Lamb波理论及层合板冲击损伤的实验研究

从理论上分析了板中Lamb波信号的传播特性,并给出Lamb波在板中传播的频散方程。理论分析及实验均表明,Lamb波的频散特性与复合材料结构损伤有着直接的联系,而且最低阶的对称和反对称Lamb波模态对层合板的损伤比较敏感,但应用Lamb波的频散效应监测结构的损伤在检测技术上还难以实现。根据板中导波形成Lamb波的共振原理,板中应力波的幅频特性很大程度上反映了Lamb波的谐振特征。因此,利用压电元件的压电阻抗谱分析应力波的各阶模态频率及振幅对结构损伤的变化,能够反映材料内部损伤与Lamb波的频散特性。文中针对表面粘贴压电元件的层合板智能结构,建立了包含Lamb波谐振模式的压电阻抗计算模型。冲击损伤试件的实验表明,由于结构损伤的出现压电阻抗谱中的模态频率及其阻抗幅值等特征信息将发生变化。因此,引入应力波损伤因子可以对结构冲击损伤的存在和程度进行初步评价。该方法基于结构的机-电动态阻抗特性,不受结构的几何形状限制,测试用的压电元件成本低,方法简单可行,有望在智能结构的健康诊断方面获得应用。     

Vibration analysis of a circular disk tensioned by rolling using finite element method

Summary The paper proposes a method in finite element analysis for estimating natural frequencies of a disk tensioned by rolling, without the use of eigenvalue analysis. The natural frequencies of a disk vary when the localized plastic deformation caused by roll-tensioning induces residual stresses. Tensioning is used for improving the dynamic stability of circular saws; the optimal condition of rolling can be predicted from natural frequency characteristics. In the proposed method, the natural frequencies after rolling are easily estimated from the mode shapes of the disk before rolling and the stress distribution after rolling. The method is based on ideas similar to thermal stress and sensitivity analysis rather than on eigenvalue analysis. The effectiveness of the method is shown by comparing the natural frequency characteristics obtained by this method with those by eigenvalue analysis. Received 18 June 1998; accepted for publication 8 April 1999     

局部损伤复合材料层合板的振动分析

本文采用了一种改进方法对局部损伤复合材料层合板进行了振动分析,将复合材料板中的损伤模拟为局部刚度的削减,并取三个损伤因子来刻画损伤的特性．利用高阶摄动法对其自由振动方程进行求解,主要计算了损伤板的自然振动频率和振动模态．相较于一阶摄动展开法,该方法在计算局部较大损伤问题中具有更高的准确度和敏感度．最后对损伤问题进行了参数研究,分析了不同的损伤因子（包括局部损伤程度、方向、面积大小）对板自由振动频率的影响．该方法为二维板局部损伤检测提供了有效精确的理论依据,并为损伤的定量评价提供了一种思路．     

弹性连接旋转柔性梁动力学分析

采用Chebyshev 谱方法对考虑根部连接弹性的平面内旋转柔性梁动力学特性进行研究. 基于Gauss-Lobatto 节点与Chebyshev 多项式方法对柔性梁变形场进行离散,通过投影矩阵法施加固定及弹性连接边界条件. 利用Chebyshev 谱方法获得了系统固有频率和模态振型数值解,通过与有限元方法及加权残余法的比较,验证了方法的有效性. 分析了弹性连接刚度、角速度比率、系统径长比及梁的长细比等参数对系统固有频率及模态振型的影响. 研究发现:由于系统弯曲模态、拉伸模态的频率随各参数的变化规律不一致,将出现频率转向与振型转换现象;随着弹性连接刚度、角速度比率及系统径长比的增大,低阶弯曲模态频率增大并超过高阶拉伸模态频率,随着梁的长细比的增大,低阶拉伸模态频率增大并超过高阶弯曲模态频率.      

Analysis of Coupled Vibration Characteristics of Wind Turbine Blade Based on Green's Functions

This paper presents the analysis of dynamic characteristics of horizontal axis wind turbine blade, where the mode coupling among axial extension, flap vibration(out-of-plane bending), lead/lag vibration(in-plane bending) and torsion is emphasized. By using the Bernoulli-Euler beam to describe the slender blade which is mounted on rigid hub and subjected to unsteady aerodynamic force, the governing equation and characteristic equation of the coupled vibration of the blade are obtained. Due to the combined influences of mode coupling, centrifugal effect, and the non-uniform distribution of mass and stiffness, the explicit solution of characteristic equation is impossible to obtain. An equivalent transformation based on Green's functions is taken for the characteristic equation, and then a system of integrodifferential equations is derived. The numerical difference methods are adopted to solve the integrodifferential equations to get natural frequencies and mode shapes. The influences of mode coupling, centrifugal effect, and rotational speed on natural frequencies and mode shapes are analyzed. Results show that:(1) the influence of bending-torsion coupling on natural frequency is tiny;(2) rotation has dramatic influence on bending frequency but little influence on torsion frequency;(3) the influence of bending-bending coupling on dynamic characteristics is notable at high rotational speed;(4) the effect of rotational speed on bending mode is tiny.     

INVESTIGATION OF THE THICKNESS VARIABILITY AND MATERIAL HETEROGENEITY EFFECTS ON FREE VIBRATION OF THE VISCOELASTIC CIRCULAR PLATES

The present study deals with free vibration analysis of variable thickness viscoelastic circular plates made of heterogeneous materials and resting on two-parameter elastic foundations in addition to their edge conditions.It is assumed that the viscoelastic material properties vary in the transverse and radial directions simultaneously.The complex modulus approach is employed in conjunction with the elastic-viscoelastic correspondence principle to obtain the solution.The governing equations are solved by means of a power series solution.Finally,a sensitivity analysis including evaluation of effects of various edge conditions,thickness variations,coefficients of the elastic foundation,and material loss factor and heterogeneity on the natural frequencies and modal loss factors is accomplished.     

基于改进灰狼优化算法的结构损伤识别

结合模态柔度矩阵、广义模态柔度矩阵和振型三个识别精度较好的指标,构造新的目标函数求解损伤识别问题。通过Nelson方法求解得到的频率与振型的导数,得到对结构刚度发生变化时更具敏感性的位置,然后在这些位置布置传感器以提取结构信息。针对原有的灰狼算法虽然全局搜索能力强,但是存在局部搜索精度差的问题,本文从初始种群和收敛因子等方面着手,改善灰狼算法的局部搜索能力及收敛速度。最后利用提出的方法,通过识别梁模型及桁架模型中的损伤单元说明本文方法的有效性。     

损伤效应对悬索2:1内共振响应影响分析

损伤是结构振动测试和运营维护中不可避免的问题，损伤效应会导致结构振动特性发生改变．本文以受损悬索为例，探究该非线性系统同时发生主共振和2:1内共振时，损伤效应对其面内耦合共振响应影响．首先基于哈密顿变分原理，引入与损伤程度、范围和位置相关的三个无量纲参数，建立受损悬索面内动力学模型，并推导其无穷维非线性运动微分方程．以2:1耦合共振为例，采用Galerkin法和多尺度法得到系统直角坐标形式的调谐方程．数值算例表明：损伤会导致悬索固有频率降低，使得频率间公倍关系发生改变，影响系统耦合共振响应；损伤会引发系统振动特性发生明显定量和定性改变，尤其是共振响应幅值及弹簧特性；损伤对直接激励模态响应幅值的影响比对内共振激发对响应幅值的影响要明显；损伤会导致霍普夫、鞍节点、叉形和倍周期分岔的位置发生偏移，从而影响分岔点附近系统的动力学行为；系统动态解和周期运动与损伤密切相关，损伤会导致系统展现出完全不同类型的吸引子．     

区间桁架结构动力特性分析的区间因子法

对于具有区间参数的桁架结构的动力特性分析问题,提出了一种新的分析方法即区间因子法。利用区间因子法,结构材料物理参数、几何尺寸均可表达为其区间因子和确定性量的乘积,进而结构的固有频率和振型也可显式表达成区间因子们的函数。利用区间算法,推导出了结构固有频率和振型的上、下限与均值的计算表达式。通过算例,分析了结构参数的不确定性对结构动力特性的影响,并验证了本文模型和方法的合理性与可行性。本文方法的优点是能够反映结构某一参数的不确定性对结构动力特性的影响。     

一种基于超声共振谱的低Q值材料共振频率提取方法

超声共振谱技术通过测量样本在超声激励下产生的固有共振频率来计算弹性参数,而共振频率的提取是整个测量过程的关键.低$Q$值(品质因数)材料由于其衰减特性,导致共振谱平缓并无法直观地从谱图上观察得到共振频率,为从中提取更为有效的共振频率, 本文提出了一种新的共振频率提取方法.采用经验模态分解法将材料频率响应自适应分解为有限个具有特殊振荡特性的固有模态函数分量,根据材料的超声共振谱先验信息选择具有共振频率特性的固有模态函数分量,并从中提取共振频率. 以短切纤维环氧树脂材料(仿骨材料, $Q \approx$25)为例, 通过实验与传统线性预测方法进行对比,计算弹性系数和工程模量. 实验结果表明新方法的计算效率高,对弱激发模态更为敏感,共振频率的匹配数量(26)多于传统方法(21)且满足5倍于弹性系数的估计要求,优化后的弹性模量更接近标准值.新方法可从低$Q$值材料平缓的频谱中提取数量足够且有效的共振频率,不仅有效提升了力学参数估计的可靠性,而且拓展了超声共振谱技术的应用范围.      

Damage assessment of tensegrity structures using piezo transducers

This paper presents the application of surface-bonded piezo-transducers for damage assessment of tensegrity structures through dynamic strain measurement and electro-mechanical impedance (EMI) technique. The two techniques are first applied on a single module tensegrity structure, 1 m×1 m in size and their damage diagnosis results compared. A single piezoelectric-ceramic (PZT) patch bonded on a strut measures the dynamic strain during an impact excitation of the structure. Damage is identified from the changes in global frequencies of the structure obtained from the PZT patch’s response. This is compared with the damage identified using the EMI technique, which is a signature based technique and operates at frequencies of the order of kHz. The dynamic strain approach, which requires commonly available hardware, is found to exhibit satisfactory performance vis-à-vis the EMI technique for damage assessment of tensegrity structures. The damage diagnosis exercise is then extended to a tensegrity grid structure, 2 m×2 m size, fabricated using galvanized iron (GI) pipes and mild steel wire ropes. The damage is localized using changes in natural frequencies observed experimentally using the dynamic strain approach and the corresponding mode shapes of the undamaged structure derived numerically. The dynamic strain approach is found to be very expedient, displays competitive performance and is at the same time cost effective for damage assessment of tensegrity structures.     

A New Technique for Characterization of Low Impedance Materials at Acoustic Frequencies

Measuring the mechanical properties of low impedance rubbery polymers at acoustic frequencies is a challenging problem due to the small signal amplitudes, relatively high loss, and the long wavelength of stress waves. One such material is solid polyurea (PU), an elastomeric copolymer, which has excellent chemical, thermal, and mechanical properties and is widely used as a coating (e.g. in truck bed lining) or blast protection (advanced helmet designs and concrete structures) material. Moreover, due to its heterogeneous structure, PU has a wide transition of thermo-mechanical behavior from rubber-like to glassy compared to most engineering polymers, which translates to a broader loss spectrum in frequency domain. In this study, we have developed a new test technique by modifying the split Hopkinson pressure bar and using ball impact to measure Young’s storage and loss moduli of polyurea at kHz frequencies. This will therefore fill the frequency gap between the dynamic mechanical analysis (DMA) and ultrasonic (US) wave measurement. The measured Young’s storage and loss moduli from this technique are compared with the master curves of the moduli developed using experimental data of dynamic mechanical analysis and ultrasonic wave measurements. This technique is a direct measurement which provides more reliable data in the kHz frequency range and can be used to evaluate the reliability of other indirect estimations including master curves. The utility of this technique is not limited to polyurea and it can be used to characterize other low impedance materials at kHz frequencies.     

Identification of Damping and Dynamic Young’s Modulus of a Structural Adhesive Using Radial Basis Function Neural Networks and Modal Data

In this paper, the radial basis function neural networks (RBFNN) was applied to the problem of identifying dynamic Young’s modulus and damping characteristic of a structural adhesive, using modal data. To identify Young’s modulus from undamped model, an appropriate RBFNN using modal data (mode shape and natural frequency) in each mode is developed. Based on a previous work, in order to identify loss factor, two approaches adopted in the identification process. In the first one, a two stage RBFNN is developed. In stage I, Young’s modulus is identified from undamped model and in stage II using the results of stage I an appropriate RBFNN is developed in each mode for identification of loss factor by implementing real parts of eigenvalues of damped model. In the second approach, a one stage RBFNN is developed using real and imaginary parts of eigenvalues of damped model to identify Young’s moduli and loss factors simultaneously. The repeatability and consistency of the method is proved by repeating the identification process for several times. The validity of results is proved by comparing the results with those identified in a previous work.     

钛酸钙系电流变液在直流电场下损耗模量的研究

研究了直流电场下钛酸钙系电流变液在动态振荡剪切模式下损耗模量的变化。用流变仪测试了不同颗粒体积分数材料在不同的温度和电场下损耗模量随应变的关系曲线。讨论了颗粒体积分数、温度、电场强度以及频率对材料损耗模量的影响。以理论推导和试验数据拟合的方法给出了损耗模量与颗粒体积分数、振荡频率、温度以及电场强度等参数的半经验数学关系式。理论值对比试验结果表明,本文损耗模量表达式与试验结果符合较好,可以用于预测直流电场下钛酸钙系电流变液在动态振荡剪切模式下颗粒体积分数、温度、电场强度、频率和剪切应变对损耗模量的影响。     

DAMAGE DETECTION BASED ON OPTIMIZED INCOMPLETE MODE SHAPE AND FREQUENCY

For the purpose of structural health monitoring, a damage detection method combined with optimum sensor placement is proposed in this paper. The back sequential sensor placement(BSSP) algorithm is introduced to optimize the sensor locations with the aim of maximizing the 2-norm of information matrix, since the EI method is not suitable for optimum sensor placement based on eigenvector sensitivity analysis. Structural damage detection is carried out based on the respective advantages of mode shape and frequency. The optimized incomplete mode shapes yielded from the optimal sensor locations are used to localize structural damage. After the potential damage elements have been preliminarily identified, an iteration scheme is adopted to estimate the damage extent of the potential damage elements based on the changes in the frequency. The effectiveness of this method is demonstrated using a numerical example of a 31-bar truss structure.     

Nonlinear coupling of transverse modes of a fixed–fixed microbeam under direct and parametric excitation

Tuning of linear frequency and nonlinear frequency response of microelectromechanical systems is important in order to obtain high operating bandwidth. Linear frequency tuning can be achieved through various mechanisms such as heating and softening due to DC voltage. Nonlinear frequency response is influenced by nonlinear stiffness, quality factor and forcing. In this paper, we present the influence of nonlinear coupling in tuning the nonlinear frequency response of two transverse modes of a fixed–fixed microbeam under the influence of direct and parametric forces near and below the coupling regions. To do the analysis, we use nonlinear equation governing the motion along in-plane and out-of-plane directions. For a given DC and AC forcing, we obtain static and dynamic equations using the Galerkin’s method based on first-mode approximation under the two different resonant conditions. First, we consider one-to-one internal resonance condition in which the linear frequencies of two transverse modes show coupling. Second, we consider the case in which the linear frequencies of two transverse modes are uncoupled. To obtain the nonlinear frequency response under both the conditions, we solve the dynamic equation with the method of multiple scale (MMS). After validating the results obtained using MMS with the numerical simulation of modal equation, we discuss the influence of linear and nonlinear coupling on the frequency response of the in-plane and out-of-plane motion of fixed–fixed beam. We also analyzed the influence of quality factor on the frequency response of the beams near the coupling region. We found that the nonlinear response shows single curve near the coupling region with wider width for low value of quality factor, and it shows two different curves when the quality factor is high. Consequently, we can effectively tune the quality factor and forcing to obtain different types of coupled response of two modes of a fixed–fixed microbeam.

     

箱型结构内部爆炸破坏研究进展

结构内部爆炸破坏机理和规律是常规武器毁伤效能预测与评估、建筑物和舰船抗爆防护设计的重要支撑。基于结构内爆炸载荷、内部爆炸作用下结构塑性响应、内部爆炸作用下箱壁结构破坏模式、内部爆炸作用下多箱型结构破坏模式和分布四个方面详细论述了箱型结构内部爆炸破坏的研究现状及存在的问题,并对内部爆炸后续研究给出了建议。建议研究并建立更加复杂的结构内部爆炸载荷和破坏效应描述模型、内部爆炸作用下箱壁的动力响应机理、多箱型结构与内部爆炸波产生的耦合效应、内部爆炸作用下结构的破坏模式和破坏范围的快速准确预测方法等。     

大型引射筒呼吸振动破坏机理的实验和模拟研究

针对某大型引射筒结构,通过有限元模拟分析,找到了对应于纵向裂纹的引射筒花瓣状呼吸振动模态及其频率;应用动应力分析,发现引起该引射筒破坏的频率主要集中在200～300 Hz的低频段.并进行了相关的模态试验,得到了典型的呼吸振动模态及频率,与计算结果进行了对比;结果表明计算与试验符合得很好,验证了数值建模与分析的合理性.     

Perturbation methods for the analysis of the dynamic behavior of damaged plates

This paper presents an analytical method for the analysis of the dynamic behavior of damaged plates. The proposed approach allows the derivation of mode shapes and corresponding curvature modes for plates with various kinds of defects. Damage is modeled as a localized reduction in the plate thickness. Both point and line defects are considered to model notches or line cracks and delaminations in the plate. Small thickness reductions are considered so that the dynamic behavior of the damage plate can be analyzed through perturbations with respect to the undamaged modes. Results are presented to demonstrate the sensitivity of the curvature modes with respect to the considered low damage levels. Also, the curvature modes are used for the estimation of the strain energy of the plate and for the formulation of a damage index which can be used to provide damage location and extent information.     

DAMAGE DETECTION IN BUILDINGS USING A TWO-STAGE SENSITIVITY-BASED METHOD FROM MODAL TEST DATA

Many multi-story or highrise buildings consisting of a number of identical stories are usually considered as periodic spring-mass systems. The general expressions of natural frequencies, mode shapes, slopes and curvatures of mode shapes of the periodic spring-mass system by utilizing the periodic structure theory are derived in this paper. The sensitivities of these mode parameters with respect to structural damages, which do not depend on the physical parameters of the original structures, are obtained. Based on the sensitivity analysis of these mode parameters, a two-stage method is proposed to localize and quantify damages of multi-story or highrise buildings. The slopes and curvatures of mode shapes, which are highly sensitive to local damages,are used to localize the damages. Subsequently, the limited measured natural frequencies, which have a better accuracy than the other mode parameters, are used to quantify the extent of damages within the potential damaged locations. The experimental results of a 3-story experimental building demonstrate that the single or multiple damages of buildings, either slight or severe,can be correctly localized by using only the slope or curvature of mode shape in one of the lower modes, in which the change of natural frequency is the largest, and can be accurately quantified by the limited measured natural frequencies with noise pollution.