An inverse procedure for identification of loads on composite laminates

An inverse procedure is presented to determine the transient line loads on a surface of composite laminate. The procedure recovers the time history as well as the distribution functions of the line loads based on the displacement responses at one receiving point. It is assumed that the time and spatial dependencies of the loading function are separable. The hybrid numerical method is used to obtain two kernel functions, dynamic Green's function as well as the response function of Heaviside step excitation of the composite laminates. The displacement response to a load with an arbitrary force function is expressed in a form of convolution, where the continuous convolution functions are spatially and temporally discretized. The loading functions are recovered by optimizing a set of proposed error (objective) functions. Numerical verifications were performed to identify loads on composite laminate for both concentrated and extended cases. Very good agreements have been obtained in terms of both load distribution and its magnitude, where calculation converged within a small number of iterations.     

Inversion of loading time history using displacement response of composite laminates: Three-dimensional cases

Summary An inverse procedure is proposed to reconstruct the time history of transient loads on the surface of composite laminates from the knowledge of dynamic displacement response at only one receiving point. A hybrid numerical method (HNM) is adopted as the forward solver to compute the dynamic displacement response of composite laminates subjected to arbitrary loads. By introducing a kernel displacement function — the dynamic displacement response of composite laminates excited by a point stepimpact load and the displacement response subjected to a load with an arbitrary force function are expressed in a form of convolution integral. The force history is reconstructed by employing an inversion algorithm, in which the least-squares optimization method being adopted to deconvolute the integral. Both point loads and loads with small spatial distribution are investigated and numerical verifications are given. The robustness of the procedure in the presence of noise is also investigated. Good agreements between the identified and true functions for all cases demonstrate the effectiveness of the present inverse procedure. The present inverse procedure is useful for determining impact loads on material surface using response on a point remote to the impact point.     

Inverse identification of time-harmonic loads acting on thin plates using approximated Green’s functions

In this paper, a non-iterative technique is proposed for the transverse load identification on Kirchhoff plates using approximate Green’s functions (AGFs). In this way, we firstly employ the recently introduced meshless method to construct the AGFs, as the combination of a series of Trefftz basis, i.e. Exponential basis functions (EBFs), and the fundamental solutions of the governing equation. As will be explained, using a proper set of EBFs, as well as a collocation technique, enables us to construct the AGFs for different types of domain shape and boundary conditions. In the second step, a set of artificially generated results, in the absence of realistic experimental results, are used to express the plate’s response field, i.e. deflection or velocity fields, as a series of AGFs through a collocation technique. It will be shown how the constant coefficients of the response series are related to the intensity of the reconstructed force at a set of selected points. The proposed method is capable of constructing both distributed and concentrated loads with desirable accuracy. This ability is shown in the solution of three sample problems of the static and time-harmonic force recovery.     

A New Iterative Regularization Method for Solving the Dynamic Load Identification Problem

In this paper, a new iterative regularization method (ITR) is presented to solve the reconstruction of multi-source dynamic loads acting on the structure of simple supported plate. Based on a quadratical convergence method, this method is used to compute the the approximate inverse of square matrix. The theoretical proofs and numerical test show that the proposed method is very effective. Finally, the present method is applied to the identification of the multi-source dynamic loads on a surface of simply supported plate. Numerical simulations of two examples demonstrate the effectiveness and robustness of the present method.     

波纹膜片的非线性稳定

应用轴对称旋转扁壳的基本方程,研究了在任意载荷作用下各种边界条件的波纹膜片的非线性稳定问题。采用格林函数方法,将扁壳的非线性微分方程组化为非线性积分方程组。再使用展开法求出格林函数,即将格林函数展开成特征函数的级数形式,积分方程就成为具有退化核的形式,从而容易得到非线性代数方程组。应用牛顿法求解非线性代数方程组时,为了保证迭代的收敛性,选取位移作为控制参数,逐步增加位移,求得相应的载荷。作为算例,首先研究了带中心平台三波纹膜片的局部失稳现象,然后讨论了由于缺陷的存在,波纹膜片有可能出现的极值点失稳,这是一种类似扁球壳的总体失稳现象。解答可供波纹膜片的设计参考。     

Dynamics response of complex defects near bimaterials interface by incident out-plane waves

Dynamics response of an elliptical cavity and a crack (on different sides) near bimaterials interface under incident out-plane waves is studied by applying the methods of complex variables and Green’s function. Firstly, based on “conjunction,” the analytical model is divided along the horizontal interface into an elastic half-plane possessing an elliptical cavity and a full elastic half-plane containing a crack. Using complex variables, the scattering displacement field of the half-plane containing an elliptical cavity under incident out-plane waves is then derived. According to the method of Green’s function, the corresponding Green’s functions of two half-planes impacted by an out-plane source load are further deduced. Combined with “crack division,” a crack at the full elastic the half-plane is created, and thus, expressions of displacement and stress are derived while the cavity coexists with the crack. Undetermined antiplane forces are loaded on the horizontal surfaces for conjunction of two sections and then solved by a series of Fredholm integral equations on account of continuity conditions of the interface. Finally, this paper focuses on the discussion of the influence law of different parameters on the dynamics response of complex defects near bimaterials interface by comprehensive numerical results.     

一种基于最优输出跟踪的多源动态载荷识别方法

基于最优输出跟踪的基本思想,提出了一种时域内多源动态载荷识别的方法。该方法从结构动力响应出发,设计一个最优输出跟踪器并构造性能指标,将载荷识别问题转变为最优输出跟踪问题。通过Adams法求解微分方程,实现了多源动态载荷的识别,并采用L曲线法确定了性能指标中的关键参数。数值算例表明,所述的载荷识别方法能够在响应数据含有噪声的情况下,有效稳定地实现多源动态载荷的重构,具有较强的抗噪能力。     

高速移动列车荷载作用下层状饱和地基-轨道耦合系统的动力响应

基于Biot流体饱和多孔介质理论,求得层状饱和地基表面移动荷载的动力格林函数,进而建立2.5维间接边界元方法,研究了高速移动列车荷载作用下层状饱和地基-轨道耦合系统的动力响应。该文通过与已有结果的比较验证了方法的正确性,并以均匀饱和半空间地基和饱和基岩上单一饱和土层地基为模型进行了数值计算,分析了列车移动速度和饱和土层等对动力响应的影响。研究表明,层状饱和地基和均匀饱和地基对应的动力响应有着显著的差别;列车移动速度接近饱和地基的Rayleigh波速时,会引起饱和地基-轨道耦合系统的共振,产生较大的动力响应;饱和地基不透水情况下动力响应最大,饱和地基透水情况下动力响应次之,干土情况下动力响应最小。另外,饱和土孔隙率、饱和基岩与饱和土层刚度比、饱和土层厚度等也对动力响应具有重要影响。     

整体平动自由结构载荷时域识别技术研究

研究整体平动自由结构载荷识别的Green函数法及应用途径。建立测点绝对运动加速度与动态激励力卷积关系,采用截断奇异值分解的正则化方法求解反卷积问题。以受轴向激励自由梁为对象,考虑不变及变截面模量两种情形,讨论整体平动及变形运动在核函数中的构成比例与核函数矩阵病态特性关系,分析结构整体刚度及测点部位局部刚度对载荷反演精度影响机制及测点布置需考虑的刚度因素,提高正则化方法计算稳健性;分析复杂的组合薄壁结构,以一点响应反求其在牵制释放实验中所受冲击载荷进行结构瞬态响应有限元仿真,比较多点仿真与实测结果,验证反求方法的有效性。     

基于格林函数的多跨钻柱系统的振动特性分析

随着油气勘探开发向着深层、深水及非常规等复杂领域的不断扩展,钻井面临的井况与约束条件更加苛刻,钻柱的动力学特性更加复杂,失效问题频发。该文应用格林函数理论对多跨旋转钻柱双向耦合动力学特性进行了定量分析和研究。考虑多稳定器及不同约束条件,以钻柱整体为研究对象,基于Euler-Bernoulli梁模型和Hamilton原理建立了具有广义边界约束条件及多稳定器的旋转钻柱双向耦合动力学方程。采用分离变量法、Laplace变换及Laplace逆变换求解所获得的振动微分方程,得到了旋转钻柱系统横向振动的格林函数解以及以格林函数为基础的多跨旋转钻柱系统的闭合形式的模态函数及隐式的频率方程。定量地分析了稳定器位置、弹簧刚度系数与稳定器个数对钻柱系统振动特性的影响。数值结果表明:稳定器位置与固有频率的关系曲线中有相应阶次数目的峰值;随着等效弹簧的刚度系数的增大,系统的固有频率随之增大,但当刚度增加到一定值时,系统的一阶和二阶频率将趋于稳定。研究结果有助于深化对多跨旋转钻柱的动力学特性规律的认识,为提高钻速、减少钻柱失效及钻柱钻井技术的应用提供了新的研究方法和理论依据。     

Distributed dynamic load identification based on shape function method and polynomial selection technique

A new approach based on shape function method of moving least square fitting (SFM_MLSF) and polynomial selection technique is proposed in this paper for distributed dynamic load identification. The distributed dynamic load is represented as a product of spatial distribution function and time history, and the two parts are assumed to be independent. The modal transformation of structural dynamic equation throws light on the fact that all modal loads share the same form with the distributed dynamic load in time domain. As the structural modal parameters are known, the time history of dynamic load can be precisely identified through SFM_MLSF method which approximates the local dynamic load with shape functions in the moving supporting time domain. Then, the spatial distribution function of the load is substituted as a series of basic functions, and the identification of distribution function is transformed into a linear fitting problem. Through polynomial selection technique based on error reduction ratio, the significant components are picked out from the basis function responses, which greatly improves stability and precision of the load distribution function. During the inverse analyses of both the time history and distribution function, appropriate regularization methods are still applied to overcome the unavoidable ill-conditioned problem. Numerical examples demonstrate the validity and accuracy of the proposed method.     

Green’s function for torsional waves in a cylindrically monoclinic material

Two exact Green’s functions for impulsive and time-harmonic torsional waves in a monoclinic material are presented. The impulsive Green’s function is expressed in the closed form of simple algebraic functions and its wave front shape is a torus with inclined elliptic cross section. The time-harmonic Green’s function is also obtained exactly, but in the form of definite integral. Time development of the wave front for the impulsive wave and amplitude contours for the time-harmonic wave are illustrated.     

双相压电介质中界面附近圆孔的动态性能分析

采用Green函数法研究界面附近含圆形孔洞的双相压电介质对时间谐和SH波的散射问题。首先利用复变函数的方法构造出适合于本文问题的位移Green函数和电场Green函数。然后利用契合思想，根据界面上的连续性条件建立起求解问题的第一类Fredholm型积分方程，得到了圆孔孔边周向剪应力的动应力集中系数和周向电场强度集中系数的解析表达式。最后作为算例，给出了界面附近圆孔边界的两组集中系数随入射波频率、材料的几何参数和物理参数变化的计算结果图，部分计算结果与已有文献进行了比较。     

Green函数对饱和土隧道内集中荷载作用振动位移反应的计算

由于快速列车与城市地铁的发展,饱和土隧道内集中荷载作用的反应问题日显重要。Green函数对辐射条件的满足,积分方程的精确解答,Dirichlet条件下的通用性,使它对隧道内动荷载作用的土动力反应问题计算有着特有的优越性,作者根据已求得两相饱和介质Green函数,利用Lamb积分公式,结合隧道断面特征,以解析积分法推导了集中冲击荷载与简谐荷载圆形断面隧道内振动位移反应表达式闭合解、反应时程曲线、瞬态和稳态的振动形态;并根据它们的单位脉冲响应函数结合Duhamel积分求得隧道在地震荷载作用下的动力反应。另外窗形隧道受集中冲击荷载作用相关弹性波时程曲线也在文中给出。     

STRIP DISTRIBUTED TRANSFER FUNCTION METHOD FOR ANALYSIS OF PLATES

A semi-analytical method, called the strip distributed transfer function method, is developed for analysis of plate structures that are composed of rectangular plates. In the method, a rectangular plate (substructure) is divided into a number of strips; the response of each strip is interpolated in the unknown nodal line displacements, which are functions of the strip longitudinal co-ordinate and time. The nodal line displacements are determined in an exact and closed form by the distributed transfer functions that are defined along the strips. Synthesis of the substructures using the strip distributed transfer functions yields accurate prediction of the static and dynamic response, natural frequencies and buckling loads of the structure. The proposed method is compared with some existing techniques in numerical examples.     

Computation of the Green’s function for the transverse vibration of a composite circular membrane

A new analytical method is suggested for the approximate computation of the time-dependent Green’s function for the equations of the transverse vibration of a composite circular membrane with piecewise constant varying density and tension. The method is based on the derivation of eigenvalues and eigenfunctions for an ordinary differential equation with piecewise constant coefficients and an approximate computation of the Green’s function in the form of the Fourier series with a finite number of terms relative to the orthogonal set of the derived eigenfunctions. A computational experiment confirms the robustness of the method.     

人行桥的减振优化设计研究

振动舒适度是设计大跨轻质人行桥时需要解决的关键问题之一.采用调谐质量阻尼器(TMD),可以有效降低桥梁在行人激励下的振动反应.该文基于分布参数法,提出了单跨和多跨人行桥采用STMD 及MTMD 减振系统的动力反应通用时程计算方法.在此基础上,以均方根加速度作为衡量标准,研究了单跨和多跨梁式人行桥-TMD 系统中TMD 布置位置、系统最优频率比与最优阻尼比的优化取值和减振效果等问题,提出了相应的设计建议,并通过数值算例进行了验证.     

横向有限应变对部分浸入水中平面运动柔性梁的非线性振动响应的影响

基于Hamilton原理,根据克希霍夫假设以及拉格朗日函数,得到部分浸入水中柔性梁的大挠度条件下的运动方程和边界条件。在运动方程和边界条件的推导过程中,考虑了横向有限变形,并运用格林应变张量表示非零的应变张量分量。然后,应用中心差分法对方程进行数值处理,研究不同涡旋脱落荷载作用下,横向有限应变对结构振动响应的影响。结果表明,涡旋脱落荷载超过一定幅值后,横向有限应变的影响比较明显,不应忽略。     

动态载荷时域识别的联合去噪修正和正则化预优迭代方法

系统响应可表示为单位脉冲响应函数与激励载荷的卷积,将其离散化一组线性方程组,则载荷识别问题即转化为求解线性方程组的反问题。针对响应中带有噪音时载荷识别的困难,提出了联合奇异熵去噪修正和正则化预优的共轭梯度迭代识别方法。一方面对含噪信号进行基于奇异熵的去噪处理,提高反问题求解中输入数据的精度。另一方面利用正则化方法对共轭梯度迭代算法进行预优,改善反问题的非适定性。由于从输入的响应数据去噪和正则化算法两方面同时改善动态载荷识别反问题的求解,因此可以有效地抑制噪声,提高识别精度。通过数值算例分析,表明在不同的噪声水平干扰下,其识别精度均优于常规的正则化方法,能够实现有效稳定地识别动态载荷。最后通过实验研究进一步验证了该方法的正确性和有效性。     

PENALTY FUNCTION METHOD FOR OPTIMAL DESIGN OF MULTIPURPOSE VIBRATING BEAMS

A computational design algorithm is formulated to determine the optimal area distribution of a beam which undegoes free and forced harmonic vibrations during its service life. The structural element has to serve more than one function, and this necessitates a design which meets various requirements. Hence, the constraints on the multipurpose beam involve simultaneously its dynamic response under single or multiple loads and its fundamental frequency. These problems are formulated in a mathematical programming format by expressing the area function in terms of linear splines. The resulting optimization problems are solved using suitable penalty functions. The proposed design method is illustrated by several numerical examples which show the complex tradeoffs involved in the design of multipurpose structures.