2010城市地质环境与可持续发展论坛（二号通知）

用峰值振幅比定义局部化度，用平尾刚度与垂尾刚度的比值定义耦合度. 基于T 尾结构的质量失调模型，从模态峰值振幅比、失调耦合比、常规摄动和近频摄动4个角度， 提出4个不同的局部化判据来预测T尾结构模态局部化的发生. 对一个T尾结构模型局部化 振动的数值分析结果表明: (1) T尾结构系统一般具有弱耦合性，小量的失调就可以使T尾 结构发生模态局部化; (2) T尾结构一旦发生模态局部化，不但使对称一弯模态和反对称一 弯模态的振型发生较大改变，而且其模态频率也将改变，模态频率的改变在失调量的正负区 间内具有唯一性; (3) 算例验证了4个模态局部化判据的可行性和有效性，为T尾结构的模 态局部化分析和设计提供了依据.     

结构参数对飞机高平尾振动模态局部化的影响

针对结构参数对高平尾布局尾翼振动横态局部化影响进行了研究。考虑到失调本身的不可预知性,在实际结构的基础上设计了质量正失调、质量负失调、刚度正失调、刚度负失调四种可能出现的失调尾翼模型。当失调量为±0.5时,通过模态分析法得到了翼梁和翼肋厚度不同的情况下结构的振动模态局部化度,并讨论了结构自身参数对不同失调原因引起的模态局部化的影响。结果表明:垂尾梁厚度的增加会提高振动模态局部化程度,而平尾梁厚度的影响与之相反,翼肋参数对模态局部化基本无影响;与前梁厚度相比,后梁厚度对结构振动模态局部化的影响较大;当垂尾后梁厚度增加到2.0mm时,0.5kε=-的失调模型的局部化度从0.342变为0.971,这种显著变化在结构设计中需引起注意;此外,结构参数对质量正失调和刚度负失调产生的模态局部化的影响强于质量负失调和刚度正失调。     

近海风机叶片模态局部化产生机理及定量分析研究

在摄动理论的基础上,结合失谐度、模态密集度以及模态置信准则对模态局部化的产生机理做了定量描述,并用26自由度弹簧质点结构验证了其可行性。其次,用ANSYS建立了风机叶片模型,并通过改变材料的密度和弹性模量模拟了四种失谐情况,发现风机叶片刚度和质量的小量失谐也会对其模态振型产生显著的影响,同时通过定义新的模态局部因子来定量描述风机叶片结构的模态局部化程度。最后,对风机叶片失谐振型中谐调振型的成分进行了分析,研究表明,其成分越复杂,模态局部化程度也越强。     

多档输电线非线性建模及面内自由振动分析

考虑边界条件和耦合连接条件,基于Hamilton变分原理,建立了多档输电线结构的精细化动力学模型。对两档输电线系统的特征值问题进行了研究;根据面内特征值方程,确定结构的模态函数,分析了垂跨比、跨度比等参数对面内固有频率的影响。研究结果表明,随着跨度比和垂度比的增大,各档之间横向振动耦合增强,模态频率会发生频率穿越现象。本文结合模态局部化因子描述体系的局部模态、整体模态、混合模态行为,输电线档间通过连续条件耦合,产生混合模态。结果表明,在Veering区和频率穿越区附近,某些频率接近相等,存在1:1内共振和2:1内共振模式。     

科氏效应对叶片-桨毂-轴耦合系统振动特性的影响规律研究

采用几何精确模型与阶次截断方法描述叶片的空间变形,建立了考虑科氏效应与离心刚化作用的叶片-桨毂-轴耦合系统动力学模型,推导了耦合系统振动微分方程。采用Rayleigh-Ritz法进行数值离散,计算了不同刚度比、半径比、转速和叶片数下,科氏效应对系统模态频率的影响。研究表明：叶片-桨毂-轴耦合系统模态中包含耦合和非耦合两类模态,耦合模态频率在考虑科氏效应后发生明显降低;随着半径比增加,科氏效应对第1阶耦合模态频率的影响逐渐减弱,对第2阶耦合模态频率的影响逐渐增强;转速的增加会提升耦合模态对科氏效应的敏感性;刚度比处于10~3～10~5范围内时发生叶片模态振型转换的现象,模态振型转换后科氏效应的影响更为显著;随着叶片数目的增加,科氏效应对模态频率的影响逐渐减弱。研究结果可为旋转叶片-桨毂-轴耦合系统的动力学设计提供理论参考。     

考虑温度效应的索梁面内动力学建模及特性分析

根据增量热场理论,温度变化影响下索梁结构会形成新的热应力平衡状态.因此基于已有的索梁结构非线性动力学模型,结合与斜拉索张拉力和垂度相关的无量纲参数,重新建立考虑温度变化影响下索梁结构面内振动的动力学模型,并推导其面内非线性运动方程.接着开展特征值分析,得到包含温度效应的索梁结构面内振动频率的超越方程及模态振型函数.通过算例研究温度变化对不同刚度比的索梁结构影响,得到其前四阶面内振动的模态频率与温度变化的关系曲线.研究结果表明:面内模态频率受温度变化影响明显,其影响程度与刚度比大小和模态的阶数密切相关,温度变化对低阶模态频率的影响比对高阶模态频率影响更为复杂;升温和降温对索梁结构面内振动特性的影响不对称;此外温度变化会导致频率偏转点的位置发生漂移.     

大展弦比机翼非线性颤振特性研究

为了研究大展弦比机翼水平弯曲模态参与耦合时的颤振特性,首先用考虑几何非线性的颤振分析方法研究了某大展弦比机翼的颤振特性,建立了大展弦比机翼非线性颤振分析的简化模型,即盒段模型;然后通过组合不同的水平弯曲频率、扭转频率形成不同的接近模式,系统分析了不同接近模式对盒段模型非线性动力学特性的影响规律,提出了水平弯曲频率和扭转频率发生模态交换的存在条件。在此基础上通过对盒段模型进行非线性颤振分析发现:水平一弯模态参与耦合降低了机翼传统模式的线性颤振速度,增大水平一弯的频率有助于该类颤振速度的提高;在水平一弯频率和扭转频率逐步接近时,会导致机翼颤振速度显著下降,且颤振类型会由水平一弯和垂直弯曲耦合的颤振转化为水平一弯和扭转耦合的颤振。     

振型节线角度对舵面颤振稳定性的影响

针对舵机支撑刚度支持下的舵面结构，建立了广义气动力与舵面前两阶局部刚化模态振型节线角度关系的表达式，分析广义气动力随振型节线角度的变化规律，根据Routh-Hurwitz稳定性判据研究振型节线角度对颤振临界动压的影响．研究结果表明：舵面前两阶局部刚化模态振型节线处于相对“横平竖直”的状态时，前两阶模态经由广义非定常气动载荷引起的耦合较弱，舵面的颤振临界动压较高．     

大型离心叶轮振动模态局部化特性研究

为了研究目前工程中大型流体机械离心叶轮出现的局部疲劳破坏的机理,基于现有的有限元分析方法,结合模态分析等动力学理论以及叶轮所承受的气流激励,对其动力学特性进行了研究。着重研究了离心叶轮这类周期循环对称性结构具有的不同于非周期循环结构的特殊动力学性质以及该特殊的动力学特性与叶轮疲劳破坏的联系。研究发现其存在频率通带(passbands)、频率禁带(stopbands)现象,并出现了振动模态局部化现象。另外,叶轮的动力学特性对其周期性结构失谐特别敏感,该类失谐可来自由制造误差、材料和使用中磨损出现的不均匀等多种因素。对于协调结构,在一定条件下(如系统具有高密集模态),很小的失谐量(1%)就可使结构振动模态产生急剧变化,从而出现振动模态局部化现象。对于所研究的机组,当进口预旋器导致的流体激振频率(1166.7Hz)接近叶轮的由第12阶～18阶固有频率组成的禁带(1020.3～1054.5 Hz)时,数值分析结果显示叶片进口部位出现了振幅较大的振动,与该机组实际破坏的部位相符。研究结果表明所使用的振动模态局部化分析方法能够揭示叶轮发生疲劳破坏的原因,即是一类共振型疲劳破坏现象。     

基于非约束模态刚柔耦合系统的动力刚化分析

以挠性航天器为研究对象,引入非约束模态概念,建立了含有动力刚化效应的刚柔耦合动力学模型。首先,根据Hamilton变分原理建立挠性航天器动力学模型;然后,根据非约束模态正交性分离振型,得到离散化的非约束模态的动力学模型;最后,对给定激励下动力学方程仿真,并与约束模态情况进行对比。仿真结果表明:非约束模态一次动力学模型的广义刚度随航天器转速提升而增大,且随转速的提升更加明显,出现动力刚化现象,非约束模态零次动力学模型广义刚度随航天器转速的提升出现为负的情况,不存在动力刚化现象;基于非约束模态一次动力学模型挠性附件的响应振幅较约束模态刚柔耦合系统小,且随航天器转速的提升同样不会出现发散情况,适用于航天器在任何转速情况下建模。非约束模态零次动力学模型挠性结构振动振幅随转速的提升出现发散情况,即便非约束模态建模方法优于约束模态,非约束模态零次模型也不适用于航天器高转速情况。     

The SEA Approach to Vibration Localization in a Nearly Periodic Structure

Abstract

The phenomenon of vibration localization occurring in a nearly periodic structure was investigated through a statistical energy analysis (SEA) approach. The phenomenon has been examined mostly through a wave propagation approach, where a localization factor was often employed to evaluate the strength of vibration localization. The wave propagation approach properly predicted the factor close to Monte Carlo calculations in nearly periodic structures for both weak and strong couplings. In this analytical study, the localization factor was derived from the SEA approach for a nearly periodic structure monocoupled with a weak coupling. The SEA approach sequentially breaks the structure into two-oscillator blocked substructures and proposes a way of determining the vibration localization factor with equations of energy balance. This article shows that the SEA approach is quite appropriate for calculating the vibration localization factor compared to the wave propagation approach.     

立式电机模态仿真与实验研究

振动是电机的重要性能指标。本文在MSC.NASTRAN仿真环境下,利用有限元方法对立式电机进行了电机整机的模态仿真,得到了整机的前五阶固有振动频率、振型等参数值。根据仿真结果,分析了整机的危险位置和振型。进行了电机模态试验,验证虚拟样机和数值模拟的有效性。结果表明,系统不会发生共振。最后,在力学分析的基础上对结构进行优化,为立式电机的改进和振动测试提供了参考。     

Dynamic Response as a Tool for Damage Identification

Changes in dynamic response are used to determine the magnitude and location of damage or other imperfections. The CAMOSUC (Change of Mode Surface Curvature) method is compared with earlier methods. Examples of identifying changes of real structures and models are given     

Influence of dynamic processes in a film on damage development in an adhesive base

In the process of deformation of such multilayer structures, significant stresses can arise on the foundation-coating interface because of the difference in their physical and mechanical properties, which can result in fracture or coating separation. The action of static or impact loads on damage onset and development in the adhesive layer in such multilayer structures has been investigated almost completely, but similar processes in the case of suddenly applied vibration loads have not been studied to a large extent. The latter draw attention because of the fact that even small variable actions can localize vibrations near the imperfections (inclusions, defects, etc.) and can be accompanied with an increase in the damage of the adhesion layer, which results in partial separation of the film. In the present paper, the possibility of vibration localization in damaged regions and the influence of the localization on the damage development till the film separation are studied. The first of the possible scenarios of the damage region behavior is its monotone increase. The second scenario of damage behavior is its constant stepwise growth. In this case, damage increases on some time intervals and is constant between the intervals. Under the conditions obtained in the paper, this second scenario can be transformed into the first one. The third scenario is that damage does not increase. This scenario can be realized under sufficiently large vibration load frequencies. Some conditions under which damage behavior is determined by the localized oscillating part of the solution are derived.     

失谐弱耦合卫星天线结构振动分析及预测控制

为了研究弱耦合卫星天线结构的振动控制，建立了该结构的简化计算模型，并针对该模型研 究了弱耦合卫星天线结构动力学性能的特殊性：结构失谐时的振动模态局部化现象；针对失 谐前后的结构，采用预测控制方法进行了振动控制，并与二次线性最优控制(LQR)方法的振动 抑制效果进行了对比. 仿真结果表明：弱耦合星载天线结构参数的微小失谐会导致结构振动 产生明显的模态局部化；采用预测控制方法进行结构振动控制的效果明显优于LQR控制方法， 且在失谐导致的模型失配时，预测控制方法对结构振动亦有较好的抑制；在进行此种结构的 振动主动控制时必须考虑到结构失谐的影响.     

Nonlinear response of an imperfect microcantilever static and dynamically actuated considering uncertainties and noise

The motion of a slender, clamped-free, imperfect, electrically actuated microbeam is investigated. Special attention is given to the influence of imperfections and noise on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on the subject. To this end, a geometrically nonlinear theory is adopted for the microbeam retaining geometric nonlinear terms up to the third order and considering in a consistent way the effect of initial geometric imperfections. Also, additive white noise is considered to model forcing uncertainties, and the Galerkin discretization method, using as interpolating functions the linear vibration modes, is used to obtain a modal stochastic differential equation of Itô type, which is solved by the stochastic Runge–Kutta method. A parametric analysis clarifies the influence of geometric imperfections and noise level on the natural frequencies, resonance curves, and pull-in instability. Additionally, the global dynamics is examined through the generalized cell mapping, showing the effects of uncertainties on the attractor’s probability density functions and basins of attraction.

     

空间异型双曲面钢屋盖缺陷稳定性分析及试验研究

南通体育会展中心钢屋盖为空间异型双曲面,结构高跨比和矢跨比均较小,稳定性分析是其设计中的一个关键问题。本文在体育馆缩尺模型试验基础上,对其钢屋盖结构进行了几何非线性和双非线性稳定分析,分别采用实测缺陷法、一致缺陷模态法、改进随机缺陷法考虑结点位置偏差缺陷的影响。结果表明：实测缺陷法双非线性分析结果是评估体育馆屋盖结构实际安全性的重要依据;一致模态法的临界荷载概率可靠度较低。通过改进随机缺陷法,对该屋盖结构的稳定性能有了比较全面的认识,并定量分析了设计临界荷载和一致模态法分析的临界荷载的可靠性。     

Mode Localization in Dynamics and Buckling of Linear Imperfect Continuous Structures

Localization phenomena in one-dimensional imperfect continuous structures are analyzed, both in dynamics and buckling. By using simple models, fundamental concepts about localization are introduced and similarities between dynamics and buckling localization are highlighted. In particular, it is shown that strong localization of the normal modes is due to turning points in which purely imaginary characteristic exponents assume a non zero real part; in contrast, if turning points do not occur, only weak localization can exist. The possibility of a disturbance propagating along the structure is also discussed. A perturbation method is then illustrated, which generalizes the classical WKB method; this allows the differential problem to be transformed into a sequence of algebraic problems in which the spatial variable appears as a parameter. Applications of the method are worked out for beams and strings on elastic soil. All these structures are found to have nearly-defective system matrices, so their characteristic exponents are highly sensitive to imperfections.     

Repeated buckling and its influence on the geometrical imperfections of stiffened cylindrical shells under combined loading

The present experimental study aims at providing better inputs for improvement of the buckling load predictions of stiffened cylindrical shells subjected to combined loading. The work focuses on two main factors which considerably affect the combined buckling load of stiffened shells, namely geometric imperfections and boundary conditions. Six shells with nominal simple supports were tested under various combinations of axial compression and external pressure. The vibration correlation technique is employed to define the real boundary conditions. The geometric imperfections of the integrally stiffened shells are measured in the present experiments in situ and are used as inputs to a multimode analysis which yields the corresponding “knockdown” factor for various combinations of loading. Thus, when employing the repeated buckling procedure for obtaining interaction curves, each point on the curve is adjusted (using the multimode analysis) for the measured “new” surface of the shell and this results in more realistic interaction curves. The geometrical imperfections of the preloaded shells can also serve as an input to the International Imperfection Data Bank for future studies on the correlation between the manufacturing method of the shell and their geometric imperfections.