基于曲率模态的复合材料层合板分层损伤检测方法研究

基于振动信号应用曲率模态方法对复合材料层合板分层损伤进行损伤检测。首先由数值模拟所得不同状态下损伤以及未损伤层合板振动特性参数计算其振型曲率和均布载荷曲面值曲率;然后基于损伤与未损伤层合板曲率值的差分值建立损伤识别指标进行分层损伤检测。最后,为解决差分算法对结构未损伤模型参数的依赖性问题,引用曲面光滑算法和曲率模态变化率法直接对损伤结构进行损伤提取。结果表明,运用曲率参数差分法可以很好地识别各类损伤,且对于多层层合板来说损伤所处层的位置会影响损伤指标值的大小。曲面光滑算法和曲率模态变化率法均可不依赖于未损伤结构参数识别各类损伤,且曲面模态变化率法的检测效果优于曲面光滑算法。     

复合材料板分层损伤识别的曲率模态差法

以单侧固支的分层损伤复合材料层合板为研究对象,利用有限元分析软件ABAQUS得到层合板结构振型位移分析数据,针对分层损伤进行了曲率模态分析。分析结果表明,在层板内一个区域存在分层损伤的情况下,其振型与频率的变化非常小,难以用于判断损伤位置,但分层损伤区域的曲率模态差值变化显著,采用曲率模态差法可以对层合板结构分层损伤位置进行准确判定。     

基于低秩与稀疏分解的层合板损伤定位

针对基于结构振型参数的损伤定位方法抗噪性差、对微小损伤不敏感以及对多损伤识别性能低等问题,基于振型低秩性与损伤分布稀疏性提出了一种复合材料层合板多损伤识别方法。首先,使用高斯?拉普拉斯算子（Laplacian of Gaussian,简称LoG）求解曲率模态;其次,利用鲁棒主成分分析提取曲率模态中损伤诱导产生的奇异值进行损伤定位;然后,提出了一个鲁棒损伤定位指标用于融合多个曲率模态的损伤信息;最后,使用带损伤复合材料层合板数值模拟与实验数据验证了方法的有效性。结果表明,该方法无需无损结构参考信息,便可准确地定位复合材料层合板中多个小面积损伤。     

振型曲率在板类结构动力检测中的应用

以四边简支方形弹性薄板为研究对象，通过数值计算得到板损伤前后的多阶模态参数，进而得到板面内两个方向的位移振型曲率并用于板的损伤检测研究。结果表明：当布置有足够数量的振型测点时，振型曲率及板损伤前后的振型曲率差均可用于板损伤的探测与定位，并能大致判断损伤的程度；当振型测点间距过大，或测点偏离损伤区域时，均可能导致检测的失败。     

基于间隔平滑法的复合材料分层损伤识别研究

利用有限元分析软件ABAQUS建模计算,获得层合板结构的节点振型数据,然后计算得到结构的各阶模态曲率,利用间隔平滑法计算损伤指标,最终实现对分层损伤的识别。与大多数基于振动的损伤识别方法不同,间隔平滑法不需要结构完好状态时的数据或是数值计算结果作为基准,只依赖于损伤状态的振型数据就可以实现对损伤位置的准确识别,同时还能对损伤尺寸、损伤程度的相对大小做出判断。     

AGS结构的损伤定位仿真

为了检测先进复合材料格栅结构(AG S)的损伤所在位置,提出了通过计算结构在损伤前、后模态曲率差的方法,来进行计算和分析。建立了格栅结构在有约束条件下的有限元模型,通过AN SY S中的模态分析得到模态振型位移值,计算了结构损伤前、后的模态曲率差,通过这一指标对结构的损伤进行辨识,并分析了采用多阶模态的计算效果。结果表明,通过第1阶模态振型模态曲率差的计算,可对单损伤状况做出有效的检测;对于多损伤工况,需使用前3阶模态的曲率差进行分析,才能有效检测损伤的位置。     

运用曲率模态技术的木梁损伤定量识别

为对木结构构件局部缺陷进行有效检测,结合试验模态分析和有限元模拟方法,对含不同位置、大小和数量孔洞缺陷的木梁进行研究,计算其第1阶位移模态振型和曲率模态,分析木梁损伤前后的曲率模态变化,探讨模态分析方法在木材缺陷检测中的适用性.研究结果表明:曲率模态是一个对木梁损伤比较敏感的参数,可用于对孔洞位置、大小及数量进行定量的估计;通过降低有限元模型局部单元的弹性模量能够较好地模拟木梁损伤,有限元模态分析和试验模态分析得到的位移模态振型及曲率模态吻合均较好,验证了模态分析对木梁无损检测是一种有效的方法.     

基于模态局部化和跃迁的网壳结构损伤指标

由于模态局部化和模态跃迁使结构损伤前后的振型产生较大差别,二者间的相关性发生较大程度的弱化,基于这一事实,利用结构的振型相关系数,构造出一种对网壳结构局部损伤具有高敏感性的损伤特征向量。该向量构造简单,仅使用少数振型和少量的测试自由度。通过一个网壳结构的算例分析,对所提出的损伤特征向量的性质进行了检验。结果表明,该向量不仅具有较好的空间可分辨性、损伤敏感性和噪声鲁棒性,并且对结构有限元模型误差具有一定的适应性。     

基于模态参数灵敏度分析的结构损伤识别研究

结构损伤通常以结构中刚度损失为特征。结构的损伤会引起结构参数的改变,结构参数变化会导致结构模态参数(固有频率、振型)的变化,因此寻求结构损伤与结构模态参数之间的关系十分重要。文中根据结构振动特征方程,推导了结构模态参数对结构参数改变的灵敏度表达式,建立了结构模态参数对以单元刚度为特征的结构损伤识别关系式,识别结构损伤的位置和损伤程度。文中制作了无损伤、有损伤3根悬臂梁钢板试件,测取试件结构固有频率与振型,根据无损伤试件结构图,建立了有限元模型,计算其结构固有频率与振型。将无损伤试件测得的模态参数作为有限元模型修正依据,并用两种损伤条件下测得的数据修正无损伤的有限元模型,将单元刚度作为修正参数,应用灵敏度方法来识别悬臂梁钢板试件损伤的位置和程度,其结果与实际基本一致,证明了方法的有效性。     

基于Guyan缩聚与均布载荷面曲率的柱壳损伤识别

针对工程中采用模态测试对火箭柱壳结构的蒙皮进行损伤识别时,存在高阶模态较难获取和实际结构测点自由度与模型自由度不匹配的问题,提出基于Guyan缩聚与均布载荷面曲率的损伤识别方法。通过对柱壳蒙皮有限元模型的2次Guyan缩聚,将其平动和转动自由度缩聚到法向上,并以法向的模态振型作为输入参数,构建基于均布载荷面曲率的损伤指标,数值分析了该指标对火箭柱壳蒙皮的损伤识别效果。结果表明：缩聚后的模型能够完全满足工程需求;所提方法只需低阶模态参数,不但可以识别出柱壳结构单损伤和多损伤位置,而且能够给出损伤程度的相对大小。该方法对工程实际中火箭蒙皮的损伤识别具有重要的参考价值。     

Effect of axial force on free vibration of Timoshenko multi-span beam carrying multiple spring-mass systems

The situation of structural elements supporting motors or engines attached to them is usual in technological applications. The operation of machine may introduce severe dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli–Euler single-span beams carrying a number of spring-mass system and Bernoulli–Euler multi-span beams carrying multiple spring-mass systems are plenty, but that of Timoshenko multi-span beams carrying multiple spring-mass systems with axial force effect is fewer. This paper aims at determining the exact solutions for the first five natural frequencies and mode shapes of a Timoshenko multi-span beam subjected to the axial force. The model allows analyzing the influence of the shear and axial force effects and spring-mass systems on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The calculated natural frequencies of Timoshenko multi-span beam by using secant method for non-trivial solution for the different values of axial force are given in tables. The mode shapes are presented in graphs.     

微型振动式发电机振子系统的理论计算及仿真

建立了微型振动式发电机的核心部件振子的结构模型。利用有限元的方法对振子进行了动力学分析及计算,并应用ANSYS有限元分析软件,对振子进行了计算机模拟分析,得出了敏感元的厚度、宽度对振子固有频率及最大变形量的影响。设计出了优化的振子系统结构。     

Compensation of nonlinear dynamics for energy/phase control of hopping robot

Hopping height control is one of the difficult problems in legged control. Many kinds of research employ a leg spring for the supplement of energy, and model the robot as a spring-mass model. Feedback linearization enables to cancel the nonlinear terms theoretically. However, it is difficult to identify the nonlinear terms including the parameters precisely in the real world.This paper nominalizes the robot dynamics as the desired spring-mass system applying a disturbance observer. In order to realize the desired characteristics of the spring and the mass, the disturbance including the nonlinear terms is rejected firstly by a disturbance observer. To make the mass in the workspace as constant, the nominal inertia of the disturbance observer in the joint space is varied. Next, by adding the desired virtual elastic force, the robot dynamics is nominalized as the desired spring-mass system.Based on the nominalized spring-mass dynamics, hopping-height control using energy/phase control is implemented. While energy control is often used for hopping height control, the energy/phase control enables the hopping-height control and the spring-mass oscillation simultaneously.Constant hopping-height and stepwise hopping height are realized experimentally through the proposed control method. The simulations in the case of the ideal dynamics are also conducted for comparison.     

Transverse vibrations of an Euler–Bernoulli uniform beam carrying two particles in-span

Vibrations of beams carrying different combinations of particles, heavy bodies and spring-mass systems which are located on or off resilient supports have been tackled by several researchers. Most of the approaches were based mainly on various approximate methods. In this paper an analytical solution based on the classical beam eigenvalue technique is presented for the vibrations of a beam carrying two particles. For purpose of analysis, the beam was divided into a portion from one end to the first particle, a portion between particles and a portion from the second particle to the other end. The frequency equation is expressed in closed form as a 2nd order determinant equated to zero. Schemes are presented to compute the 4 elements of the determinant and to evaluate the roots of the frequency equation. Computational difficulties were not encountered in the implementation of the schemes. The first three natural frequency parameters are tabulated for 16 combinations of the classical boundary conditions and several combinations of the location and mass of the particles. The beam mode shape is the juxtaposition of the mode shapes of the three portions of the beam. Some examples of normalised beam mode shapes and location/s of node/s are also presented. The results may be used to judge the accuracy of values obtained by approximate methods.     

A study on large mass method for dynamic problem of multiple degree-of-freedom system excited by ground acceleration time history?

We considered a numerical modeling technique called ‘large mass method’ or large mass model, which is used for a dynamic problem of a structure that is subjected to support or ground acceleration time history. Since its analytic background has not been extensively verified yet, this paper extends the previous analysis for a single degree-of-freedom system to that for the multi-degree-of-freedom springmass system to present theoretical effectiveness or rigorous comprehension of the technique. The theorems are discussed and checked by using the concept of quasi-static decomposition with simple examples. The analysis shows that the characteristics of LM model for single DOF system are conserved consistently even in multi-DOF system and that the response of LM model for spring-mass system is also composed of quasi-static part and dynamic part like the response of an original spring-mass model. Numerical tests for multi-degree-offreedom spring-mass systems show that they match well with the present analysis.     

On the eigenfrequencies of cantilevered beams carrying a tip mass and spring-mass in-span

The present study is concerned with the derivation of the eigenfrequencies and their sensitivity of a cantilevered Bernoulli-Euler beam carrying a tip mass (primary system) to which a spring-mass (secondary system) is attached in-span. After establishing the exact frequency equation of the combined system, a Dunkerley-based approximate formula is given for the fundamental frequency. Using the normal mode method, a second approximate frequency equation is established which is then used for the derivation of a sensitivity formula for the eigenfrequencies. The frequency equations of some simpler systems are obtained from the general equation as special cases. These frequency equations are then numerically solved for various combinations of physical parameters. The comparison of the numerical results with those from exact frequency equations indicate clearly that the eigenfrequencies of the combined system described above can be accurately determined by the present method.     

Impact fault detection of gearbox based on variational mode decomposition and coupled underdamped stochastic resonance

In the gear fault diagnosis, the emergence of periodic impulse components in vibration signals is an important symptom of gear failure. However, heavy background noise makes it difficult to extract the weak periodic impulse features. Therefore, the paper presents an impact fault detection method of gearbox by combining variational mode decomposition (VMD) with coupled underdamped stochastic resonance (CUSR) to extract the periodic impulse features. First, the adaptive VMD is presented to decompose the vibration signal into several intrinsic mode functions (IMFs), which can automatically determine the appropriate mode number according to the correlation kurtosis (CK) of decomposition results and extract the sensitive IMF component containing the main fault information. Next, the adaptive CUSR method is developed to analyze the selected sensitive IMF component, and the optimal system parameters are obtained by the genetic algorithm using the CK index as optimization objective function. Finally, the periodic impulse features are extracted by the output signal of CUSR system accurately. Experiments and engineering application verify the effectiveness and superiority of the proposed adaptive VMD-CUSR method for extracting the periodic impulse features in gear fault diagnosis compared to other methods.     

Mathematical modeling of a vehicle crash test based on elasto-plastic unloading scenarios of spring-mass models

This paper investigates the usability of spring which exhibit nonlinear force-deflection characteristic in the area of mathematical modeling of vehicle crash. We present a method which allows us to obtain parameters of the spring-mass model basing on the full-scale experimental data analysis. Since vehicle collision is a dynamic event, it involves such phenomena as rebound and energy dissipation. Three different spring unloading scenarios (elastic, plastic, and elasto-plastic) are covered and their suitability for vehicle collision simulation is evaluated. Subsequently we assess which of those models fits the best to the real car’s behavior not only in terms of kinematic responses but also in terms of energy distribution.     

复刚度循环对称结构复振型特性研究

定义了循环对称粘弹结构，根据复模态理论和结构的循环对称性，将循环对称粘弹结构的复振型分为循环对称复振型、循环反对称复振型以及简并复振型，与算例完全吻合。为循环对称粘弹结构动特性的扇形子结构分析奠定了坚实的基础。     

电阻电感非线性RLC电路弹簧耦合系统3次超谐共振

研究电阻和电感非线性RLC(resistance-inductance-capacitance)电路弹簧耦合系统的非线性振动,应用拉格朗日-麦克斯韦方程,建立受简谐激励的具有电阻和电感非线性RLC电路弹簧耦合系统的数学模型.根据非线性振动的多尺度法,得到系统满足3次超谐共振条件的一次近似解以及对应的定常解.对其进行数值计算,分析系统不同参数对响应曲线的影响.增大激励电压、极板面积和非线性电阻系数,响应曲线振幅和共振区变大.增大极板间距、线性电感系数和线性电阻系数,响应曲线振幅和共振区变小.系统的固有频率随极板间距增大而增大,随极板面积和线性电感系数的增大而减小.