大变形刚-柔耦合系统仿真和实验研究

通过气浮台和梁系统的刚-柔耦合动力学实验研究完备的几何非线性模型和一次近似模型在大变形情况下的适用性.首先从Green应变与位移的非线性关系式出发,用绝对节点坐标法建立了弹性梁的完备的几何非线性动力学模型,并考虑结构阻尼建立了气浮台和梁系统的刚-柔耦合动力学方程,然后利用非接触式的运动测量仪和应变仪测量特征点的速度、角速度和应变,通过理论和实验结果的数值对比验证了几何非线性动力学模型的正确性,在此基础上进一步分析基于小变形的一次近似模型的适用性.     

计及变形耦合项的平面柔性梁动力学建模及频率分析

考虑了变形产生的几何非线性效应对作大范围运动的平面柔性梁的影响，在其纵向、横向的变形位移中均考虑了变形的二次耦合变量，从非线性应变-变形位移的原理出发，说明增加耦合变量后。使得剪应变近似为零，由此得出的变形模式更符合工程实际和简化需要。考虑两个方向的变形耦合后，采用有限元离散，通过Lagrange方程导出系统的动力学方程。最后对一作旋转运动的平面柔性梁进行仿真计算，并对其固有频率进行分析研究。将本文模型所得的结论。与一次耦合动力学模型、零次近似模型进行比较，说明了三种模型的差异。得到了作旋转运动的平面柔性梁的一些新特点。     

温度场中的柔性梁系统动力学建模

研究温度场下带集中质量的柔性梁系统的动力学问题。考虑几何非线性，在纵向变形与轴向伸长的关系式中计及了与横向变形有关的二次耦合项。考虑温度变化对系统动力学性态的影响，在本构关系式中计及了热应变。用假设模态法对各柔性梁进行离散，从虚功原理出发，根据各柔性梁之间的运动学约束关系，建立了带集中质量的柔性梁系统的动力学方程。仿真结果表明．即使在转速较低的情况下，随着集中质量的增大和温度的急剧变化，纵向变形的二次耦合项的影响不容忽视，此外，温度的变化还引起轴向变形和轴向约束力高频振荡。     

黏弹性轴向运动变张力梁非线性动力学

在黏弹性轴向运动梁横向参数振动的非线性动力学行为研究中,首次计入因速度变化引起的、沿梁的径向变化的、轴向变张力的影响。给出描述变张力轴向运动梁横向非线性振动的偏微分—积分控制方程。基于微分求积法给出轴向运动梁横向非线性参数振动的数值解,通过观察梁中点的位移、速度随时间变化的历程,识别轴向运动系统的非线性动力学行为。同时,通过从数值解中提取的相图、Poincaré映射图和频谱分析,考察轴向运动梁横向振动的分岔与混沌特性,揭示了工程应用中的非线性轴向运动系统的混沌动力学行为。     

Winkler地基上有限长梁非线性自由振动

基于经典Winkler地基模型及Euler-Bernoulli梁理论,考虑梁的几何非线性效应,运用Newton第二定律建立了弹性地基上有限长梁的非线性运动方程。采用Galerkin方法对运动方程进行一阶模态截断,进而利用多尺度法求得了该系统自由振动的一阶近似解。揭示了两端简支梁的非线性自由振动特性,分析了弹性模量、长细比及地基刚度系数等参数对系统固有频率的影响。并通过该系统的位移时程曲线,分析了阻尼对弹性地基上梁运动特性的影响。     

复合材料梁的几何精确非线性建模及非经典效应

基于Hodges的广义Timoshenko梁理论对具有任意剖面形状、任意材料分布及大变形的复合材料梁进行几何精确非线性建模,采用旋转张量分解法计算梁内任意一点的应变,采用变分渐近法确定梁剖面的任意翘曲,采用平衡方程由二次渐近精确的应变能导出广义Timoshenko应变能,采用广义Hamilton原理建立梁的几何精确非线性运动方程。将所建模型用于复合材料梁的静动力分析,通过与实验数据的对比,验证了建模方法的准确性,并进一步研究了剖面翘曲及横向剪切变形非经典效应对复合材料梁的影响。研究表明,剖面翘曲对复合材料梁的静变形和固有频率有显著影响,横向剪切变形对复合材料梁的静变形和固有频率的影响与梁的长度/剖面高度比有关。     

外激励力作用下的轴向运动梁非线性振动的联合共振

研究轴向运动梁在外激励力作用下非线性振动的联合共振问题.利用哈密顿原理建立横向振动的轴向运动梁的振动微分方程,采用分离变量法分离时间变量和空间变量并利用Galerkin方法离散运动方程.采用IHB法进行非线性振动求解,分析在内共振条件且外激励作用下的联合共振问题,对周期解进行稳定性的判定.典型算例获得了不同外激励力振幅时系统非线性振动的复杂频幅响应曲线.     

热载荷作用下大变形柔性梁刚柔耦合动力学分析

从非线性应变-位移关系式出发,用虚功原理建立了热载荷作用的柔性梁的热传导方程和旋转刚体-梁系统的刚-柔耦合动力学方程.由于考虑了刚度阵的高次变形项,适用于大变形问题.对温度、弹性变形和刚体运动变量联合求解.研究了热流引起的温度梯度对弹性变形和刚体转动的影响,以及在大变形情况下的几何非线性效应.     

空间薄壁截面梁非线性有限单元模型

基于Timoshenko梁理论和Vlasov薄壁杆件理论,通过设置单元内部节点并对弯曲转角和翘曲角采取独立插值的方法,建立了可考虑横向剪切变形和扭转剪切变形及其耦合作用、弯扭耦合、以及二次剪应力影响的空间薄壁梁非线性有限元模型。以更新的拉格朗日格式描述的几何非线性应变推得几何刚度矩阵。同时考虑了材料非线性,假定材料为理想塑性体,服从Von Mises屈服准则和Prandtle-Reuss增量关系,采用有限分割法,由数值积分得到空间薄壁梁的弹塑性刚度矩阵。算例表明该文所建梁单元模型具有良好的精度,适用于空间薄壁结构的有限元分析。     

考虑几何非线性的旋转薄壁圆柱壳进动响应分析

选取悬臂旋转薄壁圆柱壳作为研究对象,利用能量法推导了其振型进动因子,并考虑了阻尼以及几何非线性的影响.应用Donnell's简化壳理论建立考虑几何非线性以及振型进动的非线性波动方程,使用Galerkin法对非线性波动方程进行离散化,获得模态坐标上的非线性微分方程组,分别应用Runge-Kutta法和谐波平衡法对其进行数值求解和近似解析求解,并分析了近似解析解的稳定性.结果表明,几何非线性不影响振型进动因子,但使系统的频率响应曲线具有多值性和跳跃性.     

Magnetic flow of viscous gas between rotating surfaces of revolution

In this work the steady laminar magnetic flow of viscous gas is considered in a narrow space (slot) between two surfaces of revolution rotating with constant angular velocities around a common axis of symmetry. The linearised equations of magnetic motion of the viscous gas flow for axial symmetry in the intrinsic curvilinear orthogonal coordinate system $\text{x, φ, y}$ are used. The obtained solutions of the equations of motion have been illustrated by examples of gas flow through the slot of constant thickness between rotating and fixed conical surfaces, and between rotating and fixed spherical surfaces.     

An approximate solution for the flow in viscous couplings

The creeping flow between two discs and in a slotted disc-plate system where one of the discs rotating is considered. The equations of motion and continuity are simplified by an order of magnitude estimation and the assumption that the gap between the discs is small. For the disc-disc system the equations of motion are decoupled and can be integrated to give a zeroth order solution which is introduced into the equations. There are integrated again to give a first order solution which depends on the Reynolds number. It is shown that a disc rotating and axially movable in a narrow gap will centre itself. The integration of the equtions of motion for the slotted disc-plate system leads to a Poisson equation with Neumann boundary conditions for the pressure. The boundary conditions are obtained with the assumption that the mass flows in radial direction are zero and the pressure gradients in circumferential direction are opposite equal. The differential equations are discretized and solved by a multigrid method. Velocities, pressure and torque are calculated. The superposed pressure distributions of the front and back side of a segment gives a resulting force exerted on the segment in axial direction.     

带有轴承间隙的裂纹转子分叉与混沌特性

在考虑到轴承间隙的同时构造了开闭裂纹转子系统的动力学模型,依据此模型对裂纹转子的非线性特性进行了分析,结果表明,转子系统不但具有周期和拟周期解,而且还出现了分叉和混沌等非线性动力学现象。同时,对带有轴承间 裂纹转子所表现的特异症状进行了研究,其结果可用于旋转机械的故障诊断。     

The Axial Nonlinear Vibration Analysis of Ball-screw about Machine Tool Feeding System

The forced state of the ball-screw of machine tool feeding system is analyzed. The ball-screw is simplified as Timoshenko beam and the differential equation of motion for the ball-screw is built. To obtain the axial vibration equation,the differential equation of motion is simplified using the assumed mode method. Axial vibration equation is in form of Duffing equation and has the characteristics of nonlinearity. The numerical simulation of Duffing equation is proceeded by MATLAB / Simulink. The effect of screw length,exciting force and damping coefficient are researched,and the axial vibration phase track diagram and Poincare section are obtained. The stability and period of the axial vibration are analyzed. The limit cycle of phase track diagram is enclosed. Axial vibration has two type-center singularity distributions on both sides of the origin. The singularity attracts vibration to reach a stable state,and Poincare section shows that axial vibration appears chaotic motion and quasi periodic motion or periodic motion. Singularity position changes with the vibration system parameters,while the distribution doesn' t change. The period of the vibration is enhanced with increasing frequency and damping coefficient. Test of the feeding system ball-screw axial vibration exists chaos movement. This paper provides a certain theoretical basis for the dynamic characteristic analysis of machine feeding system ball-screw and optimization of structural parameters.     

大型水平轴风力发电机桨叶稳定性研究

大型水平轴风力发电机桨叶为流-刚-柔耦合的周期时变多体系统。本文暂未考虑风载荷,分析了重力载荷和桨叶预锥角、转速等因素的变化对稳定性的影响。力学建模中,考虑了桨叶挥舞、摆振、扭转和轴向运动以及根部铰的挥舞、摆振和变矩等刚体运动。利用有限元法形成5节点18自由度的刚-柔混合梁单元模型,应用Hamilton原理建立桨叶动力学方程,求得对应的摄动方程,采用Newmark隐式积分方法求解。根据Floquet理论判断运动稳定性,计算了相关转换矩阵的特征值。结果表明预锥角对桨叶运动稳定性影响不容忽视。在通常的工况下,桨叶能够稳定地运转。     

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

The nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated. Based on the linear viscoelastic differential constitutive law, the extended Hamilton’s principle is utilized to derive the generalized third-order equations of motion for the axially translating viscoelastic Bernoulli–Euler beam. The coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields. The inertia force arising from the longitudinal acceleration emerges, rendering the coupling terms between the axial beam acceleration and the beam flexure. Semi-analytical solutions for the governing PDE are obtained through the separation of variables and the assumed modes method. The modified Galerkin’s method and the fourth-order Runge–Kutta method are employed to numerically analyze the resulting equations. Further, dynamic stabilization is examined from the system energy standpoint for beam extension and retraction. Extensive numerical simulations are presented to illustrate the influences of varying translating velocities and viscoelastic parameters on the underlying dynamic responses. The material viscosity always dissipates energy and helps stabilize the transverse vibration.     

Large amplitude vibration analysis of composite beams: Simple closed-form solutions

Large amplitude vibration analysis of laminated composite beam with axially immovable ends is investigated with symmetric and asymmetric layup orientations by using the Rayleigh–Ritz (R–R) method. The displacement fields used in the analytical formulation are coupled by using the homogeneous governing static axial equilibrium equation of the beam. Geometric nonlinearity of von-Karman type is considered which accounts for the membrane stretching action of the beam. The simple closed-form solutions are presented for the nonlinear harmonic radian frequency as function of central amplitude of the beam using the R–R method. The nonlinear harmonic radian frequency results obtained from the closed-form solutions of the R–R method in general show good agreement with the results obtained from simple iterative finite element formulation. Furthermore, the closed-form expressions are corrected for the harmonic motion assumption from the available literature results on the existence of quadratic and cubic nonlinearity. It is interesting to note that the composite beams can result in asymmetric frequency vs. amplitude curves depending upon the nature of direction of displacement in contrast to isotropic beams which exhibit cubic nonlinearity only and leads to symmetric frequency vs. amplitude curves with respect to sign of the amplitude.     

Hamiltonian dynamic analysis of an axially translating beam featuring time-variant velocity

A dynamic analysis is presented for an axially translating cantilever beam simulating the spacecraft antenna featuring time-variant velocity. The extended Hamilton’s principle is employed to formulate the governing partial differential equations of motion for an axially translating Bernoulli–Euler beam. Further, the assumed modes method and the separation of variables are utilized to solve the resulting equation of motion. Attention is focused on assessing the coupling effects between the axial translation motion and the flexural deformation during the beam extension or retraction operations upon the vibratory motion of a beam with an arbitrarily varying length under a prescribed time-variant velocity field. A number of numerical simulations are also presented to illustrate the qualitative features of the underlying mechanical vibration of an axially extending or contracting flexible beam. In general, the transverse beam vibration is stabilized during extension and unstabilized during retraction. The axial acceleration of a translating beam does not affect the transverse vibratory system stabilization.     

复合材料变截面旋转薄壁悬臂梁自由振动分析

基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。