Equivalent continuum modeling of beam-like truss structures with flexible joints

The paper investigated the equivalent continuum modeling of beam-like repetitive truss structures considering the flexibility of joints,which models the contact between the truss member and joint by spring-damper with six directional stiffnesses and dampings.Firstly,a two-node hybrid joint-beam element was derived for modeling the truss member with flexible end joints,and a condensed model for the repeating element with flexible joints was obtained.Then,the energy equivalence method was adopted to equivalently model the truss structure with flexible joints and material damping as a spatial viscoelastic anisotropic beam model.Afterwards,the equations of motion for the equivalent beam model were derived and solved analytically in the frequency domain.In the numerical studies,the correctness of the presented method was verified by comparisons of the natural frequencies and frequency responses evaluated by the equivalent beam model with the results of the finite element method model.

Damage Detection of Offshore Jacket Structures Using Frequency Domain Selective Measurements

The development of damage detection techniques for offshore jacket structures is vital to prevent catastrophic events. This paper applies a frequency response based method for the purpose of structural health monitoring. In efforts to fulfill this task, concept of the minimum rank perturbation theory has been utilized. The present article introduces a promising methodology to select frequency points effectively. To achieve this goal, modal strain energy ratio of each member was evaluated at different natural frequencies of structure in order to identify the sensitive frequency domain for damage detection. The proposed methodology opens up the possibility of much greater detection efficiency. In addition, the performance of the proposed method was evaluated in relation to multiple damages. The aforementioned points are illustrated using the numerical study of a two dimensional jacket platform, and the results proved to be satisfactory utilizing the proposed methodology.

DYNAMIC OPTIMIZATION FOR UNCERTAIN STRUCTURES USING INTERVAL METHOD

An interval optimization method for the dynamic response of structures with inter- val parameters is presented.The matrices of structures with interval parameters are given.Com- bining the interval extension with the perturbation,the method for interval dynamic response analysis is derived.The interval optimization problem is transformed into a corresponding de- terministic one.Because the mean values and the uncertainties of the interval parameters can be elected design variables,more information of the optimization results can be obtained by the present method than that obtained by the deterministic one.The present method is implemented for a truss structure.The numerical results show that the method is effective.

An Improved Lower Order Method of Modal Parameter Estimation for Offshore Structures Using Reconstructed Signals

For modal parameter estimation of offshore structures, one has to deal with two challenges: 1) identify the interested frequencies, and 2) reduce the number of false modes. In this article, we propose an improved method of modal parameter estimation by reconstructing a new signal only with interested frequencies. The approach consists of three steps: 1) isolation and reconstruction of interested frequencies using FFT filtering, 2) smoothness of reconstructed signals, and 3) extraction of interested modal parameters in time domain. The theoretical improvement is that the frequency response function(FRF) of filtered signals is smoothed based on singular value decomposition technique. The elimination of false modes is realized by reconstructing a block data matrix of the eigensystem realization algorithm(ERA) using the filtered and smoothed signals. The advantage is that the efficiency of the identification process of modal parameters will be improved greatly without introducing any false modes. A five-DOF mass-spring system is chosen to illustrate the procedure and demonstrate the performance of the proposed scheme. Numerical results indicate that interested frequencies can be isolated successfully using FFT filtering, and unexpected peaks in auto spectral density can be removed effectively. In addition, interested modal parameters, such as frequencies and damping ratios, can be identified properly by reconstructing the Hankel matrix with a small dimension of ERA, even the original signal has measurement noises.

Identification of Composite-Metal Bolted Structures with Nonlinear Contact Effect

The middle layer model has been used in recent years to better describe the connection behavior in composite structures.The influencing parameters including low pre-screw and high preload have the main effects on nonlinear behavior of the connection as well as the amplitude of the excitation force applied to the structure.Therefore,in this study,the effects of connection behavior on the general structure in two sections of increasing damping and reducing the stiffness of the structures that lead to non-linear phenomena have been investigated.Due to the fact that in composite structure we are faced to the limitation of increasing screw preload which tend to structural damage,so the investigation on the hybrid connection(metal-composite)behavior is conducted.In this research,using the two-dimensional middle layer theory,the stiffness properties of the connection are modeled by normal stiffness and the connection damping is modeled using the structural damping in the shear direction.Nonlinear frequency response diagrams have been extracted twice for two different excitation forces and then proposed by a high-order multitasking approximation according to the response range of the nonlinear finite element model for stiffness and damping of the connection.The effect of increasing the amplitude of the excitation force and decreasing the preload of the screw on the nonlinear behavior of the component has been extracted.The results show that the limited presented novel component model has been accurately verified on the model obtained from the vibration experimental test and the reduction of nonlinear model updating based on that is represented.The comparison results show good agreementwith a maximumof 1.33%error.

Multi-harmonic equivalent modeling for a planar repetitive structure with polynomial-nonlinear joints

How nonlinear joints affect the response of large space structures is an important problem to investigate.In this paper,a multi-harmonic equivalent modeling method is presented to establish a frequency-domain model of planar repetitive structures with nonlinear joints.First,at the local level,the nonlinear joint is modeled by the multi-harmonic describing function matrix.The element of the hybrid beam is obtained by the dynamic condensation of the beam-joint element.Second,at the global level,the displacement-equivalence method is used to model the multi-harmonic Euler continuum beam equivalent to the planar repetitive structure.Then,the pseudo-arc-length continuation method is applied to track the multi-harmonic trajectory of response.Afterwards,an experiment is conducted to validate the correctness of the modeling method,considering the effect of hanging rope and air damping.In the numerical studies,several simulation results indicate the similarity of response between a single-degree-of-freedom system with a single nonlinear joint and the system of the planar repetitive structure with a large number of nonlinear joints.Finally,the component of higher-order harmonics is shown to be important for predicting the resonance frequencies and amplitudes.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

MODAL PARAMETERS EXTRACTION WITH CROSS CORRELATION FUNCTION AND CROSS POWER SPECTRUM UNDER UNKNOWN EXCITATION

In most of real operational conditions only response data are measurable while the actual excitations are unknown, so modal parameter must be extracted only from responses. This paper gives a theoretical formulation for the cross-correlation functions and cross-power spectra between the outputs under the assumption of white-noise excitation. It widens the field of modal analysis under ambient excitation because many classical methods by impulse response functions or frequency response functions can be used easily for modal analysis under unknown excitation. The Polyreference Complex Exponential method and Eigensystem Realization Algorithm using cross-correlation functions in time domain and Orthogonal Polynomial method using cross-power spectra in frequency domain are applied to a steel frame to extract modal parameters under operational conditions. The modal properties of the steel frame from these three methods are compared with those from frequency response functions analysis. The results show that the modal analysis method using cross-correlation functions or cross-power spectra presented in this paper can extract modal parameters efficiently under unknown excitation.

Analysis of Dynamic Cross Response between Spindles in a Dual Spindle Type Multi-Functional Turning Machine

In order to meet increasing demand for higher productivity and flexibility, recently many kinds of multi-functional machine tools, which are capable of multiple machining functions or different kinds of machining processes on one machine, have been developed and widely used in manufacturing industries. In this study, a multi-functional turning lathe, which has two spindles and two turrets so that multiple turning operations and various machining processes could be performed simultaneously, has been developed. Furthermore, the equations of correlation between whole responses and cross responses of the two spindles have been derived to examine to what extent the two spindles affect each other’s vibrations.

基于高斯过程回归的铣削机器人模态参数预测

工业机器人结构频率响应函数的获取、动力学参数的辨识对机器人铣削加工预测影响显著,且模态参数具有较强的位姿依赖性。有限元法和动力学模型因难以对机器人刚度、阻尼等特性准确建模而导致失准现象的出现。为快速准确地预测铣削机器人加工空间内所有姿态下的模态参数,提出一种基于高斯过程回归的模态参数预测方法。首先探究六自由度串联机器人关节角和欧拉角对机器人铣削系统的模态参数影响,在此基础上,通过平面内245组姿态的模态敲击实验,建立针对机器人位姿变化的模态参数预测模型,揭示模态参数随机器人位姿变化的规律,使得仅需有限次的模态测试实验便可预测范围内任意位姿处的模态参数。结果表明:预测的频率响应函数曲线与实测的频率响应函数曲线结果吻合良好。

基于振动测量的热防护结构脱粘损伤检测方法

针对典型飞行器热防护结构脱粘损伤现场快速无损检测的需求,提出了一种基于敲击测量频响函数的脱粘损伤识别方法。首先,利用有限元方法建立了含脱粘损伤的热防护结构有限元模型并进行了振动特性分析,分析了脱粘损伤引起的结构局部刚度下降规律以及频响函数对脱粘损伤的敏感性;其次,确定了脱粘损伤识别的特征频率范围,给出了一个脱粘损伤指标;最后,采用力锤与激光多普勒测振仪对含脱粘的热防护结构进行了测量。实验结果表明,当脱粘面积达到60%时,脱粘损伤指标比健康件增加了1倍以上,当脱粘面积达到80%时,脱粘损伤指标为健康件的5倍以上,验证了所提出的方法能够有效识别出热防护结构的脱粘损伤。

大型汽轮发电机定子端部绕组物理参数识别及数学模型建立方法研究

从结构的数字化模型频响函数出发,利用最小二乘复频域法识别模态参数,进一步用获取的模态参数修正集中质量法推导出的物理参数,从而建立符合结构动力特性的数学模型。首先通过固支梁模型算例验证该方法的可行性;然后对600 MW大型汽轮发电机端部绕组的精细化有限元模型进行模态分析,并与实测结果进行对比,验证了该模型的合理性;此后,基于该有限元模型获取的频响函数和模态参数,识别出端部绕组的物理参数并建立其数学模型。结果表明:在75~115 Hz频率段中,最小二乘复频域法识别出的端部绕组模态与有限元结果对比表明,固有频率和阻尼比的最大误差出现在第一阶模态中,分别为0.27%和0.50%,模态振型接近;通过数学模型和有限元模型计算的端部绕组固有频率最大误差为0.27%,模态振型一致;数学模型计算的频响函数与有限元结果对比表明,测点的频响函数最高匹配度可达95%,多数测点的频响函数匹配度超过85%。该方法可为大型汽轮发电机定子端部绕组动力学的准确建模提供依据。

非均匀预紧力作用下螺栓连接框架结构频响函数计算

机械装备中的框架结构大多通过螺栓连接在一起,各螺栓之间出现非均匀预紧会对框架结构的振动特性参数(如频响函数)产生明显的影响。基于有限元法提出了一种考虑螺栓非均匀预紧的框架结构频响函数计算方法。按照频响函数的定义,根据模态叠加原理推导出适用于螺栓连接框架结构频响函数的计算公式;从服务于频响函数计算的需求出发,基于ANSYS软件阐述了螺栓非均匀预紧的模拟及提取包含非均匀预紧的框架结构刚度及质量矩阵的方法;给出了基于ANSYS和Matlab两种软件平台对螺栓连接框架结构频响函数进行计算的分析流程;以一个包含4个连接螺栓的框架结构为对象进行了实例研究,用试验证明了所提频响函数计算方法的合理性,在此基础上从试验及仿真两个角度分析了螺栓预紧力对框架结构频响函数的影响。结果表明,随着螺栓预紧力的增加,框架结构固有频率及频响函数峰值均变大。

悬臂结构地震响应分析的广义单自由度模型研究

针对有限元方法存在计算时间过长的缺点,不适用于需要多次响应分析的结构抗震性能评估问题。进行了悬臂结构线性地震响应分析的广义单自由度模型研究,提出了多项式形函数和基于多项式形函数的单自由度模型,并通过与有限元分析结果的对比分析,调查了基于多项式形函数的单自由度模型对典型地震波激励下结构响应分析的有效性。结果表明:提出的基于多项式形函数的广义单自由度模型平均误差为7.20%,为提高建模准确性,建议采用水平集中荷载施加方法进行多项式形函数参数估计。

Regularized automatic frequency response function acquisition of a milling robot operating in a high-dimensional workspace

Because robotic milling has become an important means for machining significant large parts,obtaining the structural frequency response function(FRF)of a milling robot is an important basis for machining process optimization.However,because of its articulated serial structure,a milling robot has an enormous number of operating postures,and its dynamics are affected by the motion state.To accurately obtain the FRF in the operating state of a milling robot,this paper proposes a method based on the structural modification concept.Unlike the traditional excitation method,the proposed method uses robot joint motion excitation instead of hammering excitation to realize automation.To address the problem of the lack of information brought by motion excitation,which leads to inaccurate FRF amplitudes,this paper derives the milling robot regularization theory based on the sensitivity of structural modification,establishes the modal regularization factor,and calibrates the FRF amplitude.Compared to the commonly used manual hammering experiments,the proposed method has high accuracy and reliability when the milling robot is in different postures.Because the measurement can be performed directly and automatically in the operation state,and the problem of inaccurate amplitudes is solved,the proposed method provides a basis for optimizing the machining posture of a milling robot and improving machining efficiency.

基于频响函数辨识机械结合部动态参数的研究

进行机械结构的动力分析与动态优化设计时,为获得比较准确的结构边界条件,结合部参数辨识成为其中一项关键技术。结合工程实际,应用频响函数辨识结合部刚度与阻尼参数的方法进行参数识别,对能否获取完备频响函数进行了研究,并作出相应的求解策略。该方法避开了对频响函数直接求逆,运用最小二乘原理将矛盾方程转化为定解方程,保证了数值计算的稳定。一般情况下,结合部处绝对阻尼值要远远小于绝对刚度值,为了更准确地辨识出阻尼值,需采用对阻尼进行二次辨识。该方法具有一定的工程实用价值,而且辨识过程简单。算例证实了该方法具有很高的辨识精度。

机械结合部动态刚度辨识与实验研究

机械结合部动态特性参数辨识最常用的方法是频响函数法。然而,实测频响函数数据即使经过降噪处理,仍受到噪声的污染,使得在数值运算时导致辨识结果出现不适定性。为解决这一问题,使得辨识结果能够真实反映结合部特性,提出采用条件数方法对实验数据进行处理之后,再进行参数辨识。为使条件数足够小,采取求平均值的办法,将条件数大于平均值的频率剔除,只保留状态值小于平均值的频率,将所保留下的频率进行比较,找出有交集的频率,并在这些频率下进行参数辨识,从而能够避免发生不适定问题。从仿真算例、实验研究结果表明,条件数法能够解决利用频响函数法辨识结合部参数时出现的不适定问题,从而提高了辨识精度。

基于不完备频响函数辨识结合部等效参数的研究

研究了输出信息不完备情况下结合部等效动力学参数的辨识问题,阐述了一种较为通用的结合部等效动力学参数辨识方法。首先采用实验与有限元法相结合,辨识出试验中难以获取的频响函数,构造出完备频响函数。然后通过完备频响函数,运用迭代算法辨识出结合部等效动力学参数。在辨识过程中,建立损失函数模型,将问题转化为求解损失函数的最小值问题。该方法不需要求出模态参数,所以同样适用于大阻尼系统或者模态密集系统的结合部参数辨识。由于只需部分易测的频响函数,所以具有很好的工程应用性。最后通过算例验证了本方法具有很高的辨识精度。

栓接结合部动态特性辨识方法

由于栓接结合部自身非线性特性、测试时噪声信号的干扰以及求解时引起数值误差的影响,使得在利用频响函数(Frequency response functions,FRFs)进行参数辨识时会出现不适定问题。为避免产生不适定问题,使得辨识结果更能真实反映栓接结合部特性,利用子结构综合法建立法向与切向栓接结合部动力学模型,并利用加权函数法使每个辨识方程式的系数都维持在同一水准。运用FRFs法对栓接结合部等效动力学参数进行辨识,并将其作为初始值,采用迭代法求出栓接结合部参数在整个频段的灵敏度,根据灵敏度确定选取的试验数据,再进行参数辨识。通过试验研究比较,结果表明采用频响函数辨识栓接结合部等效参数时,利用灵敏度法能够提高辨识精度,消除辨识时不适定问题的产生。

栓接结合部动态特性参数辨识新方法

利用频响函数法辨识栓接结合部等效动力学参数时,由于实验测量、噪声干扰及数值运算(矩阵求逆)等所致误差,使辨识结果出现不适定性。为避免此问题的产生,使辨识结果能真实反映栓接结合部动态特性,提出新的辨识方法。建立含栓接结合部的整体结构有限元模型,据栓接结合部不同等效刚度与等效阻尼与整体结构归一化频率关系,确定栓接结合部等效刚度与等效阻尼的取值范围,并取该范围的平均值为初值,以实验与仿真整体结构频响函数误差最小为目标确定栓接结合部等效刚度与等效阻尼值。通过实验研究及与文献[16]结果比较表明,采用该方法可达准确辨识栓接结合部等效参数之目的。