LINEAR ACTIVE STRUCTURES AND MODES (Ⅰ)--BASIC CONCEPTS AND PROPERTIES

Some basic concepts about the active structures were firstly explained, and the main subjects to study in the field of active structure dynamics were synthesized. For the linear active structures, the annotations on the modes were done in detail. The physical meanings of the right and left eigenvectors were explained. The right eigenvectors are the modal shapes and the modal responses of an active structure depend on the left ones. The adjoint structure of an active structure was defined and the reciprocity theorem was interpreted. For two active structures, which are adjoint to each other and with the reciprocal gain-matrices, the right and left eigenvector are reciprocal. The relationship between an active structure and the corresponding passive structure is expressed with the transfer functions, which is employed to resolve the estimation problems.     

DYNAMIC ANALYSIS OF A LOADED SHOULDER-POLE DURING WALKING

建立了扁担挑物的动力学模型和动力学方程,并进行了数值求解。扁担挑物时存在三种频率,即重物类似于单摆的振动频率、挑运者的步行频率和扁担-重物系统铅垂方向的振动频率。计算结果表明,为了获得较好的挑担体验,三种频率应该相互协调。当人挑担行走的频率为扁担-重物系统铅垂方向振动频率的70%,$\sim$,80%时,肩部铅垂附加动反力为重物重力的30%左右且与肩部铅垂运动同相,当重物类似于单摆的振动频率为人步行频率的25%,$\sim$,30%时,重物的摆角和肩部受到的水平附加动反力均较小,从而有利于人挑担行走。     

圆平板挤压膜实验及其参数识别

完成了简谐激励下水中平行圆板的挤压膜振动实验．用最小二乘法识别出非线性粘性挤压膜力模型中的４个系数．不同挤压膜厚、不同频率和不同振幅情况的数值模拟结果与实验值吻合较好．研究结果表明，所用模型可较好地描述粘性挤压膜运动，识别出的系数在一定范围内给出良好精度的数值模拟．     

对胡海昌的小参数法的补充

专著提出了计算特征向量摄动的一种非模态展开法，本文对这一方法中参数μ或者矩阵μ如何选取的问题进行了研究，分析了μ的数学本质，并指出对于重特征值问题，μ只要是一个适当选定的标量常数既可，无需是个矩阵。     

Extraction-condensation method for solving large sets of equations in FE analysis

In static and dynamic analysis of a large complex structure, one may merely be interested in the stresses and displacements at some important locations. A new solution technique for structural analysis with FEM is proposed in this paper by which those important unknowns are separated from the rest. In static analysis the important unknows can be found directly. In dynamic analysis all mass and exciting forces can be condensed onto a small number of predetermined points in order to make the dynamic analysis much simplified. A large scale problem can be solved with a small capacity computer quickly.     

计算圆板大振幅非线性振动频率的平均刚度法

本文用平均刚度法研究圆板大振幅非线性振动的频率问题，导出了相应的非线性广义特征值方程，构造了一种避免发散并能加速收敛的加权平均迭代法，计算结果与Ｋａｎｔｏｒｏｖｉｃｈ时间平均法的解十分吻合。     

A Wavelet-Balance Method to Investigate the Vibrations of Nonlinear Dynamical Systems

The scope of this paper is to introduce a new wavelet-balanceprocedure allowing to give a genuine time-scale representation ofvibrations of nonlinear dynamical systems by adopting a waveletmultiresolution approach. In a former paper, a wavelet-Galerkinoriented procedure was developed to analyze vibrations of lineartime-periodic systems. The topic is here to extend the process tothe nonlinear case using a perturbation technique. The underlyingidea consists in successively balancing the linearized equationsof motion into wavelet spaces with increasing resolution scales.Here we demonstrate the wavelet-balance procedure may accuratelyexhibit both transient and stationary vibrations of any nonlinearproblem in general, whatever smooth nonlinearity shape or externalforcing may be. In addition, wavelets inherit of fairly goodtime-frequency localization properties that are likely to permitthe investigation of strong nonlinear problems. Numericalexperiments achieved on a well known Duffing oscillator involvinga cubic nonlinearity then illustrate the procedure. Simulationsattest the relevance of the method by comparison with eitherpurely numerical results obtained with a Runge–Kutta integrationscheme or with an analytical study based on the multiple scalesmethod. We demonstrate that this semi-analytical semi-numericalperturbation method permits to capture stable limit cycles of theDuffing oscillator and its related amplitude spectrum response orstill responses to pulse-like excitations. Finally, key propertiesof the method are discussed and future prospective works areoutlined.     

Crack Localization in Stepped Beams

A method for crack localization, based on so-called Local Modal Crack Sensitivity (LMCS), has recently been proposed by one of the Authors. As a major feature, the method only involves measuring eigenfrequencies. The method has already been used for beams of uniform cross section and homogeneous boundary conditions. In this paper, the method is extended to stepped beams, with both homogeneous and non-homogeneous boundary conditions. Experimental results confirm its usefulness for crack localization. Satisfactory localization of a second crack was also possible, so confirming the effectiveness of the method.     

APPLICATION OF WAVELET TRANSFORM TO BIFURCATION AND CHAOS STUDY

I.IntroductionThetypesofmotionforanonlinearvibrationsystemmaybeperiodic,quasiperiodicorchaotic.Foragivensetofparametersofthesystem,Poincarkmap,powerspectral,waveformandLyapunovexponentareusuallyutilizedtoseewhethertheresponseofthesystemischaoticornot,butitisdiftlculttodeterminepreciselytheexistingdomainsorattractingbasinsofdifferenttypesofmotionsinparametricspaceorinitialvaluespaceonlyfromgraphicsstudy,andcomputingLyapunovexponentistimeconsuming.Aswavelettransformcanreveallocalpropertyinboth…     

基于加速度响应控制时MTMD的地震特性

研究了由多个刚度和阻尼保持为常量且频率呈线性分布的TMD形成的MTMD的地震特性。基于虚拟激励法和Kanai Tajimi及Clough Penzien地震谱 ,建立了结构 MTMD系统的加速度传递函数 ,进而导出了设置MTMD时结构的加速度动力放大系数 (ADMF)明确表达式。于是MTMD的优化准则选择为 :结构最大加速度动力放大系数的最小值的最小化 [Min .Min .Max .ADMF]。通过最优搜寻得MTMD的最优频率间隔、平均阻尼比、调谐频率比和相应的控制有效性指标。选择结构受控频率与地震卓越频率比的不同取值 ,研究地震卓越频率对MTMD最优参数及有效性的影响