Damping function estimation based on modal receptance models and neural nets

 A method for the estimation of an isotropic material damping based on the isotropic, augmented Hooke's law (AHL) and the concept of isotropic, modal and material damping functions is proposed. The method is a straightforward application of standard neural net (NN) back propagation techniques combined with back propagation of simulation errors using “response-to-damping parameter” mapping based on an analytical, modal receptance model incorporating AHL damping. Damping parameters are estimated by fitting the receptance model iteratively, using NN technique, to measured receptance data. Owing to the response model used, the proposed estimation technique provides new possibilities to completely separate pure damping properties from geometry, elastic (static) data and undamped modal data. The method is applicable to homogeneous materials and cases where cross coupling, due to damping, between the modes can be neglected. Even though in this sense restricted, the technique may be applied to a wide class of cases, including cases with very high damping and highly overlapping damped modes. Necessary background theory, including a suitable NN structure, for application of the method is presented. The estimation procedure is demonstrated for a plexiglas (PMMA) plate (modal loss factors ≈ 0.1 at room temperature) used as experimental test case. Very good agreement between measured receptances and responses predicted using the estimated damping function parameters is obtained. Validation was done using both modal and direct finite element (FE) computations.     

Non‐linear finite element modal approach for the large amplitude free vibration of symmetric and unsymmetric composite plates

A theoretical analysis is presented for the large amplitude vibration of symmetric and unsymmetric composite plates using the non‐linear finite element modal reduction method. The problem is first reduced to a set of Duffing‐type modal equations using the finite element modal reduction method. The main advantage of the proposed approach is that no updating of the non‐linear stiffness matrices is needed. Without loss of generality, accurate frequency ratios for the fundamental mode and the higher modes of a composite plate at various values of maximum deflection are then determined by using the Runge–Kutta numerical integration scheme. The procedure for obtaining proper initial conditions for the periodic plate motions is very time consuming. Thus, an alternative scheme (the harmonic balance method) is adopted and assessed, as it was employed to formulate the large amplitude free vibration of beams in a previous study, and the results agreed well with the elliptic solution. The numerical results that are obtained with the harmonic balance method agree reasonably well with those obtained with the Runge–Kutta method. The contribution of each linear mode to the maximum deflection of a plate can also be obtained. The frequency ratios for isotropic and composite plates at various maximum deflections are presented, and convergence of frequencies with the number of finite elements, number of linear modes, and number of harmonic terms is also studied. Copyright © 2005 John Wiley & Sons, Ltd.     

EXACT MODAL SYNTHESIS TECHNIQUES USING RESIDUAL CONSTRAINT MODES

A new exact modal synthesis method for finding natural frequencies and modes of structures is proposed, in which the exact residual constraint modes based upon an incomplete set of normal modes of substructures with fixed interfaces are expressed in two parts. These are the static constraint modes and a residual term with which it represents exactly the effect of normal modes not retained. The modal synthesis uses a Ritz procedure and an iterative technique is presented for solving the non-linear equations of modal synthesis. This has the advantage that the results given by its first iteration are exactly those given by the Craig–Bampton–Hurty modal synthesis method, which leads to rapid convergence of subsequent iterations. The proposed method is an improvement of Hu's exact modal synthesis method and is also shown to have as its limit the method of exact dynamic condensation. Numerical examples show that using the proposed method yields superior accuracy when only a few lower modes are used. © 1997 by John Wiley & Sons, Ltd.     

Higher order eigensensitivities‐based numerical method for the harmonic analysis of viscoelastically damped structures

This paper presents an efficient numerical method for the harmonic analysis of viscoelastically damped structural systems characterized by a frequency‐dependent structural damping matrix, making use of the complex mode superposition method. Departing from the undamped eigensolution, the proposed numerical method updates the complex and frequency‐dependent eigenpair avoiding the solution of a complex eigenproblem for each computational frequency. The complex eigenvalues and eigenvectors are updated within the desired tolerance by an adaptive step‐size control scheme using the first‐ and higher order eigenderivatives. The influence on the computation time of the considered number of eigenderivatives and the tolerance is discussed, and the efficiency of the proposed numerical method for the harmonic analysis of viscoelastically damped large‐ordered structural systems is proved. Finally, a practical application is presented where the harmonic response of a constrained layer damping cantilever beam subjected to a base motion is analyzed. The complex and frequency‐dependent eigenvalues and eigenvectors are computed, the modal contributions to the total response are determined, and the total response is approximated by the complex mode superposition method. Finally, the approximated response is validated with the exact one computed by the direct frequency method and with that experimentally measured. Copyright © 2011 John Wiley & Sons, Ltd.     

Multifidelity component interface reduction and modal truncation augmentation

A Hurty-Craig-Bampton (HCB) reduced order component can have unnecessarily large dimension if it contains many interface degrees of freedom. This is often the case for high spatial resolution models. Furthermore, for such high-fidelity models, their static constraint modes can be expensive to compute. To overcome these problems, a component mode synthesis method with interface reduction is developed using multifidelity models. The interface reduction basis is computed from the assembled system by coarsening each substructure's mesh, but keeping the model resolution at the interface intact. It is shown that such a mesh coarsening has a small effect on the interface reduction basis quality. Using this reduction basis, the dimension of the static constraint modes problem can be reduced and the modes computed at a low cost. When few interface modes can be used without significant loss of accuracy, it is possible to enrich the HCB basis with modal truncation augmentation (MTA) vectors to increase accuracy at a small extra cost. The accuracy of a procedure that utilises MTA vectors together with the multifidelity interface reduction is investigated. The method's performance and accuracy are illustrated on a planar problem and a more complex problem from industry.     

板壳结构振动功率流的子结构线导纳法研究

采用子结构点导纳方法分析铺壳耦合结构振动特性时,需要将衔接线划分为一系列的点进行求解,较为烦琐.针对这一问题,该文提出了改进的子结构线导纳方法.首先建立了铺板和圆柱壳的耦合振动模型;然后采用模态展开法分别求解铺板和圆柱壳的机械线导纳,得到振动传递方程中的线导纳矩阵;最后求解耦合振动方程分析铺板与圆柱壳的振动功率流特性.将结果分别与ANSYS 和AutoSEA 的计算结果进行对比分析表明:该文提出的改进方法能够在宽频带内有效地计算板壳耦合结构的振动功率流特性,且求解过程简单,适于线衔接复杂结构的振动特性分析.     

An optimal method for the solution of the constrained eigenvalue/response problem for large structures comprising rigidly-connected substructures

Dynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating-point operations which must take place and the on-board computer memory required. The proposed method makes use of a stable co-ordinate transformation which reduces the mass matrix for the constrained composite-system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite-system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.     

重频结构模态灵敏度分析的高精度截模态算法

基于全模态展开定理,提出了计算重频阻尼结构模态灵敏度的全模态算法和高精度截模态算法。首先通过引入松驰因子的移频法克服了重频现象对模态灵敏度分析的影响,给出了重频模态灵敏度的全模态算法,并从理论上分析了这种算法的误差来源及控制方法;其次通过分析各阶模态在模态灵敏度的全模态线性展开式中的贡献作为截断准则来实施截断,从而提出了重频结构模态灵敏度分析的高精度截模态算法,并给出了其误差分析方法。提出的高精度截模态算法仅需少量模态,即可获得对称及非对称系统任一重频模态的灵敏度信息,无论是理论分析还是数值计算的结果均表明了该算法的正确性及高效性。     

基于谱峭度的谐波模态检测方法

在旋转机械领域,周期激励的存在使运行模态分析中含有谐波模态。根据结构模态和谐波模态的谱峭度值的不同,该文提出了基于谱峭度的谐波模态辨识方法。首先,给出了谱峭度的定义及其无偏估计算法;其次,从理论上证明应用此方法不需要滤波处理,并提出了简单且易于实现的优化方法;然后,应用频域空间域分解算法分离出谐波模态去除其对结构模态的影响;最后,通过仿真及实验成功检测出了谐波模态并消除其影响,验证了方法的有效性和可靠性。     

基于VMD-SSI的结构模态参数识别

针对结构的弱模态易淹没在噪声中导致模态识别遗漏的问题,该文提出了一种基于变分模态逐步抽取高能量模态的结构弱模态识别方法。该方法采用自回归模型功率谱准确选取高能量模态的初始中心频率;利用变分模态抽取法进行高能量模态分量的分解,接着将去除高能量模态成分的信号代替原始结构响应,重复进行下一阶高能量模态的初始中心频率选取和模态成分分解;对各模态分量进行主成分分析法实现振型识别。进一步,通过地震激励下的十自由度数值算例验证该方法在非平稳激励下弱模态识别的有效性;利用IASC-ASCE健康监测工作组开发的4层框架基准模型试验进行数据分析,验证该方法在实际应用中的有效性。结果表明,所提方法能够用于地震激励下含噪情况的结构弱模态识别。

     

Experimental and numerical investigations for the free vibration of cantilever trapezoidal plates

Abstract

Based on the advantages of non‐contact and full field measurement, the optical technique called amplitude‐fluctuation electronic speckle pattern interferometry (AFESPI) with an out‐of‐plane setup is employed to investigate the free vibration of cantilever trapezoidal plates with various taper ratios and sweep‐back angles. Twenty different plate configurations are analyzed, including triangular and trapezoidal plates, and the first seven vibration modes of each plate are measured. The AF‐ESPI method is very convenient for measuring vibrating objects because no contact is required in contrast to classical modal analysis using accelerometers. Based on the fact that clear fringe patterns will appear only in resonance, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present technique. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Excellent agreements are obtained for both results of resonant frequencies and mode shapes. The influences of taper ratios and sweep‐back angles on the vibration behavior of cantilever trapezoidal plates are also demonstrated in terms of the dimensionless frequency parameter.     

基于弹性-黏弹性对应原理的复合材料层合板模态阻尼预测:理论及其有限元实现

提出一种利用通用有限元软件求解复合材料结构模态阻尼的有限元方法。该方法基于扩展弹性-黏弹性对应原理,定义出具有频率依存性的黏弹性复合材料复刚度矩阵,并借助ABAQUS提供的二次开发接口UMAT将其编入求解器中,结合复特征值法求解任意铺层层合板的模态阻尼。与已有的理论方法相比,本模型的计算结果更为接近实验数据。从而验证了本文提出的数值分析方法的有效性和精确性,为利用ABAQUS软件分析各向异性材料阻尼提供了一条有效途径。     

Data-driven modal surrogate model for frequency response uncertainty propagation

A method is developed for propagation of model parameter uncertainties into frequency response functions based on a modal representation of the equations of motion. Individual local surrogate models of the eigenfrequencies and residue matrix elements for each mode are trained to build a global surrogate model. The computational cost of the global surrogate model is reduced in three steps. First, modes outside the range of interest, necessary to describe the in-band frequency response, are approximated with few residual modes. Secondly, the dimension of the residue matrices for each mode is reduced using principal component analysis. Lastly, multiple surrogate model structures are employed in a mixture. Cheap second-order multivariate polynomial models and more expensive Gaussian process models with different kernels are used to model the modal data. Leave-one-out cross-validation is used for model selection of the local surrogate models. The approximations introduced allow the method to be used for modally dense models at a small computational cost, without sacrificing the global surrogate model’s ability to capture mode veering and crossing phenomena. The method is compared to a Monte Carlo based approach and verified on one industrial-sized component and on one assembly of two car components.     

基于模态综合法和模态叠加法的密集模态结构响应重构

提出一种基于模态综合法和模态叠加法的密集模态结构响应重构方法,通过两次坐标变换将全结构缩聚为自由度更少的超单元模型,将超单元模型的模态分为密集模态和剩余模态。通过经验模态分解法分离出已知响应中单阶的剩余模态响应,进而重构出待测位置的剩余模态响应,待测位置的密集模态响应可由模态振型和剩余模态计算得到,通过模态叠加法实现在密集模态下的时域响应重构。进行了数值模拟研究,将待测位置响应的理论值与重构值进行比较以验证该方法的精度和效率,此外还详细研究了主模态数量、子结构划分方式、测量噪声和阻尼对重构结果的影响。结果表明：该文方法通过模型缩聚大大减少了重构的数据量,并且改善了传统EMD方法不能分离频率间隔较小的模态而无法实现响应重构这一不足,无论密集模态存在与否都可适用于结构的应力、应变、位移、加速度等多种动力响应的重构。     

Highly convergent dynamic models obtained by modal synthesis with application to short wave pulse propagation

A general approach for obtaining the matrices of a substructure ensuring minimum modal frequency errors of the whole structure is presented. The mass and stiffness matrices of a small component domain of selected dimension are obtained by applying the modal synthesis of a limited number of close‐to‐exact modes such that after assembling a larger joined domain model the modal convergence rate of the latter should be as high as possible. The goal is achieved by formulating the minimization problem for the penalty‐type target function representing the cumulative relative modal frequency error of the joined sample domain and by applying the gradient descent minimization method. After the optimum matrices of a component domain are obtained, they can be used in any structure as higher‐order elements or super‐elements. The well‐known generalized mass matrices obtained as a weighted sum of lumped and consistent components can be treated as a special case of the presented approach. The obtained dynamic models are used for modelling short transient waves and wave pulses propagating in elastic or acoustic environments by using a only a few nodal points per pulse length. Copyright © 2004 John Wiley & Sons, Ltd.     

体自由度颤振飞行试验的边界预测方法研究EI北大核心CSCD

体自由度颤振频率低,参与颤振的模态频率在亚临界状态往往已经极为接近,加之基于大气紊流激励的颤振飞行试验数据信噪比通常较低,增加了体自由度颤振飞行试验模态辨识以及颤振预测的难度。对此提出了一种基于Matrix Pencil模态辨识方法的体自由度颤振预测方法。通过随机减量技术对输出响应信号进行系集平均,得到随机衰减标记;运用Matrix Pencil方法拟合随机衰减标记获取模态参数,并通过频率和阻尼稳定判据筛选真实模态,再通过阻尼比与颤振稳定性判据变量外插获取颤振点。通过对仿真数据与试验数据的应用,可得到以下结论:Matrix Pencil模态辨识方法能有效辨识密集的颤振模态,并获得清晰的模态辨识稳态图。基于阻尼比及稳定性判据变量外插获得的颤振预测结果较为合理,其中DTFM(Discrete-Time Flutter Margin)判据变量的下降趋势更明显,外插结果与试验值更接近。该方法适用于体自由度颤振飞行试验的亚临界预测。     

Modal criteria for optimization of structures through active structural acoustic control

This paper deals with modal criteria allowing optimization of structures through active structural acoustic control (ASAC) based on the independent modal strategy control (IMSC). The aim of the paper is to propose efficient criteria allowing to process optimization of structures by determining the most important modes to control considering only the location of the excitation on the structure. A generalized modal synthesis is used to study the coupled fluid–structure system. Modal criteria are proposed in order to determine the best choice for the controlled modes used in IMSC method. The way the ASAC will be applied is not discussed in the paper. Numerical simulations are computed to show the efficiency of the method, considering a simple vibroacoustic structure. Copyright © 2010 John Wiley & Sons, Ltd.     

A simple and effective single‐step time marching technique based on adaptive time integrators

In this work, a novel time marching procedure is presented in which adaptive time integration parameters are locally computed, allowing different spatial and temporal distributions. As a consequence, a more versatile technique arises, enabling an enhanced performance. The main features of the proposed technique are: (1) it is simple; (2) it has guaranteed stability; (3) it is an efficient non‐iterative adaptive single‐step procedure; (4) it provides enhanced accuracy; (5) it enables advanced controllable algorithmic dissipation in the higher modes; (6) it is truly self‐starting; and (7) it is entirely automatic, requiring no input parameter from the user. The proposed technique is very complete, providing the main positive attributes that are requested from an effective time marching procedure. Numerical results are presented along the paper, illustrating the excellent performance of the method. Copyright © 2016 John Wiley & Sons, Ltd.     

Transverse modal analysis of finline with finite metallization thickness

Abstract

The transverse modal method is extended to analyze the dispersion characteristics of dominant and higher order modes in finlines with finite metallization thicknesses. The approach is based on a hybrid mode formulation. Numerical data are presented to show the effect of metallization thickness for unilateral and bilateral finlines. The results are also compared with those from other methods to verify the accuracy.     

非亏损对称系统的子结构灵敏度综合方法

本提出了一种利用子结构灵敏度综合对非亏损对称系统进行特征对灵敏度分析的方法。本利用固定界面模态综合和子结构约束模态以及约束主模态的二阶灵敏度，实现了非亏损对称系统的重特征值灵敏度分析。算例表明了本的方法是行之有效的。