Accurate and efficient a posteriori account of geometrical imperfections in Koiter finite element analysis

The Koiter method recovers the equilibrium path of an elastic structure using a reduced model, obtained by means of a quadratic asymptotic expansion of the finite element model. Its main feature is the possibility of efficiently performing sensitivity analysis by including a posteriori the effects of the imperfections in the reduced nonlinear equations. The state‐of‐art treatment of geometrical imperfections is accurate only for small imperfection amplitudes and linear pre‐critical behaviour. This work enlarges the validity of the method to a wider range of practical problems through a new approach, which accurately takes into account the imperfection without losing the benefits of the a posteriori treatment. A mixed solid‐shell finite element is used to build the discrete model. A large number of numerical tests, regarding nonlinear buckling problems, modal interaction, unstable post‐critical and imperfection sensitive structures, validates the proposal. Copyright © 2017 John Wiley & Sons, Ltd.     

Suppression of Motion-induced Residual Vibration of a Cantilever Beam by Input Shaping

Input shaping is an effective means for suppressing motion-induced residual vibration of lightly damped structures. Here, to demonstrate the ideas of various input shaping schemes for continuous structures, the model system of a cantilever beam, whose base is to be displaced by a prescribed distance, is considered. The cantilever-beam motion is modeled by the damped Bernoulli-Euler beam equation, and is then decomposed into normal vibration modes. For the particular system set up here, the modal equations of motion are linear and uncoupled, and consequently are integrated analytically. It is then shown that, by completing the cantilever base movement in a series of properly calculated steps (i.e., by shaping the input command of the dynamical system), so as to annihilate the dominant vibration modes through destructive interference, the overall induced vibration of the cantilever can be significantly suppressed. In particular, the “zero-vibration” (ZV) and “zero-vibration-and-derivative” (ZVD) input shaping schemes previously proposed for discrete systems are adapted and applied to the continuous beam here. The theoretical results are also supported by experiments.     

Estimation of the Dynamic Properties of Non‐linear Packaging Materials Using a Reverse Multiple Input/Single Output Based Approach

During the distribution phase, packaged consignments are exposed to a variety of environmental hazards (such as vibrations) that, if excessively severe, may cause damage to or even destroy the product. Structural deterioration can be tracked by monitoring variations in the packaging system's modal parameters, particularly its natural frequency (stiffness). Natural frequency estimates are often extracted using a least‐squares regression curve fit, applied to an estimate of the system's frequency response function (FRF). FRF estimates are generally obtained using the Fourier transform with a single input and single output (SISO). This approach is suitable for many applications; however, as the non‐linearity of the system under analysis increases, the ability of this technique to accurately monitor changes in the system will decrease. In addition, when the excitation to the non‐linear system is varied (increased or decreased amplitude), a SISO‐based approach may indicate a shift in natural frequency (as a result of the varied input) even though no change in the condition of the system has occurred. This paper discusses an approach that is designed to separate the linear component of the system's FRF using a reverse multiple input/single output (RMISO) algorithm. Such separation will allow traditional modal parameter extraction (curve fitting) techniques to be used to monitor the condition of non‐linear systems. The paper presents the results of experiments in which expanded polystyrene samples were subjected to broad‐band random base excitation with a free‐moving load placed atop the cushion sample. Continuous acceleration measurements of the vibration table and the free‐moving load were used to compute the FRFs of the cushions, and the differences between a conventional (SISO) approach and the proposed RMISO‐based parameter extraction technique were evaluated. Copyright © 2014 John Wiley & Sons, Ltd.     

基于动态递归神经网络的半主动控制结构响应预测

提出了一种多输入多输出分支动态递归神经网络模型,利用梯度下降法推导了网络权值调整公式。该模型针对结构控制中结构状态变量、控制变量和外激励荷载对结构的响应有不同的影响,采用分支输入递归处理,不但结构响应预测精度好,而且大大提高了动态网络的学习和训练效率。应用该模型对线性结构和非线性结构在变阻尼控制和外荷载激励下结构的响应进行了数值仿真,表明所提的动态递归神经网络可以达到较高的预测精度。该模型为利用神     

Data based model free hysteresis identification for a nonlinear structure

In the last two decades, the damage detection for civil engineering structures has been widely treated as a modal analysis problem and most of the currently available vibration-based system identification approaches are based on modal parameters, namely the natural frequencies, mode shapes and damping ratios, and/or their derivations, which are suitable for linear systems. Nonlinearity is generic in engineering structures. For example, the initiation and development of cracks in civil engineering structures as typical structural damages are nonlinear process. One of the major challenges in damage detection, early warning and damage prognosis is to obtain reasonably accurate identification of nonlinear performance such as hysteresis which is the direct indicator of damage initiation and development under dynamic excitations. In this study, a general data-based identification approach for hysteretic performance in form of nonlinear restoring force using structural dynamic responses and complete and incomplete excitation measurement time series was proposed and validated with a 4-story frame structure equipped with smart devices of magneto-rheological (MR) damper to simulate nonlinear performance. Firstly, as an optimization method, the least-squares technique was employed to identify the system matrices of an equivalent linear system of the nonlinear structure model basing on the excitation force and the corresponding vibration measurements with impact test when complete and incomplete excitations; and secondly, the nonlinear restoring force of the structure was identified and compared with the test measurements finally. Results show that the proposed data-based approach is capable of identifying the nonlinear behavior of engineering structures and can be employed to evaluate the damage initiation and development of different structure under dynamic loads.     

A model updating strategy of non‐linear vibrating structures

The objective of this paper is to present a model updating strategy of non‐linear vibrating structures. Because modal analysis is no longer helpful in non‐linear structural dynamics, a special attention is devoted to the features extracted from the proper orthogonal decomposition and one of its non‐linear generalizations based on auto‐associative neural networks. The efficiency of the proposed procedure is illustrated using simulated data from a three‐dimensional portal frame. Copyright © 2004 John Wiley & Sons, Ltd.     

Model reduction for dynamical systems with quadratic output

Finite element models for structures and vibrations often lead to second order dynamical systems with large sparse matrices. For large‐scale finite element models, the computation of the frequency response function and the structural response to dynamic loads may present a considerable computational cost. Padé via Krylov methods are widely used and are appreciated projection‐based model reduction techniques for linear dynamical systems with linear output. This paper extends the framework of the Krylov methods to systems with a quadratic output arising in linear quadratic optimal control or random vibration problems. Three different two‐sided model reduction approaches are formulated based on the Krylov methods. For all methods, the control (or right) Krylov space is the same. The difference between the approaches lies, thus, in the choice of the observation (or left) Krylov space. The algorithms and theory are developed for the particularly important case of structural damping. We also give numerical examples for large‐scale systems corresponding to the forced vibration of a simply supported plate and of an existing footbridge. In this case, a block form of the Padé via Krylov method is used. Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient uncertainty quantification of dynamical systems with local nonlinearities and uncertainties

Idealized modeling of most engineering structures yields linear mathematical models, i.e., linear ordinary or partial differential equations. However, features like nonlinear dampers and/or springs can render nonlinear an otherwise linear model. Often, the connectivity of these nonlinear elements is confined to only a few degrees-of-freedom (DOFs) of the structure. In such cases, treating the entire structure as nonlinear results in very computationally expensive solutions. Moreover, if system parameters are uncertain, their stochastic nature can render the analysis even more computationally costly. This paper presents an approach for computing the response of such systems in a very efficient manner. The proposed solution procedure first segregates the DOFs appearing in the nonlinear and/or stochastic terms from those DOFs that involve only linear deterministic operations. Second, the responses of nonlinear/stochastic terms are determined using a non-standard form of a nonlinear Volterra integral equation (NVIE). Finally, the responses of the remaining DOFs are computed through a convolution approach using the fast Fourier transform to further increase the computational efficiency. Three examples are presented to demonstrate the efficacy and accuracy of the proposed method. It is shown that, even for moderately sized systems (∼1000 DOFs), the proposed method is about three orders of magnitude faster than a conventional Monte Carlo sampling method (i.e., solving the system of ODEs repeatedly).     

σ‐Stability and characterization of all σ‐stabilizing compensators

Abstract

In feedback stabilizing compensator design for linear systems, mere BIBO (bounded‐input‐bounded‐output) stability is not sufficient since it does not provide a margin of decay rate, e. g., the compensated feedback system may still become insufficiently stable. In this paper, we will define the notion of σ‐stability and will give a complete parametrization of all σ‐stabilizing compensators in terms of a free design parameter via the fractional representation approach. Any σ‐stabilizing compensator will guarantee a decay rate margin σ of the compensated system. Also we will use the state space techniques to obtain the required factors in that parametrization of all σ‐stabilizing compensators.     

膜结构极小曲面找形的一种自适应有限元分析

找形分析是膜结构设计中的关键环节,但在数学上,膜结构的极小曲面找形分析是一个高度非线性问题,一般无法求得其解析解,因此数值方法成为重要工具。近年来,基于单元能量投影法（EEP法）的一维非线性有限元的自适应分析已经取得成功,基于EEP法的二维线性有限元自适应分析也被证实是有效、可靠的。在此基础上,该文提出一种基于EEP法的二维非线性有限元自适应方法,并成功将之应用于膜结构的找形分析。其主要思想是,通过将非线性问题用Newton法线性化,引入现有的二维线性问题的自适应求解技术,进而实现二维有限元自适应分析技术从线性到非线性的跨越,将非线性有限元的自适应分析求解从一维问题拓展到二维问题。该方法兼顾求解的精度和效率,对网格自适应地进行调整,最终得到优化的网格,其解答可按最大模度量逐点满足用户设定的误差限。该文综述介绍了这一进展,并给出数值算例用以表明该方法的可行性和可靠性。     

Fields of nonlinear cladding optical waveguides excited by butt-coupled linear waveguides at medium power levels

The evolution of medium power fields of nonlinear optical waveguides is investigated numerically. The analysis method is based on mode matching of local normal modes of bounded waveguides. Nonlinear cladding waveguides are butt-coupled to linear waveguides. The path of a medium power level beam winds between the film and the nonlinear cladding. The input beam travels toward the nonlinear modal field, at which point the beam is not stationary. After the beam passes the location, it is forced to turn back. The lateral shift of an incident waveguide affects the path of a beam. Saturation and linear absorption lessens the oscillation of a winding path.     

A modal correction method for non-stationary random vibrations of linear systems

The computational effort in determining the dynamic response of linear systems is usually reduced by adopting the well-known modal analysis along with modal truncation of higher modes. However, in the case in which the contribution of higher modes is not negligible, modal correction methods have been introduced to improve the accuracy of the dynamic response, for both deterministic and stochastic input. In the latter case the random response is usually corrected via various methods determined as rough extensions of methods originally proposed for deterministic input. Consequently the efficiency of the correction methods is not suitable, from both theoretical and computational points of view. In this paper, a new approach to cope with the non-stationary response of linear systems is presented. The proposed modal correction method provides a correction term determined as a pseudo-stationary contribution of the equation governing either first-order or second-order statistics. Owing to the fact that no truncation criteria are well established for random vibration study, the proposed modal correction method offers a suitable vehicle for determining very accurately the stochastic response of MDOF linear systems under Gaussian stationary and non stationary excitation as evidenced in the numerical applications.     

Optimization method for the determination of the most unfavorable imperfection of structures

The paper presents an optimization method for direct determination of the most unfavorable imperfection of structures by means of ultimate limit states. When analyzing imperfection sensitive structures it turns out that the choice of the shape and size of initial imperfections has a major influence on the response of the structure and its ultimate state. Within the optimization algorithm the objective function is constructed by means of a fully nonlinear direct and first order sensitivity analysis. The method is not limited to small imperfections and also allows the imposition of “technological” constraints on the shape of the imperfection, thus making it possible to avoid unrealistically low ultimate loads. When carefully constructed, the objective function and constraints remain linear enabling the use of numerically efficient and readily available linear programming algorithms. Imperfection analyses are shown for thin-walled girders and a cylinder to demonstrate the applicability and efficiency of the proposed method.     

自适应桁架结构局部力反馈振动控制及其主动构件的配置研究

本文主要研究利用自适应桁架结构自身的主动构件实现控制结构动态特性的理论和有效性以及主动构件的最优配置问题。首先，基于自适应桁架结构的有限元模型，将主动构件的弹性内力直接用于实现反馈控制桁架结构的振动特性；然后，引用模态耗散能因子和模态应变能因子的概念，研究了主动构件的优化配置问题。通过一平面自适应桁架结构的优化配置计算和数值仿真，说明了文中提出的控制方法和主动构件优化配置的有效性。     

Bifurcation analysis of nonlinear time‐periodic time‐delay systems via semidiscretization

Bifurcations of the periodic stationary solutions of nonlinear time‐periodic time‐delay dynamical systems are analyzed. The solution operator of the governing nonlinear delay‐differential equation is approximated by a sequence of nonlinear maps via semidiscretization. The subsequent nonlinear maps are combined to a single resultant nonlinear map that describes the evolution over the time period. Fold, flip, and Neimark‐Sacker bifurcations related to the fixed point of this map are analyzed via center manifold reduction and normal form theorems. The analysis unfolds the approximate stability properties and bifurcations of the stationary solution of the delay‐differential equation and, at the same time, allows the approximate computation of the arising period‐1, period‐2, and quasi‐periodic solution branches. The method is demonstrated for the delayed Mathieu‐Duffing equation, and the results are verified by numerical continuation.     

水下工程结构的损伤诊断分析

主要通过动力有限元对结构损伤前后的动力特性进行分析，从而实现对水下结构的损伤进行诊断。采用结构损伤前后的固有频率的变化对结构是否损伤进行判定，采用结构的动力响应对结构的损伤程度进行判定，采用结构的单元模态应变能对结构的损伤位置进行判定。并以某一水下作业结构为研究对象，用ANSYS软件对其损伤进行模拟诊断分析。     

基于模态价值分析的结构动力学模型降阶

针对小阻尼和无阻尼结构，提出了一种模态价值分析方法，用于在模态坐标下的动力学模型降阶问题。在得到系统动力学方程的基础上，首先进行模态分析，然后由模态参数和系统的输入输出矩阵计算各模态的价值，最后选择若干价值最大的模态向量形成变换矩阵对系统进行降阶。通过两个算例说明本文方法是对通常选择低频模态的降阶方法的改进，提高了低阶模型的精度。     

Rheological-dynamical analogy: design of viscoelastic and viscoplastic bar dampers

An analytical procedure is developed for computing the dynamic response of bar dampers using the rheological-dynamical analogy. This method is very efficient when applied to inelastic deformations, because it reduces a material nonlinear problem to a linear dynamical problem, which allows the use of modal analysis. Two types of damping are considered: viscous damping in the case of linear analysis; and hysteretic damping caused by inelastic deformations of the damper. Based on the formulas of the two types of damping, an iterative procedure for the design of viscoelastic and viscoplastic bar dampers is derived.     

基于变分模态分解的模态参数识别研究

基于变分模态分解(VMD),提出一种新的结构模态参数识别方法:①通过自由振动试验或通过随机减量法从结构随机振动响应中获取结构自由衰减振动响应(FDR),并采用VMD方法从FDR中分解出结构模态响应;②通过经验包络法(EE)计算模态响应瞬时频率,并通过一种该研究新提出的方法计算模态响应瞬时阻尼比;③结构的模态振型向量可通过处理所有可用传感器得到的模态响应得到。瞬时模态频率和模态阻尼比可以捕获模态参数的任何瞬态变化。通过一系列数值和试验算例验证了该方法的有效性,突出了该方法的优势,并对该方法抗噪声性能进行了研究。研究表明,该方法适用于线性和非线性系统,且可用于识别具有密集模态和瞬态特性的系统。