参强联合作用非线性结构动力学实验建模

搭建以L 型梁为实验研究对象的参强联合作用多自由度非线性振动实验系统, 将增量谐波平衡非线性识别理论运用到实验建模方法中, 建立了L 型梁的动力学控制方程. 通过对不同激励频率和不同响应情况下的数值模拟与实验数据的比较, 验证了基于增量谐波平衡识别的实验建模方法对多自由度参强联合作用非线性动力学结构的有效性, 以及动力学控制方程的普适性.     

基于渐近均匀化方法的准周期梁结构等效刚度数值实现方法研究

相比周期梁结构,准周期梁结构沿轴向梯度变化,具有更大的设计自由度,能够获得更好的结构性能。由于其非均质性,一般将其均匀化为具有等效性质的均质梁结构,但现有工作很少涉及准周期梁结构等效性质的计算。本文针对由周期梁结构映射而成的准周期梁结构,通过引入雅可比矩阵,基于渐近均匀化方法推导的单胞方程及其等效性质计算列式,并建立了其单胞方程及等效刚度的有限元求解列式。该方法可以处理沿轴向变形的任意微单胞构型,数值算例验证了其正确性和有效性。     

人行荷载下梁式结构振动分析的DQ-IQ混合法

为了评估人行荷载作用下梁式结构的振动舒适度,利用微分求积-积分求积,即DQ-IQ混合法求解移动荷载作用下梁的振动响应。人行荷载作用下梁式结构的振动控制方程是含Dirac函数的偏微分方程,首先利用IQ法离散与时间相关的Dirac函数,再利用DQ法把控制方程转化为二阶常系数微分方程,最后利用Newmark算法求解微分方程。以某钢结构连廊为例,利用DQ法计算结构自振频率并与解析解进行对比,结果验证了节点选取和边界条件施加的合理性,再利用DQ-IQ混合法和振型叠加法分别计算了不同行走步频下连廊的响应,计算结果表明,DQ-IQ混合法具有较高的可靠性和精确性。DQ-IQ混合法也可以推广到诸如车辆荷载作用下路面或桥梁的动力响应等其他移动荷载下结构的振动分析。     

梁式结构受移动荷载作用非平稳随机振动的DQ-PEM方法

针对梁式结构受移动荷载作用的非平稳随机振动问题,提出了一种综合利用微分求积法和虚拟激励法DQ-PEM的新方法。梁式结构受移动荷载作用的振动控制方程为含Dirac函数的偏微分方程,利用微分求积(DQ)-积分求积法(IQ)法将其振动控制方程转化为不含Dirac函数的常微分方程。同时,将表示荷载位置变化的Dirac函数视为移动荷载的非平稳化函数,再结合虚拟激励法的思想,可得梁式结构在确定性荷载作用下的虚拟响应,进而得到其非平稳随机响应。通过工程算例验证了该方法的准确性与有效性,并进一步讨论了不同速度和不同边界条件下梁式结构受移动荷载作用的随机振动问题。     

基于等效刚度的矩形孔蜂窝梁钢框架结构内力计算方法

蜂窝梁钢框架结构因梁截面沿长度周期性变化,不能直接采用普通钢框架结构矩阵位移法计算框架内力和位移．本文基于等效刚度法推导了矩形孔蜂窝梁的等效抗弯刚度、抗剪刚度和轴向刚度,建立了矩形孔蜂窝梁的单元刚度方程,提出了矩形孔蜂窝梁钢框架内力和位移计算方法．算例理论计算结果与有限元分析结果表明,两种方法计算结果非常接近．本文提出的等效刚度法概念清晰,准确性好,适用于计算蜂窝梁钢框架结构的内力和位移．     

基于广义卡尔曼滤波的桥梁结构物理参数识别

基于广义卡尔曼滤波提出了随机荷载作用下桥梁结构物理参数的识别方法。首先,以荷载为观测对象,推导出基于有限元模型的桥梁结构系统的观测方程,以结构待识别的物理参数为状态向量,建立系统状态方程;然后,对该状态方程和观测方程构成的非线性参数系统应用广义卡尔曼滤波,从而识别出结构的物理参数。对一座简支梁桥和一座三跨连续梁桥在不同工况下的物理参数识别进行了数值仿真,结果表明本文方法能够准确地识别桥梁结构全部刚度参数、质量参数和阻尼参数,且具有很强的抗噪性能,从而验证了本文方法的有效性和鲁棒性,可应用于识别大型桥梁结构的物理参数。     

横向载荷作用下轴向运动梁的屈曲失稳以及非线性振动特性

梁的轴向运动会诱发其产生横向振动并可能导致屈曲失稳,对结构的安全性和可靠性产生重大的影响。本文重点研究了横向载荷作用下轴向运动梁的屈曲失稳及横向非线性振动特性。基于Hamilton变分原理,建立了横向载荷作用下轴向运动梁的动力学方程,获得了梁的后屈曲构型。使用截断Galerkin法,将控制方程改写成Duffing方程的形式。用同伦分析方法确定载荷作用下轴向运动梁的非线性受迫振动的封闭形式的表达式。结果表明,后屈曲构型对轴向速度和初始轴向应力有明显的依赖性。通过同伦分析法得出非线性基频的显式表达式,获得了初始轴向力会影响非线性频率随初始振幅和轴向速度的线性关系。另外,轴向外激励的方向也会改变系统固有频率。     

底层大空间高层结构自由振动的实用计算方法

本文以连杆节间为界，按弹性支座上和Ｔｉｍｏｓｈｅｎｋｏ悬臂梁建立力墙部分的振动方程，按一般框架建立框架部分的振动方程，根据力，变形协调条件，形成底层大空间高层建筑结构的自由振动，并据此计算其自由振动。     

考虑恒载效应的拱形梁静力近似解

应用虚功原理,推导了考虑恒载效应影响时拱形梁在活载作用下的非线性微分方程,得到了方程的近似闭合解。根据方程的解,讨论了恒载大小及结构自身刚度(矢高、跨度、惯性矩及惯性半径等)不同因素在考虑恒载效应时对拱形梁静力特性的影响。通过与Takabatake得到的直梁解析解结果及作者在其他文献提出的有限元方法对拱形梁分析结果的比较,验证了本文非线性微分方程及其求解公式。结果表明,本文给出的非线性微分方程对于拱形梁和直线梁具有通用性,初始恒载的存在减小了拱形梁在活载作用下的静力反应,这种影响与恒载的大小及结构自身的刚度有关,对轻型结构的设计提出了一些建议。     

On one dynamic problem for structurally inhomogeneous beams

A method is developed for studying the dynamic deformation of structurally inhomogeneous beams consisting of homogeneous isotropic layers with different mechanical characteristics. The method is based on the virtual-displacement principle. The equation of motion is derived in vector and scalar forms for arbitrary loads, boundary conditions, and cross-sections with one and two axes of symmetry. The efficiency of the method is demonstrated by solving, as an example, the dynamic deformation problem for a hinged layered beam with a rectangular cross-section under harmonic loading. Mechanical effects are revealed, which describe the influence of the beam structure and the mechanical properties of beam components on the dynamic compliance in comparison with the relevant homogeneous beam with the same geometry __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 90–98, November 2007.     

变刚度梁挠度曲线的Green函数法求解

在变刚度梁的线弹性问题中,求解梁受静力荷载的挠度曲线常用解法有积分法与单位荷载法.本文从变刚度梁挠度曲线的微分方程出发,给出了变刚度梁挠度曲线的Green函数法解答,并分析了该解法的优点.从推导结果可以看到,本文提出的公式具有统一、精确、简洁、适合电算的特点,在编制杆系结构计算软件中将具有重要应用价值.     

A new semi-analytical method for the non-linear static analysis of an infinite beam on a non-linear elastic foundation: A general approach to a variable beam cross-section

We propose a new non-linear method for the static analysis of an infinite non-uniform beam resting on a non-linear elastic foundation under localized external loads. To this end, an integral operator equation is newly formulated, which is equivalent to the original differential equation of non-uniform beam. By using the integral operator equation, we propose a new functional iterative method for static beam analysis as a general approach to a variable beam cross-section. The method proposed is fairly simple as well as straightforward to apply. An illustrative example is presented to examine the validity of the proposed method. It shows that just a few iterations are required for an accurate solution.     

Flutter analysis of rotating beams with elastic restraints

The aeroelastic stability of rotating beams with elastic restraints is investigated. The coupled bending-torsional Euler-Bernoulli beam and Timoshenko beam models are adopted for the structural modeling. The Greenberg aerodynamic model is used to describe the unsteady aerodynamic forces. The additional centrifugal stiffness effect and elastic boundary conditions are considered in the form of potential energy. A modified Fourier series method is used to assume the displacement field function and solve the governing equation. The convergence and accuracy of the method are verified by comparison of numerical results. Then, the flutter analysis of the rotating beam structure is carried out, and the critical rotational velocity of the flutter is predicted. The results show that the elastic boundary reduces the critical flutter velocity of the rotating beam, and the elastic range of torsional spring is larger than the elastic range of linear spring.     

杆系结构多荷载识别的三角级数分析法

本文提供了一种识别杆系结构受到多荷载的作用的三角级数识别方法.将集中荷载展成三角级数且借助结构力学中的位移法建立了单根基本梁(梁单元)的位移方程,利用位移测量值反演所受到的集中荷载大小和位置.算例表明本文所用级数收敛性较好,可获得稳定的收敛值.     

基于子结构解耦的连接特性识别新方法

连接部件动态特性的准确辨识对预测装配式机械结构的动力学行为有重要意义. 针对传统基于子结构解耦的连接结构动力学特性识别方法难以直接利用可测量数据进行辨识及辨识结果受噪声影响显著等问题, 本文提出了一种新方法. 首先, 提取子结构解耦基本方程在测试自由度上的分量, 并经矩阵变换得到显含连接动刚度矩阵的形式, 而后由真实连接动刚度矩阵分解为已知的初始矩阵与待求的增量矩阵, 推导了具有收敛性质的增量型方程以增强界面自由度较多时辨识的数值稳定性, 并采用多项式拟合动刚度将其转化为了拟合系数的频域估计方程, 按给定准则选取合适的频率点联立方程后, 得到了只需装配体测试自由度上的频响函数来辨识连接特性的迭代公式. 最后, 以若干算例说明了算法的具体流程. 对10自由度弹簧?质量块系统进行了数值仿真, 验证了所提方法的正确性及抗噪性; 对包含一处胶接连接的T形梁结构和包含两处螺栓连接的L形梁结构进行了试验, 所辨识连接结构与残余结构重组的装配体有限元模型计算的频响函数与测量值在较宽频带内吻合较好, 表明了该方法能有效识别实际装配体结构中的连接特性.      

体外预应力索与简支梁耦合振动的特性

体外预应力结构是一种由体外索和普通结构组成的预应力组合结构,被广泛地应用在各类结构中。基于体外预应力索与梁耦合振动的振动特性,建立体外预应力梁振动模型,推导出了不同体外预应力束线型等直线弹性梁的自振频率方程。在体外预应力钢束混凝土梁电磁激振器扫频试验中,测试了不同预应力条件下梁的基频。理论和试验研究表明体外预应力束线型、预应力束拉伸刚度和梁振型模态对梁自振频率的影响是明显的。     

Generalized-order perturbation with explicit coefficient for damage detection of modular beam

A general method is formulated to estimate damage location and extent from the explicit perturbation terms in specific set of eigenvectors and eigenvalues. At first, perturbed orthonormal equation is generated from the perturbation of eigenvectors and eigenvalues to obtain the k-th explicit perturbation coefficients. At second, perturbed eigenvalue equation is generated from the perturbation of eigenvector and eigenvalue, and first-order expansion of the stiffness matrix to obtain other explicit perturbation coefficients. Stiffness parameters are computed from these equations using an optimization method. The algorithm is iterative and terminates under certain criteria. A fixed–fixed modular beam with various numbers of elements is used as test structure to investigate the applicability of the developed approach. By comparison with the Euler–Bernoulli beam, discretization errors are analyzed. In six elements beam, first-order algorithm converges faster for small percentage damage. Second-order algorithm is more efficient for medium percentage damage. For large percentage damage, the second-order algorithm converges more effectively. Meanwhile, for eight elements large percentage damage and ten elements small percentage damage, second-order algorithm converges faster to the termination criterion.     

Transient elastic wave propagation in an infinite Timoshenko beam on viscoelastic foundation

This paper presents an effective numerical method for solving elastic wave propagation problems in an infinite Timoshenko beam on viscoelastic foundation in time domain. In order to use the finite element method to model the local complicated material properties of the infinite beam as well as foundation, two artificial boundaries are needed in the infinite system so as to truncate the infinite beam into a finite beam. This treatment requires an appropriate boundary condition derived and applied on the corresponding truncated boundaries. For this purpose, the time-dependent equilibrium equation of motion for beam is changed into a linear ordinary differential equation by using the operator splitting and the residual radiation methods. Simultaneously, an artificial parameter is employed in the derivation. As a result, the high-order accurate artificial boundary condition, which is local in time, is obtained by solving the ordinary differential equation. The numerical examples given in this paper demonstrate that the proposed method is of high accuracy in dealing with elastic wave propagation problems in an infinite foundation beam.     

AN APPROXIMATE ANALYSIS OF FREQUENCY RESPONSE OF A CRACKED HINGEDHINGED BEAM

A new method based on a modified line-spring model is developed forevaluating the natural frequencies of vibration of a cracked beam.This model inconjunction with the Euler-Bernoulli beam theory,modal analysis and linear elasticfracture mechanics is applied to obtain an approximate characteristic equation of acracked hinged-hinged beam.By solving this equation the natural frequencies aredetermined for different crack lengths in different positions.The results show goodagreement with the solutions through finite element analysis.The present method maybe extended to analyze other cracked complicated structures with various boundaryconditions.     

非线性粘弹性Timoshenko梁动力学行为的分布

本文讨论了有限变形粘弹性Timoshenko梁的动力学行为。首先由Timoshenko梁的理论和分数导数型本构关系给出了梁的控制方程。其次为了便于求解,采用Galerkin方法对系统进行了简化,并比较了1阶和2阶截断系统的动力学性质,它们具有相同的定性性质,说明Galerkin方法的合理性。给出了求解包含分数积分的积分－微分方程的一种新方法,以便求解系统的长时间的解。综合利用非线性动力系统中的经典方法,揭示了梁在有限变形情况下丰富的动力学行为,并分别考察了载荷参数的材料参数对结构的动力学行为的影响。