NONLINEAR DYNAMIC SIMULATION OF AN AXIALLY SLIDE-SPIN ROCKET FLEXIBLE SYSTEM WITH CLEARANCE

A hybrid approach is presented to investigate the dynamic behavior of an axially slide-spin flexible rocket with nonlinear clearance. The equations of motion of the flexible rocket are derived based upon Euler-Bernoulli beam theory and Hamilton principle and the finite element method. The characteristics of clearance between the spinning rocket and launcher are considered to be piecewise linear. Numerical solution is developed by direct integration method and demonstrates the validity of the method. The coupled dynamic behavior of axial motion and transverse vibrations of rocket are analyzed, and the influences of axially moving acceleration, spin speed, linking stiffness of elastic "shoes", and the nonlinearity of clearance on the motion attitude of rocket are studied.     

Identification of prestress force from measured structural responses

A method for the identification of prestress force of a prestressed concrete bridge deck is presented using the measured structural dynamic responses. A Euler–Bernoulli beam finite element model is used to represent the bridge deck, and the prestress force is modelled as the axial prestress force in each beam element. The state-space approach is used to calculate the dynamic responses of the structure and the sensitivities of dynamic responses with respect to the structural parameters, such as the prestress force, flexural rigidity, etc. The prestress force in each beam element is taken to be a system parameter, and it is expressed explicitly in the system equation for forward analysis. The prestress force in each element is identified using a sensitivity-based finite element model updating method in the inverse analysis. Data obtained from a single or multiple accelerometers or strain gauges are used in the identification. Both sinusoidal and impulsive excitations are illustrated to give very good results. Two numerical simulations are presented to illustrate the effectiveness and robustness of the proposed method. Laboratory work on an axially prestressed concrete beam is also included as a practical application.     

Dynamics of an axially moving Bernoulli-Euler beam: Spectral element modeling and analysis

The spectral element model is known to provide very accurate structural dynamic characteristics, while reducing the number of degree-of-freedom to resolve the computational and cost problems. Thus, the spectral element model for an axially moving Bernoulli-Euler beam subjected to axial tension is developed in the present paper. The high accuracy of the spectral element model is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, wave characteristics, and the static and dynamic stabilities of a moving beam are investigated.     

Stick-slip vibration of a moving oscillator on an axially flexible beam

This study investigates the stick-slip vibration between an axially flexible beam fixed at both ends and an oscillator moving on the beam. After deriving the equations of motion for the stick and slip states, the stick-slip vibrations between the oscillator and the beam are analyzed. In addition, to obtain the irregularly changed contact position due to the axial deformation of the beam and oscillator movement, a mathematical expression for the contact position is derived. It is found that the long-period stick-slip vibration is influenced mainly by the oscillator and the short-period vibration is influenced mainly by axial deformation of the beam. Furthermore, the dynamic responses show that even if a high damping ratio is applied to the oscillator, stick-slip vibration due to axial deformation of the beam can occur. Finally, the analysis shows that a kind of the internal resonance occurs between the oscillator and the beam when the harmonics of the natural frequency of the oscillator match the natural frequencies of the beam.

     

Vibration analysis of a simply supported beam under moving mass based on moving finite element method

In this paper, a moving finite element (MFE) method is proposed to perform the dynamic analysis of a simply supported beam for a moving mass (MM). The MFE method treats the moving mass as a moving part of the entire system, so that the transverse inertial effects caused by the moving mass may easily be taken into account. The solution to the beam’s dynamic behaviors including its displacement is obtained via a Newmark-β method; the effects of the velocity and weight of the MM on the beam’s dynamic behaviors are further discussed. The numerical examples show that the inertial effects of the MM significantly affect the transverse responses of the simply supported beam.     

轴向运动简支-固支梁的横向振动和稳定性

研究一端简支一端固支轴向运动梁的横向振动和稳定性。提出在给定边界条件下确定一匀速运动梁固有频率和模态函数的方法。当轴向运动速度在其常平均值附近作简谐波动时,应用多尺度法给出轴向变速运动梁参数共振时的不稳定条件。用数值仿真说明相关参数对固有频率和不稳定边界的影响。     

Vibration analysis of a simply supported beam under moving mass based on moving finite element method

In this paper, a moving finite element (MFE) method is proposed to perform the dynamic analysis of a simply supported beam for a moving mass (MM). The MFE method treats the moving mass as a moving part of the entire system, so that the transverse inertial effects caused by the moving mass may easily be taken into account. The solution to the beam’s dynamic behaviors including its displacement is obtained via a Newmark-β method; the effects of the velocity and weight of the MM on the beam’s dynamic behaviors are further discussed. The numerical examples show that the inertial effects of the MM significantly affect the transverse responses of the simply supported beam.     

轴向运动矩形板的谐波共振与稳定性分析

针对轴向运动矩形薄板的非线性振动问题,在给出薄板运动的动能和应变能的基础上,应用哈密顿变分原理,推得几何非线性下轴向运动薄板的非线性振动方程。通过位移函数和应力函数的设定,并应用伽辽金积分法,得到四边简支边界约束条件下受横向激励载荷作用轴向运动薄板的达芬型振动方程。利用多尺度法对系统的非线性谐波共振问题进行求解,得到稳态运动下关于共振幅值的幅频响应方程。依据李雅普诺夫运动稳定性理论对定常解的稳定性进行分析,得到解的稳定性判别式。通过数值算例,得到不同横向载荷和轴向速度下共振幅值的变化规律曲线图以及对应的相图,讨论分岔点变化以及倍周期运动规律,分析横向激励载荷和轴向运动速度对系统非线性动力学行为的影响。     

附有滑动质量的旋转柔性梁动力学特性研究

提出用弹簧-质量系统抑制旋转柔性梁的振动,建立Euler-Bernoulli梁的动力学模型.对方程进行无量纲化,并在质量为慢时变运动、旋转角速度和角加速度为梁变形同阶小量时,对非线性方程进行近似简化,分析弹簧-质量系统对梁振动特性的影响机理.利用多尺度方法对非线性方程近似求解,在主共振、内共振条件下,研究梁和质量运动幅值随质量位置和调协参数的变化趋势.     

Rotary inertia and temperature effects on non-linear vibration, steady-state response and stability of an axially moving beam with time-dependent velocity

Free non-linear transverse vibration of an axially moving beam in which rotary inertia and temperature variation effects have been considered, is investigated. The beam is moving with a harmonic velocity about a constant mean velocity. The governing partial-differential equations are derived from the Hamilton's principle and geometrical relations. Under special assumptions, the two partial-differential equations can be mixed to form one integro-partial-differential equation. The multiple scales method is applied to obtain steady-state response. Elimination of secular terms will give us the amplitude of vibration. Additionally, the stability and bifurcation of trivial and non-trivial steady-state responses are analyzed using Routh-Hurwitz criterion. Eventually, numerical examples are presented to show rotary inertia, non-linear term, temperature gradient and mean velocity variation effects on natural frequencies, critical speeds, bifurcation points and stability of trivial and non-trivial solutions.     

轴向运动功能梯度梁的横向振动

新型非均匀复合材料,功能梯度材料具有防止脱层和减缓热应力等优良性能,将其应用于功能梯度梁的结构有着非常重要的工程应用价值。基于Euler-Bernoulli梁理论和Hamilton原理,建立轴向运动功能梯度梁横向自由振动的运动微分方程,其中假设功能梯度梁的材料特性沿梁厚度方向按各组分材料体积分数的幂函数连续变化;再对运动微分方程和边界条件进行量纲一处理,采用微分求积法对其进行离散化,导出系统的广义复特征方程,然后计算分析轴向运动功能梯度简支梁横向振动复频率的实部和虚部随量纲一轴向运动速度、梯度指标等参数的变化情况,并讨论量纲一轴向运动速度和梯度指标对功能梯度梁的横向振动特性以及失稳形式的影响。     

基于广义正交函数和正则化的移动荷载识别法

为了识别桥上移动荷载,把车/桥系统抽象为承受一组移动荷载的简支梁,用有限元方法建立桥梁振动方程,根据测试的桥梁响应,由广义正交函数根据模态叠加原理确定模态响应及其导数,用正则化技巧得到稳定的识别结果。数值模拟和试验结果表明,该方法用于识别桥上移动荷载是有效的、可行的     

A reduced time-varying model for a long beam on elastic foundation under moving loads

Dynamics of a long beam on the elastic foundation subjected to moving loads is studied in the present paper. The sliding window technique is used to dynamically truncate the long beam and a reduced time-varying beam system is obtained. The Hamilton’s principle is employed to establish the equations of motion of the reduced system. The variable separation method is adopted to solve dynamical responses of the reduced system. Examples of a long simply supported Timoshenko beam on the nonlinear foundation subjected to a single moving load and multiple loads are included. Numerical results of the reduced model compared with the ones obtained from the moving element model adapted in literature are carried out to show the validity and the good efficiency of the method proposed in the present paper.     

轴向运动耦合热弹梁的稳定性分析

研究了轴向运动梁的耦合热弹稳定性.根据轴向运动梁的运动微分方程和考虑变形影响时的热传导方程,得出了温度场和变形场耦合情况下梁的耦合热弹运动微分方程.对两端简支轴向运动梁耦合热弹振动的复频率进行了数值计算,得出了无量纲复频率与无量纲运动速度之间的关系曲线.分析了无量纲热弹耦合因子、无量纲运动速度和梁的长高比对梁的临界速度和稳定性的影响.     

移动质量-梁耦合系统的动态响应分析

在建立了移动质量-梁耦合系统振动方程的基础上,针对时变力学系统采用Newmarkβ逐步积分法进行求解.对不同运动状态移动质量作用下的简支梁动态响应进行研究,得到在移动质量的初速度和加速度两个运动参数变化的情况下梁的挠度变化规律.数值模拟结果表明:移动质量作用下,梁的挠度曲线是以一定频率围绕静挠度线的一种类正弦波,移动质量的惯性作用对梁动态响应的影响不能忽略.     

Analysis of the dynamic stress of planar flexible-links parallel robots

This paper presents a method for the dynamic stress analysis of planar parallel robots with flexible links and a rigid moving platform. The finite element-based dynamic model of flexible parallel robots is proposed. The relation between elastic deformations and elastic displacements of the flexible links is investigated, considering the coupling effects of elastic motion and rigid motion. The elastic deformations of links are calculated. Considering the effects of bending-shearing strain and tensile-compression strain, the dynamic stress of the links and its position are derived by using the Kineto-Elastodynamics theory and the Timoshenko beam theory. Due to the flexibility of the links, the dynamic stresses are well illustrated through numerical simulation. Compared with the results of the finite element software SAMCEF, the numerical simulation results show the good coherence and advantages of the analysis method. The dynamic stress analysis is demonstrated to have a significant impact on the analysis, design and control of flexible parallel robots.     

计及二阶效应的大位移柔性梁杆系统动力学分析

结合小变形条件下梁杆单元精确有限元方法和大位移随动坐标法,建立了计及二阶效应的大位移运动柔性梁单元的动力学方程.首先从小变形结构入手,建立考虑二阶效应的柔性梁压弯力学模型,推导出二阶理论条件下平面压弯梁的精确有限元方程,进而获取二阶理论条件下梁单元精确刚度阵.运用大位移随动坐标法建立大位移几何非线性弹性梁杆单元平衡方程,使用柔性多体动力学的相对描述方法推导大位移梁单元在局部坐标系下的动力学方程.通过结点位移、速度和加速度在随动坐标系与整体坐标系间的相互关系得到梁单元在整体坐标系下的包含二阶效应的动力学方程.对某型港口起重机臂架系统的变幅工况进行了计及二阶效应的弹性动力分析.     

NONLINEAR DYNAMIC BEHAVIOR OF VISCOELATIC TPANSMISSION BELT

The nonlinear dynamic responses of viscoelastic axially transmssion belts are investigatedand the Kelvin viscoelastic differential constitutive model is employed to characterize the materialproperty of belts. The generalized equation of motion is obtained for a viscoelatic axially transmissionbelts with geometric nonlinearity first, and then is reduced to be a set of second-order nonlinear ordi-nary differential equations by applying Galerkin's method. Finally the effects of viscosity parameterand elastic parameter and the moving velocity of the belts on the transient responses are investigatedby the research of digital simulation.     

柔顺机构动力学建模新方法

由于柔性杆大变形所引起的几何非线性因素的影响,柔顺机构动力学模型的建立变得更加复杂、困难。基于此,在充分考虑柔性杆大变形特性的基础上,基于简化思想,提出一种柔顺机构动力学建模的新方法。该方法主要以末端受纯弯矩、垂直力以及固定—导向等3种模式下的柔性杆为研究对象,根据欧拉—伯努利方程,并结合伪刚体模型所得边界条件,利用最小二乘原理,拟合柔性杆的变形曲线方程;通过求解变形曲线对时间的导数,得到其上任意点的速度,进而推出柔性杆的动能表达。基于伪刚体模型,根据功能转换关系,推导出柔性杆的变形势能。在此基础上,建立平行导向柔顺机构的动力学模型。最后,结合具体算例,通过对几种不同模型所得系统频率比较分析,验证了该方法的有效性。     

Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm

This study focuses on extraction of frequency information of a linear time-varying system using free response data. Frequency information is obtained from the pseudo-modal parameters that were defined in a previous study. A subspace-based identification algorithm is introduced. An improved version is proposed to make the algorithm less sensitive to measurement noise. An axially moving cantilever beam is used as the experimental system. A dynamic model is presented to show that lateral vibration of the axially moving cantilever beam is governed by a linear time-varying model. A computer simulation is conducted to compare the true pseudo-modal parameters and approximate ones that can be identified using the improved algorithm. The experimental study focuses on the capabilities of the algorithm and the factors that affect the identification results. A method of grouping identified structural pseudo-natural frequencies is proposed. Limitations of the algorithm are discussed.