the dynamics of the corresponding normal form restricted to the associated two-dimensional center manifold. The bifurcation diagram near the Bogdanov–Takens bifurcation point is drawn according to the obtained normal form. We show that the change of delay can result in heteroclinic orbit, homoclinic orbit and unstable limit cycle.