随机参数非线性系统在确定性荷载下的随机响应分析

应用摄动法和随机中心差分法,研究了具有随机参数的非线性系统在确定性荷载下的随机响应,得到了均方响应的一种近似迭代关系.并分析了随机参数反对称层合板的统计特性.     

随机参数非线性系统在确定性荷载下的随机响应分析

应用摄动法和随机中心差分法,研究了具有随机参数的非线性系统在确定性荷载下的随机响应,得到了均方响应的一种近似迭代关系.并分析了随机参数反对称层合板的统计特性.     

黏弹性系统随机响应分析

应用等效非线性化方法分析了高斯白噪声激励作用下强非线性黏弹性系统随机响应。首先,通过广义谐和变换,黏弹性作用力可近似等效为拟线性阻尼和拟线性刚度两部分,进而原系统简化为无黏弹性项的非线性随机系统。其次,选取一类具有待定参数的等效非线性系统类。该等效非线性系统类具有精确稳态解,且和简化后的非线性随机系统具有相同的特性。然后,根据简化系统和等效非线性系统类之差的均方值最小原则,最终确定等效非线性系统类中的待定参数。最后以该系统的精确稳态随机响应近似表示原系统的随机响应。本文所提方法得到的解析结果与蒙特卡洛模拟方法得到的结果符合较好,证实了该方法的正确性。     

具有结构阻尼的复合材料薄壁梁的动力失速非线性颤振特性

研究具有结构阻尼的复合材料薄壁梁动力失速非线性颤振特性。采用受ONERA非线性气动力作用的复合材料薄壁梁的气弹模型分析非线性气弹稳定性;采用复合材料薄壁梁的模态阻尼分析模型进行结构阻尼预测,复合材料结构阻尼对复合材料薄壁梁气弹系统稳定性影响通过引入比例阻尼矩阵的方式予以考虑。采用Galerkin法对具有结构阻尼的气弹方程进行离散化,同时利用片条理论对非线性广义气动力进行计算。借助特征值方法及时域积分法分析复合材料薄壁梁非线性颤振边界及气弹响应的稳定性。通过数值分析,揭示复合材料结构阻尼、纤维铺层角对复合材料薄壁梁非线性颤振边界影响。结果表明,结构阻尼用于抑制复合材料薄壁梁的动力失速非线性颤振,增强气弹稳定性,具有十分明显作用效果。     

基于时域响应灵敏度分析的非线性系统参数识别

基于响应灵敏度分析的有限元模型修正法已广泛应用于线性结构系统的局部损伤和裂纹参数等的识别。尝试将该方法推广应用到非线性系统的参数识别中。从非线性系统运动方程出发,通过数值积分得到系统的强迫振动响应,对系统的物理参数求导得到时域响应对参数的灵敏度,从而构造相应的响应灵敏度矩阵用于参数识别反问题。以Holmes-Duffing非线性系统和物理工程中有着广泛应用的双重sine Gordon非线性系统的参数识别为例,说明方法的应用过程。算例研究了不同的初始参数和测量噪声对识别结果的影响,结果表明响应灵敏度法能准确快速识别非线性系统的参数,并且具有对测量噪声不敏感的优点。     

螺栓法兰结构双连接面耦合振动分析EI北大核心CSCD

螺栓法兰连接结构广泛应用于机械结构和航空航天结构,由其构成多个结构组件(如火箭舱段)之间的连接面,引入的非线性动力学特性会显著影响整体结构动力学响应。不同于以往研究中所聚焦的单个非线性连接面对结构响应影响问题,针对具有两个螺栓法兰连接面的组合结构开展非线性耦合振动分析,研究连接结构动力学参数对结构响应的支配效果,以便获得有效控制结构响应的关键非线性特征。基于螺栓法兰连接结构等效双线性弹簧模型,建立双连接面螺栓法兰结构多自由度耦合振动模型,分别讨论了在不同形式的激励作用下的响应和相空间特性,揭示系统的阻尼敏感性及特定参数条件下的超谐波和亚谐波共振现象,最后分析弹簧刚度比及部段质量比对结构响应的影响。     

一种针对含非线性子结构多点耦合运输包装系统的解耦方法

目的 考虑到运输包装系统耦合形式复杂,包装材料及包装结构具有非线性特性,不容易测量局部物理参数,需要对传统逆向子结构方法进行优化,使之能够求解非线性多点耦合系统中子结构的动态响应特性。方法 使用描述函数法将非线性的运输包装系统线性化,测量其在若干特定振动幅值下的频率响应函数;之后,应用逆向子结构方法和参数识别方法,计算包装件的模态参数;最后,拟合包装件模态参数与振动幅值之间的关系,构建函数来描述包装件的动态响应特性。结果 在集总参数模型中,解耦预测值与实际值吻合;在有限元模型中,对响应峰值的预测误差小于5%,对响应跳跃现象所在频率的预测误差小于3%。结论 该研究将传统逆向子结构方法的应用范围拓展到了非线性多点耦合系统,对复杂运输包装系统动力学模型的构建和防振包装的设计具有指导意义。     

高耸柔性建筑结构非平稳非线性动力方程统计线性化分析的等效参数计算

采用统计线性化分析方法,研究了高耸柔性建筑结构在非平稳地震激励下考虑几何非线性效应时等效参数的计算方法,推导了等效参数阵以等效参数向量的有限单元计算表达式,解决了统计线性化分析方法应用于大型复杂结构非线性随机响应分析的关键问题,并采用迭代的计算方法对洛阳电视塔结构的非零均值非平稳时变系统的响应进行了计算。     

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。     

窄带随机噪声参数激励下非线性碰撞系统的响应

研究了单自由度非线性单边约束碰撞系统在窄带随机噪声参数激励下的响应问题,窄带噪声采用有界随机噪声模型。用Zhurav lev变换将碰撞系统转化为连续的非碰撞系统,然后用随机平均法得到了关于慢变量的随机微分方程。在没有随机扰动情形,给出了系统响应幅值满足的代数方程;在有随机扰动情形,结合线性化方法和矩方法给出了系统响应幅值二阶矩近似解的解析表达式。讨论了系统阻尼项、非线性项、窄带随机噪声的带宽、中心频率和振幅以及碰撞恢复系数等参数对于系统响应的影响。理论计算和数值模拟表明,系统响应将随激励频率和振幅的增大而增大,而随系统阻尼和非线性强度的增大而减少。并发现了随机跳跃现象,即当随机激励的振幅超过某个阈值时,系统的稳态响应将从零解跳跃为一个较大的非零解;而当随机扰动的强度超过某个阈值时,系统的稳态响应将从一个较大的非零解跳跃为零解。     

基于贝叶斯理论的非线性结构模型修正及其动力可靠度分析EI北大核心CSCD

提出一种基于贝叶斯推理的非线性结构模型修正方法,同时考虑激励的随机性,建立了复合随机振动系统的动力可靠度分析方法。利用实测结构动力响应主分量的瞬时特征参数作为非线性指标构建似然函数,结合拒绝延缓自适应(Delayed Rejection and Adaptive Metropolis,DRAM)算法和高斯过程替代模型实现了非线性结构模型修正及其参数的不确定性量化。根据首次超越破坏准则,利用广义概率密度演化方法,分别对仅考虑激励随机性的确定性模型和同时考虑结构参数与激励不确定性的复合随机振动模型进行动力可靠度分析,并利用蒙特卡洛随机抽样方法验证了计算结果的准确性。研究结果表明:基于振动响应瞬时特征参数的贝叶斯推理方法能够快速、准确地实现结构的非线性模型修正及其参数的不确定性量化。与具有初始设计参数名义值的确定性模型相比,考虑参数不确定性的复合随机模型的动力可靠度总体偏低,因此,在结构安全评估中应考虑非线性模型参数不确定性的影响,使评估结果更加安全、可靠。     

Uncertainty analysis based on sensitivity applied to angle-ply composite structures

This article describes a finite element-based formulation for the statistical analysis of the response of stochastic structural composite systems whose material properties are described by random fields. A first-order technique is used to obtain the second-order statistics for the structural response considering means and variances of the displacement and stress fields of plate or shell composite structures. Propagation of uncertainties depends on sensitivities taken as measurement of variation effects. The adjoint variable method is used to obtain the sensitivity matrix. This method is appropriated for composite structures due to the large number of random input parameters. Dominant effects on the stochastic characteristics are studied analyzing the influence of different random parameters. In particular, a study of the anisotropy influence on uncertainties propagation of angle-ply composites is carried out based on the proposed approach.     

Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: prediction and identification procedures

This paper describes firstly, the calculation of the Power Spectral Density Function (PSDF) for the stationary response of SDOF nonlinear second-order dynamical systems excited by a white or a broad-band Gaussian noise, and secondly, the identification of a single-degree-of-freedom (SDOF) nonlinear dynamical second-order dynamical system driven by a broad-band or a colored Gaussian noise. The two aspects are based on the use of a stochastic linearization method with random parameters which is an efficient way of approximating the PSDF. The gain obtained by this method is shown on a SDOF nonlinear dynamical system. In addition, it is shown that the stochastic linearization method with random parameters is an efficient approach for identifying a SDOF nonlinear dynamical system.     

非线性随机振动问题中的一种改进的非高斯矩方法

近年来非线性随机振动问题已越来越受到重视。本文提出非线性随机振动问题中非高斯矩方法的改进形式。其特点是计算简便,能适用于更为普遍的非线性情形,而其精度与现有的非高斯矩方法相接近。     

Time-varying reliability method based on linearized Nataf transform

In actual engineering, material properties, load effects, and other factors of mechanical structures change due to long-term use. In order to understand the operation of a mechanical structure in real time, it is crucial to obtain the dynamic trajectory of its reliability. Considering the time variability of a mechanical structure over time, uncertain random variables are introduced to express the uncertainty of various parameters of structures, and the Wiener process is used to describe the strength degradation process of structures so as to solve the calculation problem of time-varying reliability of mechanical structures. Based on the advanced first-order and second moment method (AFOSM), the proposed linearized Nataf change is used to complete the transformation from related nonnormal variables to independent standard normal variables in order to simplify the calculation process of reliability solution and solve the reliability calculation problem of random parameters subjected to arbitrary distribution. The deduced random variable sensitivity factor indicates the degree of influence of different random variables on the reliability of the mechanical structure, providing a theoretical basis for the optimal design and maintenance of a mechanical structure. The proposed method is analyzed using the cantilever beam and compared with the nonlinear Nataf transform and verified by the Monte Carlo simulation results. The results show that the proposed method can effectively solve the reliability sensitivity problem of structural system strength degradation.     

桥梁地震需求中随机参数的重要性分析方法研究

桥梁结构的地震需求不仅受地震动随机性的影响,而且受结构中随机参数的影响。为了分析各随机参数对结构地震需求的影响水平,提出采用重要性分析方法对各随机参数进行重要性排序。以常见的简支梁桥及连续梁桥为例,基于结构的非线性动力时程分析,分别采用Monte-Carlo数值模拟方法及核密度估计方法计算得到各随机参数基于方差的重要性测度指标及矩独立重要性测度指标。结果表明,对于中小跨径梁桥,针对桥墩、桥台及支座等不同构件的地震需求,随机参数的重要性排序并不完全相同,但是支座剪切模量、上部结构质量及阻尼比等参数对各构件地震需求的影响水平均排在前列;和Tornado图形法等局部敏感性分析方法相比,重要性分析方法在研究某个参数的重要性时能够考虑其他随机参数的影响,其应用更加合理。     

模糊随机桁架结构在模糊随机激励下的动力响应

研究了模糊随机参数桁架结构在模糊随机荷载激励下的复合模糊随机振动动力响应的问题。同时考虑结构的物理参数、几何尺寸和外载荷幅值的模糊随机性,从Duham e l积分式出发,利用振型迭加法求出了结构动力响应模糊随机变量的表达式;再由随机函数的矩法推导出结构模糊随机动力响应的模糊数字特征。最后,通过算例考察了结构参数和作用荷载的模糊随机性对结构动力响应的影响,并用M on te C arlo数值法对算例进行模拟,验证了文中模型和分析方法是可行有效的。     

A solution method for linear and geometrically nonlinear MDOF systems with random properties subject to random excitation

A method for computing the lower-order moments of response of randomly excited multi-degree-of-freedom (MDOF) systems with random structural properties is proposed. The method is grounded in the techniques of stochastic calculus, utilizing a Markov diffusion process to model the structural system with random structural properties. The resulting state-space formulation is a system of ordinary stochastic differential equations with random coefficients and deterministic initial conditions which are subsequently transformed into ordinary stochastic differential equations with deterministic coefficients and random initial conditions. This transformation facilitates the derivation of differential equations which govern the evolution of the unconditional statistical moments of response. Primary consideration is given to linear systems and systems with odd polynomial nonlinearities, for in these cases there is a significant reduction in the number of equations to be solved. The method is illustrated for a five-story shear-frame structure with nonlinear interstory restoring forces and random damping and stiffness properties. The results of the proposed method are compared to those estimated by extensive Monte-Carlo simulation.     

A Rate Dependent Constitutive Model for Glass-Fibre / Epoxy-Matrix Woven Fabrics

This paper deals with the modelling until rupture of composite structures made of glass-fibre / epoxy-resin woven fabrics submitted to dynamic loadings. The model is built at the mesoscale of the elementary ply. It takes into account the slightly nonlinear brittle behaviour of the fibres under tensile sollicitations, their nonlinear behaviour in compression as well as the strongly non linear and irreversible behaviour of the ply in shear. Strain rate effects are also introduced and special attention is paid to the objectivity of the model in the context of finite element calculation. Therefore the choice of a delayed damage mesomodel coupled with viscoplasticity is made. In order to identify the values of the parameters of the model, an optimization procedure based on a gradient-free direct search method has been developed. As a logical proceeding to this study, the model ability to avoid strain localization and mesh dependence is then checked on simple uniaxial examples. The last part of this paper is devoted to structural calculation. The results of the simulations of both the impact on composite plate and the crushing of thin-walled tube demonstrate the capability of the model to reproduce observed physical phenomena.     

钢筋砼结构非线性随机地震响应分析

考虑地震作用和结构参数的随机性,建立了钢筋砼结构药非线性随机动力学模型。文中导出了随机结构动力分析的非线性随机有限元法的增量列式,并据此对多层钢筋砼结构进行了弹塑性随机地震响应分析。计算结果与该建筑物的实际震害作了对比,效果良好。还讨论了动力模型中随机变量对响应量的影响。