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．     

有摩擦时悬臂细长大杆大挠度弯曲的解

在专用汽车开发中,遇到有磨擦时细长杆受集中载荷时大挠度弯曲变形件的设计问题,本文利用数值积分法对此进行讨论,提出有摩擦时细长杆悬臂梁所受最大弯矩计算方法,同时就磨擦力对变形的影响进行了分析,为此类杆件的强度计算提供依据。     

悬臂梁振动可靠性分析的研究

本文把悬臂梁的固有频率、激振力频率、平均应力、应力幅和疲劳极限处理为随机变量，提出了悬臂梁在强迫振动时不发生共振和疲劳损坏的可靠性分析方法。     

Nonlinear Dynamics of a Cantilever Beam Carrying an Attached Mass with 1:3:9 Internal Resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.     

磁约束双层夹心悬臂梁的振动分析

采用在约束层端部上设置永磁体的新方法可使阻尼层获得比传统约束阻尼处理方法更高的剪应变，从而增强粘弹层的阻尼耗能，降低共振峰。本文应用Hamilton原理，推导了全覆盖双层约束阻尼悬臂梁的运动方程，对模型进行了实验验证；分析了不同物理和几何参数下该方法的减振效果。研究表明，磁约束能提高阻尼减振效果。随着阻尼层厚度的增加，无磁约束的共振峰降低较少，而有磁约束的共振峰急剧降低，减振效果明显。阻尼层剪切模量G的变化对磁约束减振效果的影响较大；当G小于一定值时，减振效果明显，但当G大于一定值时，减振效果急剧降低。在不同的约束层弹性模量和厚度下，磁约束仍起作用。此外，分析了具有较大控制力的主被动混合磁约束振动控制方法的可行性。     

不确定边界条件下悬臂梁裂纹参数识别方法研究

基于Bernoulli-Euler梁振动理论,以等效弹簧来模拟裂纹引起的局部软化效应和由非完全固支边界条件引起的转角效应。推导了悬臂梁在不确定边界条件下确定其振动频率的特征方程,直接利用该特征方程,提出一种有效估计裂纹参数的优化方法,通过计算测量频率和理论频率之间的误差目标函数最小化即可识别裂纹参数-裂纹位置和深度。最后,应用两个实例-理想固支边界条件下和非完全固支边界条件下的悬臂梁实验来说明本文方法的有效性。实验结果表明:只需梁结构前三阶频率即可识别裂纹位置和深度。对于理想边界条件下的裂纹参数识别,在测量频率存在小误差情况下,该方法仍能给出比较满意的结果,对于非完全固支边界条件下的裂纹参数识别,利用本文方法能得到比Narkis的方法更精确的裂纹位置识别结果。同时本文方法还能给出比较满意的裂纹深度识别结果。     

热/均布载荷下双材料悬臂梁的解析解

基于弹性介质的二维本构关系和热传导理论，采用逆解法，研究了双材料悬臂梁在热／机械载荷作用下的问题，通过假设双材料悬臂梁构件的应力函数，利用应力、位移边界条件和连续性条件，给出了其位移、应力分布的表达式。     

Global Bifurcations and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam

This paper presents the analysis of the global bifurcations and chaotic dynamics for the nonlinear nonplanar oscillations of a cantilever beam subjected to a harmonic axial excitation and transverse excitations at the free end. The governing nonlinear equations of nonplanar motion with parametric and external excitations are obtained. The Galerkin procedure is applied to the partial differential governing equation to obtain a two-degree-of-freedom nonlinear system with parametric and forcing excitations. The resonant case considered here is 2:1 internal resonance, principal parametric resonance-1/2 subharmonic resonance for the in-plane mode and fundamental parametric resonance–primary resonance for the out-of-plane mode. The parametrically and externally excited system is transformed to the averaged equations by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is applied to find the explicit formulas of normal forms associated with a double zero and a pair of pure imaginary eigenvalues. Based on the normal form obtained above, a global perturbation method is utilized to analyze the global bifurcations and chaotic dynamics in the nonlinear nonplanar oscillations of the cantilever beam. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Silnikov type single-pulse homoclinic orbit in the averaged equation for the nonlinear nonplanar oscillations of the cantilever beam. These results show that the chaotic motions can occur in the nonlinear nonplanar oscillations of the cantilever beam. Numerical simulations verify the analytical predictions.     

自由端受集中力作用下压电悬臂梁弯曲问题解析解

本文对由横观各向同性压电介质构成的悬臂梁，在自由端受集中力作用下的弯曲问题进行了研究。首先根据问题的特点，得到简化的线弹性压电悬臂梁的基本方程。然后根据正交各向异性材料悬臂梁应力分布特点，采用逆解法，建立了该问题的应力函数与电势分布函数，进而得到精确多项式解析解。该解析解形式简单，便于应用。文中对自由端受集中力的常规材料和压电材料悬臂梁的挠度也进行了比较。     

悬臂梁中开闭裂纹的损伤识别

利用裂纹诱导弦挠度函数,建立了悬臂Euler-Bernoulli中开闭裂纹位置、深度、初始张开角等损伤参数的识别方法。为此,首先将梁中开闭裂纹等效为单向扭转弹簧,给出了考虑裂纹缝隙效应的裂纹梁等效抗弯刚度,并得到悬臂Euler-Bernoulli开闭裂纹梁弯曲挠度的显式闭合解及裂纹诱导弦挠度函数,证明了裂纹诱导弦挠度的分段线性函数。其次,基于单向扭转弹簧的性质,建立了通过多步加载进行梁中开闭裂纹参数及其上下侧属性的识别方法。最后,通过数值算例验证了本文所建立的开闭裂纹损伤识别方法的适用性和可靠性,考察了裂纹分布位置、深度和初始张开角以及裂纹识别区间和挠度测量误差等参数对识别结果的影响,结果表明:当裂纹处于张开状态时,裂纹处裂纹诱导弦挠度斜率改变量随着施加荷载的增加而增加;当裂纹闭合时,其裂纹诱导弦挠度斜率改变量将保持为常量;裂纹损伤参数的识别误差随测量误差的增加而增加,但整体识别结果具有较高的精度,较好的鲁棒性。     

Stabilization of the Parametric Resonance of a Cantilever Beam by Bifurcation Control with a Piezoelectric Actuator

In this work, bifurcation control using a piezoelectric actuator isimplemented to stabilize the parametric resonance induced in acantilever beam. The piezoelectric actuator is attached to the surfaceof the beam to produce a bending moment in the beam. The dimensionlessequation of motion for the beam with the piezoelectric actuator on itssurface is derived and the modulation equations for the complexamplitude of an approximate solution are obtained using the method ofmultiple scales. We then acquire the bifurcation set that expresses theboundary of the stable and unstable regions. The bifurcation set ischaracterized by the modulation equations. Next, we determine the orderof feedback gains to modify these modulation equations. By actuating thepiezoelectric actuator under the appropriate feedback, bifurcationcontrol is carried out resulting in the shift of the bifurcation set andthe expansion of the stable region. The main characteristic of thestabilization method introduced above is that the work done by thepiezoelectric actuator is zero in the state where the parametricresonance is stabilized. Thus zero power control is realized in such astate. Experimental results show the validity of the proposedstabilization method for the parametric resonance induced in thecantilever beam.