失谐周期结构中弹性波与振动的局部化

基于弹性波传递矩阵方法，研究了失谐周期结构中弹性波与振动的局部化问题．给出了结构中弹性波传递矩阵的一般表达式，采用奇异值分解方法，分别计算了谐和与失谐周期结构中的局部化因子，并对其进行了分析讨论．对周期结构中波传播与振动局部化的分析方法可用于结构的优化设计．     

失谐周期结构中振动局部化问题的研究进展

周期结构在工程中有很多应用实例, 其具有频率通带和禁带等特殊力学性质. 失谐 可使周期结构的力学特性产生本质变化, 即失谐周期结构中存在振动局部化现象. 局部化破坏了周期结构模态的规则性, 在外激励下会使结构某些部位的响应幅值过 大, 产生能量积聚, 甚至导致结构发生疲劳破坏. 因此分析失谐周期结构中振动和 能量的传播方式与规律具有重要的理论与实际意义, 可以为重要子结构的振动控制 和减振设计提供理论依据. 针对一维直线型周期结构、循环周期结构以及二维周期 结构等, 综述了其中的振动局部化问题的研究现状,主要集中于力学模型的建立、 振动局部化问题的研究内容、分析方法和主要研究结果等, 并提出了值得进一步研 究的问题.     

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。     

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.     

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。     

周期波导中弹性波局部化问题的研究

基于弹性波传递矩阵方法，对周期波导中弹性波局部化问题进行了分析研究。根据互易性原理和能量地恒定律，给出了结构弹性波传递矩阵的一般表达式。采用两种求解局部化因子的计算方法，分别计算了谐和与失谐周期波导中的局部化因子，并对其进行了分析讨论。本文对周期波导中波传播与振动局部化的分析方法和计算结果可用于结构的优化设计。     

失谐周期弹性支撑多跨梁中的波动局部化

分析研究了失谐周期弹性支撑多跨梁中的波动局部化问题,采用传递矩阵方法给出了系统的传递矩阵,采用Wolf提出的计算Lyapunov指数的方法,确定了局部化因子,作为算例,给出了结构中局部化因子的数值结果,分析了跨长的失谐程度、线弹簧和抗弯弹簧的无量纲刚度对弹性波局部化的影响。     

失谐整体叶盘多模态振动抑制的吸振器阵列方法

整体叶盘是新一代高性能航空发动机的关键部件,具有结构紧凑、重量轻和推重比高等优点,但也存在结构阻尼低、模态密度高和随机失谐问题,导致其通过共振区域时振幅大,显著影响整体叶盘结构的可靠性和疲劳寿命.为有效抑制失谐整体叶盘的多模态振动,提出一种由一系列吸振器环状布置而成的吸振器阵列减振方法,通过设置多组匹配不同模态的吸振器,实现对多模态共振峰值的抑制.为揭示吸振器阵列方法的多模态减振机理,采用具有代表性的集中参数模型构建整体叶盘-吸振器阵列系统的动力学分析模型,结合解析形式的功率流分析方法,分析吸振器质量、频率调谐精度、阻尼水平以及吸振器个数等关键参数对吸振器阵列减振性能的影响.搭建了吸振器阵列方法验证实验台,并通过实验验证了吸振器阵列方法的效果.分析结果表明:吸振器阵列方法能够有效控制叶片主导与叶片-轮盘耦合型模态,能够以较小的质量实现对谐调与失谐整体叶盘多模态共振的高效抑制,减振性能的鲁棒性较好.     

考虑榫接接触刚度的叶轮耦合振动特性计算方法研究

对叶片轮盘典型榫接结构的接触刚度进行了分析,给出了叶轮间接触刚度的计算方法;建立了叶片轮盘榫接耦合计算模型,采用对称循环分析方法对叶轮进行振动特性计算,得到叶轮耦合结构在不同工作转速下的振型及频率;对叶轮耦合结构进行锤击模态试验得到实际频率值。本文计算值与实测值在前3阶的相对误差分别为2.38%、1.58%、3.18%,误差均较小,验证了本文方法的可行性。     

齿轮系统非线性振动研究进展

围绕圆柱齿轮系统的参数振动和间隙非线性振动问题, 较为详细地评述了20年来国 际上的研究进展情况. 文中首先说明了齿轮系统啮合过程非线性振动的基本概念, 包括基本 的力学模型、数学模型、不同类型的分析系统和求解方法; 然后分别评述了时变轮齿啮合刚 度参数振动问题和齿侧间隙非线性振动问题的研究进展. 此后讨论了同时 包含齿侧间隙和时变啮合刚度时齿轮非线性振动问题方面的研究. 最后,建议了齿轮系统 非线性振动方面今后的研究重点.     

Dynamics of Nonlinear Cyclic Systems with Structural Irregularity

The dynamics of weakly coupled, nonlinear cyclic assemblies are investigated in the presence of weak structural mistuning. The method of multiple scales is used to obtain a set of nonlinear algebraic equations which govern the steady-state, synchronous (modal-like) motions for the structures. Considering a degenerate assembly of uncoupled oscillators, spatially localized modes are computed corresponding to motions during which vibrational energy is spatially confined to one oscillator (strong localization) or a subset of oscillators (weak localization). In the limit of weak substructural coupling, asymptotic solutions are obtained which correspond to (i) spatially extended, (ii) strongly localized, and (iii) weakly localized modes for fully coupled systems. Throughout the analysis, the influence of structural mistunings on the resulting solutions are discussed. Additionally, numerical solutions (including linearized stability characteristics) are obtained for prototypical two- and three-degree-of-freedom (DoF) systems with various structural mistunings. The numerical results provide insight into the strong influence of structural irregularities on the dynamical behavior of nonlinear cyclic systems, and demonstrate that the combined influences of structural mistunings and nonlinearities do not lead to uniform improvement of motion confinement characteristics.     

Mode Localization Induced by a Nonlinear Control Loop

We present the analysis of a nonlinear controlsystem that is used to excite and maintain a specified amplitude ofoscillation in the Jet Propulsion Laboratory vibratory gyroscope.This experimental application shows that nonlinear localizationthrough active means can be implemented in a practical system when itis desirable to confine the response to a favorable mode. Theclosed-loop system response predicted by the model shows very closeagreement with the experimental results for a significant range ofcontroller parameters. We also experimentally demonstrate that theactively localized motion is eliminated through bifurcation, similarto what was observed in previous passive localization studies appliedto extended flexible oscillators.     

DYNAMIC STRESS ANALYSIS OF GAS TURBINE ROTOR AIRFOILS USING THERMOELASTIC TECHNIQUES

The SPATE system provided a means for experimental ther-moelastic analysis of high frequency modes of vibration of a complicated turbine impeller which did not facilitate analysis with conventional methods due to low stress response and high modal density.
Testing also demonstrated a unique experimental stress analysis technique which was applied to a blade and vane airfoil and exhibited excellent stress distribution correlation with an established experimental technique (brittle lacquer) and with analytical stress distributions predicted by NASTRAN.
Full field dynamic stress analysis of gas turbine compressor airfoils accomplished using thermoelastic techniques provided an efficient method of determining optimum strain gage locations for monitoring rig and engine vibratory stress.
Significant cost savings could be realized using this technique from: (1) reduction in the amount of instrumentation required to characterize airfoil dynamic behavior and (2) increased vibratory response mode coverage thereby preventing the re-running of engine test programs to measure vibratory stress response levels of unexpected resonances encountered during initial engine testing.
Care is required when using SPATE results for vibratory modes resulting in high bi-axial stress distributions since the system output indicated stress magnitudes based on the sum of the principal stresses which could be significantly higher than either of the individual principal stresses.     

Passive vibration absorber effect on the machining surface quality of a flexible workpiece

This paper presents a study of the vibratory behaviour of a flexible workpiece subject to a milling end operation. Indeed, this vibratory behaviour is critical, especially when the excitation frequency is near to the resonance. For this reason, passive vibration suppression is considered in order to attenuate the dynamic response of the milled workpiece and decrease the dynamic effect on the resulting machined surface roughness and flatness. In order to confirm the efficiency of the passive vibration suppression, the vibratory behaviour and the quality (roughness and flatness) of a machined surface are studied without and with passive absorber (TMD) using a finite-element model.     

Linear,nonlinear dynamics,and sensitivity analysis of a vibratory ring gyroscope

The linear and nonlinear dynamic responses of a vibratory ring gyroscope are investigated in this study focusing on the response mechanism of such a vibratory gyroscope. It is found that the nonlinear equations governing the drive and sense directions are coupled through both inertial linear and geometric nonlinear terms. Nonlinear responses are studied based on the full coupled nonlinear dynamic equations. The varying amplitude on the sense direction is analyzed for different input angular rates. The effect of nonlinearity on the ring gyroscope system is performed by comparing the results of nonlinear responses to those of linear responses. The contributions of some parameters to the amplitude responses and gyroscope sensitivity are analyzed, the conclusions of which provide guidelines to improve the sensitivity of the vibratory ring gyroscopes.     

Simplification of the forced response of mistuned bladed disks using multiple scales techniques

Nonlinear Dynamics - Mistuning can produce a considerable increase of the vibratory forced response of the blades compared with that of the tuned bladed disk. This situation can lead to high cycle...     

A comparative experimental study on the use of three denoising methods for bearing defect detection

In the conditional maintenance of mechanical components by vibratory analysis, one distinguishes two types of analyses which are necessary for obtaining a reliable diagnosis. The first analysis lies in the detection of potential defects; there are currently various succeeded methods based on the treatment of the vibratory signals allowing the localization of a defect. One can quote among these methods the analysis of spectrum (with constant resolution (RC) or percentage of bands constant (PCB)), the analysis of envelope, the analysis cepstrale, the analysis time-frequencies or the analysis time-scales (wavelet). The second analysis is interested in the determination and the evaluation of severity of a defect detected to estimate the influence of this defect on the operation of a mechanism. The scalar indicators which make it possible to estimate the gravity of a defect are indicators known as total which are based on the statistical analysis of a temporal signal. However, the signals resulting from accelerometer sensors are the results of a mixture of sources of vibrations, sources being able to be allotted to one or more defects and are generally polluted by noise. This work presents the three principal methods of denoising and the study of their influence on the scalar parameters (kurtosis, factor peak, value rms) and this within the framework of the detection of defects of the chippings types of bearings.     

On the efficacy of charging a battery using a chaotic energy harvester

Nonlinear Dynamics - Introduction of stiffness nonlinearities to broaden the frequency bandwidth of vibratory energy harvesters has the adverse influence of complicating the response behavior of...     

Dynamic analysis of a disc brake under frictional and thermomechanical internal loading

The study of the vibratory response of a mechanical system as complex as a disc brake needs to consider the complexity of the problem induced by the coupling of tribological, thermomechanical and dynamical effects. Experimental consideration are discussed here for two set ups at the full scale of the disc brake and at a local scale focussed on the third body interface. A numerical model with thermomechanical and dynamical couplings is then presented, followed by a substantial discussion.     

Torus doublings and chaotic amplitude modulations in a two degree-of-freedom resonantly forced mechanical system

This work studies the response of a weakly non-linear vibratory system with two degrees-of-freedom when the system is excited near resonance. The two linear modes are in 1:3 internal resonance. The asymptotic method of averaging and direct numerical integration are used to obtain the response of the system. Over a range of excitation frequencies and modal damping, the averaged equations in slow time are found to possess limit cycle solutions. These solutions undergo period doubling bifurcations to chaotic solutions. The averaging theory then implies the existence of amplitude modulated motions, the exact nature of modulations not being well defined. Numerical simulation of the original vibratory two degree-of-freedom system shows that the system does undergo amplitude modulated motions. For sufficiently large damping, only periodic modulations arise in the form of a 2-torus. For lower damping, the 2-torus can undergo doubling and ultimate destruction to result in a chaotic attractor. Poincare sections of steady state solutions are used to characterize the various types of amplitude modulated motions.