全地面起重机起升变幅协调策略研究

在大臂长重载作业时,由于伸缩臂的非线性变形被吊物在起升离地或就位时会瞬间发生摆动.考虑了轴向载荷的二阶效应,利用微分方程法和坐标转换法对臂架末端发生的非线性变形位移进行了数值求解.在此基础上考虑了臂架自重变形的影响,对起升加载过程中工作幅度的变化值进行了讨论,并结合逐步渐进法提出了一种基于预先设置变幅液压缸伸缩长度的起...     

约束阻尼板增材式拓扑渐进法减振动力学优化

研究阻尼结构的阻尼材料最优布局问题。基于虚功原理,构建约束阻尼板振动微分方程,从约束阻尼板若干基本假设出发并根据阻尼板自由振动微分方程,推导了结构模态阻尼比表达式。建立了以阻尼单元相对密度为拓扑设计变量,模态阻尼比最大为优化目标,阻尼材料用量为约束的阻尼结构拓扑优化数学模型。以阻尼单元模态阻尼比敏度为寻优方向的依据,采用增材式渐进法(AESO)求解优化模型,并依据拓扑优化准则在结构上不断敷设阻尼材料。编程实现了AESO算法,仿真计算表明:采用AESO优化时,阻尼材料主要敷设于结构的模态应变较大位置,且不会产生棋盘格现象,并且优化后的结构一阶模态阻尼比较优化前可增加83.6%,而常规渐进法带来的增幅仅72.13%。为进一步验证优化效果,还对结构进行了谐响应分析,结果表明采用增材式渐进法优化时,结构可获得更佳减振效果。     

列车用橡胶堆旁承的两种本构模型振动特性研究

对列车用橡胶堆旁承以Mooney-Rivlin模型和Yeoh模型进行建模,利用ABAQUS计算分析软件计算出两种模型在相同载荷下的载荷位移曲线,分别计算出其非线性刚度特性;对橡胶堆旁承建立振动微分方程,将求得的两种本构模型的非线性刚度代入微分方程中,通过求解微分方程求得两种本构模型的相频和幅频特性,得出两种本构模型的振动传递特性。该研究结果在橡胶元件设计中有一定的意义。     

任意载荷作用下变截面柔性构件变形特性的分析与研究

考虑任意载荷作用下变截面柔性构件的变截面特征及变形的非线性问题,建立了任意载荷作用下变截面柔性构件变形求解的二阶非线性微分方程.采用离散化的数值计算方法,利用泰勒级数展开式对微分方程进行求解,给出了求解的一般过程.采用上述方法对承受不同载荷的变截面柔性构件的变形进行了分析,并采用有限元法进行了仿真分析,通过对比所得结果验证了该分析方法与微分方程的正确性.     

基于几何非线性大型带式输送机动力学仿真

用离散单元模型建立了基于胶带悬垂度的带式输送机非线性运动微分方程，推导了胶带等效刚度表达式，分析其非线性特性及对运动微分方程的影响。提出并建立了三台电动机和液力偶合器组成的驱动系统的数学模型，并据此设计动态仿真软件BDS。对一条带式输送机的动态性能进行了数值计算，其结果与国外软件计算结果进行比较，发现两者比较接近；对离散单元模型和连续介质模型等三个模型之间的张力波波动速度进行比较，结果十分吻合。最后分析了数值解和步长之间的关系。     

动质量对悬臂梁振动抑制的数值分析和实验研究

在简谐激励下,实验研究端部动质量对悬臂梁共振响应的抑制能力,发现抑振效果与质量位置和质量比有直接关系,动质量和梁的高频碰撞振动现象。提出包含碰撞效应的数学模型,用振型叠加法,将耦合的非线性偏微分方程变为时变非线性微分方程。计算无量纲梁端部位移和碰撞力。结果显示,提出的模型基本上描述了系统的动态特性,在一定程度上理论和实验结果是一致的。     

大挠度后屈曲倾斜梁结构的非线性力学特性

基于弹性梁的几何非线性大挠度屈曲理论,建立两端固定对称倾斜支撑梁结构的大挠度后屈曲控制微分方程,采用几何非线性隐式变形协调关系来表达强非线性超静定边值问题,得到描述倾斜梁大挠度后屈曲行为的精确解析解.采用数值方法求解含有第一、二类椭圆积分的强非线性微分方程,给出不同倾角梁结构从初始屈曲到后屈曲并发生两态跳转过程中的位形曲线及非线性刚度.根据最小能量原理和挠曲线拐点个数,分析对称屈曲模态与非对称屈曲模态之间相互跳转的内在联系及其对结构非线性刚度突变的影响,得到了屈曲模态之间的转换条件.跳转过程的数值仿真表明,倾斜支撑梁结构发生大挠度后屈曲时具有明显的双稳态特性且只出现低阶(1、2阶)屈曲模态,仿真计算结果与试验结果相一致.     

带周向挡片的迷宫密封动力特性的研究

迷宫密封腔内的气体流动,可以通过由双控制体模型导出的基本方程组来表示。在此基础上,针对带周向挡片的迷宫密封,提出了利用优化原理求解其静态非线性偏微分方程组的方法,然后在静态解基础上,将方程组线性化,最终计算出密封的动力特性系数。计算结果表示,用这种方法得出的结果,与试验结果有较好的一致性。     

矩形弹性壳液耦合系统的非线性振动分析

从流体运动微分方程组和边界条件出发,利用拉格朗日方程,建立矩形弹性壳液耦合系统的非线性振动方程组,并进行数学仿真计算,得到产生稳定的低频大幅重力波的条件及重力波和壳的幅频曲线,数值计算结果与实验现象吻合较好.     

含间隙的斜齿轮副扭振分析与试验研究

建立了科齿轮副的间隙型非线性扭振模型，其中考虑了斜齿轮副的啮合综合误差，齿侧间隙和时变啮合刚度。采用三维有限元法计算了斜齿轮副啮合刚度，用三次样条插值拟合得到时变啮合刚度函数。用数值积分方法对系统的非线性动力学微分方程进行了求解，获得了斜齿轮副在外转矩作用下受静态传动误差激励的非线性稳态强迫响应，并对系统的动态响应进行了测试，试验和理论计算结果了一致性证实了本文所提出模型和解法的正确性。     

双层幕墙热气流有限分析计算软件及应用

本文阐述双层通风幕墙在温差作用下的计算模型，建立热气流的动量方程、连续性方程和温度场方程。运用有限分析法，将通道分成有限段单元，把耦合非线性微分方程解耦寻求解析解，再转换为全局数值解。设计有限分析计算程序，并开发双层幕墙热气流有限计算软件。最后给出计算实例。     

几种数值算法在弹道微分方程组解算中的仿真与比较

本文简述了数值分析的应用范围,介绍了微分方程几种不同的数值解法,及其在弹道解算中的应用。在简化弹丸弹道动力学微分方程的基础上,通过 Mablab 软件编写欧拉法、梯形法、经典四阶龙格库塔法程序,计算动力学微分方程组近似解及各种方法的局部截断误差和计算时间。通过对结果的分析比较,明确了几种经典解法在弹道解算中的优劣,为弹道解算方法的选择提供了依据。     

Non-linear non-uniform torsion of thin-walled beams

A theoretical and experimental investigation is made to study the non-linear behaviour of thin-walled elastic beams of open sections subjected to non-uniform torsion. The differential equations describing the behaviour and the associated boundary conditions are presented. A perturbation solution is carried out to obtain the torque-rotation characteristics and also the axial strain distribution. The accuracy of the perturbation solution is checked against a numerical solution of the governing equation.

A set of experimental tests on two I-sections is carried out to verify the theoretical calculation. It is shown that the torque-rotation behaviour exhibits a hardening non-linear characteristic. The agreement between theory and test results is reasonable.     

The finite volume flic method and its stability analysis

In this study, a general finite volume Fluid-in-cell method (FVFLIC) for solving the Navier—Stokes equations is introduced. The stability of the numerical method is then analysed by directly using two-dimensional Euler equations instead of a linear model equation. This direct approach to the analysis of non-linear stability is based on the Taylor expansion of the discretized Euler equations and some basic principals that have been used for analysing linear model equations. The exact forms of numerical viscosity or truncation errors are derived and discussed. The influences of the numerical viscosity as well as the artificial viscosity on numerical solutions are investigated. Results from this analysis can be used to construct appropriate artificial viscosity terms. Based on the above methodology, a stability criterion is proposed for the calculation of time steps for general three-dimensional computation using non-orthogonal grids.     

疲劳多裂纹问题的Tayor级数解法

疲劳多裂纹问题是老龄结构可靠性分析中受到广泛关注的问题,在可靠性分析中需要反复求解多裂纹扩展方程,对计算方法的精度和效率提出了很高的要求。Taylor级数法是代数,微分方程的一种新的数值解法,其在线性问题中的理论和应用已经比较完善和成熟,本文将Taylor解法进一步用于非线性的疲劳多裂纹扩展方程的求解,对非线性项可以表达为多元多项式的问题,完善了Taylor级数方法的理论,通过计算实例验证了方法的精度和求解效率。     

利用Lyapunov指数分析机械手反馈控制中的混沌运动

给出了一种适用于一般混沌系统最大Lyapunov指数计算的数值算法，并应用于Duffing方程系统、Lorenz系统和Roessler系统．验证了该方法的有效性。分析了平面两自由度机械手基于多变量比例微分反馈控制中的混沌现象，在给定的几种特定参数条件下，计算了机械手混沌模型的最大Lyapunov指数，结果表明机械手在反馈控制下会出现混沌运动。     

压电谐波电机驱动系统非线性主共振分析

为了探索压电谐波电机的机械-压电系统的非线性共振特性,设计了一种集压电驱动、谐波传动和活齿传动为一体的机电集成压电谐波电机。在非线性压电和非线性弹性效应的基础上,建立了驱动系统非线性机电耦合动力学方程。利用Linz Ted-Poincaré法推导了驱动系统非线性主共振响应方程,得出了主共振幅频响应曲线,分析了不同非线性效应对主共振响应的影响,最后通过四阶Runge-Kutta数值法验证了解析解的正确性。结果表明:在两种非线性效应中,非线性压电效应对主共振响应的影响是主要的;压电堆主共振出现在偏离固有频率较远处,且随着频率改变响应值出现跳跃现象;数值解与解析解响应曲线吻合较好。     

A Galerkin method for the steady state analysis of harmonically excited non-linear systems

A Galerkin method for the computation of the steady state of harmonically excited non-linear systems in the frequency domain is presented. The non-linear differential equations of motion are transformed, via the Galerkin technique, to a minimized system of non-linear algebraic equations in the frequency domain. These equations are then solved by a specially developed iteration procedure based on Powell's minimization method. The solution technique proves to be suitable for non-linear systems with arbitrary and numerous non-linearities (e.g. joints with clearance, non-linear springs and dampers).     

A study of Berger equations applied to non-linear vibrations of elastic plates

The equations of motion based on Berger's hypothesis have been widely used in the non-linear free vibration analysis of elastic plates mainly because of the simplicity of these equations. A rational mechanical basis for these equations has not yet been found. In the present paper, the variationally derived in-plane boundary conditions are examined with specific reference to the plates with edges free of in-plane stress resultants. It is shown that for this boundary condition the Berger equations can result in zero non-linearity. A formal basis for the Berger equations is then critically discussed. Approximate modal equations governing the non-linear, free, flexural vibrations of a few plate geometries are presented and compared with the von Kármán results. The numerical study reveals that the Berger equations do not yield consistently accurate results, and the results show an entirely different pattern of deformation. These observations may justify certain reservations regarding the general applications of the Berger equations.     

Scrutiny of non-linear differential equations Euler-Bernoulli beam with large rotational deviation by AGM

The kinematic assumptions upon which the Euler-Bernoulli beam theory is founded allow it to be extended to more advanced analysis. Simple superposition allows for three-dimensional transverse loading. Using alternative constitutive equations can allow for viscoelastic or plastic beam deformation. Euler-Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams and geometrically nonlinear beam deflection. In this study, solving the nonlinear differential equation governing the calculation of the large rotation deviation of the beam (or column) has been discussed. Previously to calculate the rotational deviation of the beam, the assumption is made that the angular deviation of the beam is small. By considering the small slope in the linearization of the governing differential equation, the solving is easy. The result of this simplification in some cases will lead to an excessive error. In this paper nonlinear differential equations governing on this system are solved analytically by Akbari-Ganji’s method (AGM). Moreover, in AGM by solving a set of algebraic equations, complicated nonlinear equations can easily be solved and without any mathematical operations such as integration solving. The solution of the problem can be obtained very simply and easily. Furthermore, to enhance the accuracy of the results, the Taylor expansion is not needed in most cases via AGM manner. Also, comparisons are made between AGM and numerical method (Runge-Kutta 4th). The results reveal that this method is very effective and simple, and can be applied for other nonlinear problems.