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1.
导出作大范围刚体运动弹性薄板包括了几何非线性和中面变形之间的相互耦合(耦合变形)的动力学控制方程.分析了几何非线性和耦合变形各自对系统动力学性质的影响,得到了在传统方法上只考虑几何非线性,系统将通过同宿轨分岔过渡到混沌运动;若在传统方法上考虑耦合变形,系统稳定且数值解收敛,与实际情形相符.  相似文献   

2.
耦合变形对大范围运动柔性梁动力学建模的影响   总被引:1,自引:0,他引:1  
柔性梁在作大范围空间运动时,产生弯曲和扭转变形,这些变形的相互耦合形成了梁在纵向以及横向位移的二次耦合变量。本文考虑了变形产生的几何非线性效应对运动柔性梁的影响,在其三个方向的变形中均考虑了二次耦合变量,利用弹性旋转矩阵建立了准确的几何非线性变形方程,通过Lagrange方程导出系统的动力学方程。仿真结果表明,在大范围运动情况下,仅在纵向变形中计及了变形二次耦合量的一次动力学模型,与考虑了完全几何非线性变形的模型具有一定的差异。  相似文献   

3.
作大范围空间运动柔性梁的刚-柔耦合动力学   总被引:5,自引:4,他引:1  
刘锦阳  李彬  洪嘉振 《力学学报》2006,38(2):276-282
研究带中心刚体的作大范围空间运动梁的刚-柔耦合动力学问题.从精确的应变-位移关系式出发,在动力学变分方程中,考虑了横截面转动的惯性力偶和与扭转变形有关的弹性力的虚功率,用速度变分原理建立了考虑几何非线性的空间梁的刚-柔耦合动力学方程,用有限元法进行离散.通过对空间梁系统的数值仿真研究扭转变形和截面转动惯量对系统动力学性态的影响.  相似文献   

4.
考虑几何非线性和热效应的刚-柔耦合动力学   总被引:1,自引:0,他引:1  
温度增高和温度梯度会引起梁的纵向、横向变形位移,在一定程度上对刚-柔耦合规律产生影响.该文考虑热应变,从平面梁的非线性的应变与位移关系式出发,建立了刚体运动、弹性变形和温度相互耦合的有限元离散的热传导方程和动力学方程.研究热流作用下的中心刚体-简支梁系统的刚-柔耦合动力学性质,揭示了几何非线性项和热应变对弹性变形和刚体运动影响.  相似文献   

5.
一类刚-柔耦合系统的建模与稳定性研究   总被引:37,自引:2,他引:35  
肖世富  陈滨 《力学学报》1997,29(4):439-447
对于由中心刚体带有柔性梁附件组成的这一类简单刚 柔耦合系统,目前文献广泛采用的Euler Bernouli梁模型中考虑的刚 柔运动耦合项有严重的缺陷.本文对于物理本构关系线性的有限变形梁,分别采用微元法和变分法建立了该系统大挠度非线性动力学方程组.本文使用严格的方法来研究此非线性耦合动力学模型,采用能量 动量矩组合方法构成Liapunov函数,严格证明了此非线性系统平凡解的积分范数稳定性以及具有鲜明物理意义的最大模范数稳定性.本文对文献中引用的三类线性化模型,采用假设模态法,对中心刚体匀速转动时梁的振动作了数值仿真,进一步验证了本文的结论.上述结果,对选择刚 柔耦合系统正确的动力学模型是有益的.  相似文献   

6.
针对航天器的柔性附件,将其简化为常见的大范围运动空间柔性梁结构。根据柔性体的非线性变形原理,考虑了弯曲和扭转的非线性因素的影响,在柔性梁的三个变形方向上均考虑了变形的二次耦合项。利用有限元方法进行离散并用Lagrange方程建立了非线性变形模式下的动力学方程,包含了较为完全的刚度矩阵和各种耦合项。对一大范围运动的空间梁进行了仿真计算,表明在运动速度较大并且基座具有大范围运动时,一次耦合模型与本文模型有一定差异,且初始变形对两种模型也会产生影响。  相似文献   

7.
针对超长柔臂架系统在回转吊装运动中的非线性动力学行为,开展了模型构建与振动特性分析。考虑大型起重机臂架的刚柔耦合运动特征与吊装大挠度效应,利用混合坐标系描述了吊臂刚柔耦合运动,在臂头随动坐标系上描述吊重与钢丝绳的偏摆运动;通过初应力法构建了结构的几何非线性刚度矩阵;采用拉格朗日方程,推导并给出了综合考虑超长柔臂架刚柔耦合效应、几何非线性效应、惯性力效应的动力学分析模型。通过对某轮式起重机的动力仿真分析,结果表明:超长柔臂架在吊臂几何非线性效应影响下,吊重偏摆幅度增大,周期延长;吊载愈重,几何非线性效应对吊臂振动及吊重摆动的影响愈明显;轻载吊装吊臂振动主要由回转惯性力引起,但重载时吊臂振动规律取决于吊重偏摆振动。分析结果为臂架结构设计及控制系统设计提供了依据。  相似文献   

8.
运用柔性多体系统刚柔耦合动力学理论,研究了作大范围回转运动柔性梁的碰撞动力学问题.考虑柔性梁的横向变形,以及横向变形引起的纵向缩短项即非线性耦合变形项.采用基于Hertz接触理论及非线性阻尼理论的非线性弹簧阻尼模型来求解碰撞过程中产生的碰撞力,运用第二类拉格朗日方程建立了系统的刚柔耦合碰撞动力学方程.编制仿真软件进行动力学仿真计算,得到了碰撞力和系统动力学响应,对比分析了不同动力学模型对系统动力学响应的影响.同时研究了碰撞导致的柔性梁横向变形传播的波动特性.  相似文献   

9.
考虑轴和盘的质量及轴的几何非线性,建立了在周期轴向载荷作用下具不对称粘弹性支承弹性盘轴转子系统的非线性动力学方程.基于Lyapunov运动稳定性理论和Floquet判据,对系统的线性和非线性动力稳定性进行了分析.  相似文献   

10.
对在平面内做大范围转动的中心刚体-柔性梁系统的刚柔耦合建模理论进行了深入研究,建立了系统的高次耦合动力学模型. 该动力学模型考虑了柔性梁横向弯曲变形和纵向伸长变形,且在纵向位移中计及由于横向变形而引起的纵向缩短项,即非线性耦合变形项,并保留了与非线性耦合项相关的一些高阶项,最终得到了系统的高次刚柔耦合动力学方程. 由此得到的动力学方程不仅能适用于柔性梁的小变形问题,也同样适用于大变形问题,弥补了一次近似耦合模型在处理柔性梁大变形问题上的不足. 通过与绝对节点坐标法以及一次近似耦合模型的对比验证了高次耦合模型的正确性.  相似文献   

11.
Here, the large amplitude free flexural vibration behavior of symmetrically laminated composite skew plates is investigated using the finite element method. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Kármán's assumptions is introduced. The nonlinear matrix amplitude equation obtained by employing Galerkin's method is solved by direct iteration technique. Time history for the nonlinear free vibration of composite skew plate is also obtained using Newmark's time integration technique to examine the accuracy of matrix amplitude equation. The variation of nonlinear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, fiber orientation and boundary condition.  相似文献   

12.
采用有限元方法研究了结构在热载荷作用下变形与热传导之间的耦合特性.分析表明,结构变形较小,非线性效应很弱时,变形对材料的热传导系数影响很小,对结构的温度分布几乎没有影响;当变形增大,非线性效应增强时,变形对材料的热传导特性影响显著,热载荷作用下结构的温度变化和变形与现行不考虑热-机耦合效应所得结果产生明显差异.因此,为实现压电智能结构形状(振动)的精确控制,分析及实施控制时须考虑热-机耦合及变形对热传导系数的影响.  相似文献   

13.
It is noted that the behavior of most piezoelectric materials is temperature dependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in the case of finite deformation. On the other hand, for the purpose of precise shape and vibration control of piezoelectric smart structures, their deformation under external excitation must be ideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response under finite deformation. In this study, the governing equations of piezoelectric structures are formulated through the theory of virtual displacement principle and a finite element method is developed. It should be emphasized that in the finite element method the fully coupled piezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developed is then applied to simulate the dynamic and steady response of a clamped plate to heat flux acting on one side of the plate to mimic the behavior of a battery plate of satelite irradiated under the sun. The results obtained are compared against classical solutions, whereby the thermal conductivity is assumed to be independent of deformation. It is found that the full-coupled theory predicts less transient response of the temperature compared to the classic analysis. In the steady state limit, the predicted temperature distribution within the plate for small heat flux is almost the same for both analyses. However, it is noted that increasing the heat flux will increase the deviation between the predictions of the temperature distribution by the full coupled theory and by the classic analysis. It is concluded from the present study that, in order to precisely predict the deformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and the deformation dependent thermal conductivity should be taken into account. Project supported by the National Natural Science Foundation of China (Nos. 10132010 and 50135030) and the Foundation of In-service Doctors of Xi'an Jiaotong University.  相似文献   

14.
Strain analysis of the ligament of a plate with a large hole indicates that both geometric and material non-linearity may take place. Geometric non-linearity may occur even when the material is strained elastically. This may explain the disagreement in the results obtained recently, for the stress concentration factors, by several investigators. The experimental analyses were conducted on an aluminum plate, using electrical resistance strain gages, and on a polyurethane rubber sheet using photography. The strain concentration factor was found to vary from 1 to 2 depending on the level of deformation.  相似文献   

15.
吕述晖  王奎华  张鹏 《力学学报》2015,47(1):169-173
针对桩与连续梁组合这一基础形式,研究了梁-桩-土竖向耦合振动特性. 首先,将桩假设为一维黏弹性杆件,采用平面应变模型模拟桩侧成层土对桩的动力作用. 同时,桩顶对梁的支撑简化为竖向点支撑. 然后,分别根据一维杆件纵向振动理论和Timoshenko梁理论给出桩和梁的竖向振动控制方程并求解,进而借助离散傅里叶逆变换获得在梁上瞬时激振下梁和土层以上桩段的时域响应半解析解. 通过与有限元模拟结果对比,验证了解的合理性. 在此基础上,讨论了梁几何参数和桩身缺陷对梁-桩-土竖向耦合振动特性的影响.  相似文献   

16.
Here, the large amplitude free flexural vibration behaviors of thin laminated composite skew plates are investigated using finite element approach. The formulation includes the effects of shear deformation, in-plane and rotary inertia. The geometric non-linearity based on von Karman's assumptions is introduced. The non-linear governing equations obtained employing Lagrange's equations of motion are solved using the direct iteration technique. The variation of non-linear frequency ratios with amplitudes is brought out considering different parameters such as skew angle, number of layers, fiber orientation, boundary condition and aspect ratio. The influence of higher vibration modes on the non-linear dynamic behavior of laminated skew plates is also highlighted. The present study reveals the redistribution of vibrating mode shape at certain amplitude of vibration depending on geometric and lamination parameters of the plate. Also, the degree of hardening behavior increases with the skew angle and its rate of change depends on the level of amplitude of vibration.  相似文献   

17.
In this study, non-linear free vibration of micro-plates based on strain gradient elasticity theory is investigated. A general form of Mindlin’s first-strain gradient elasticity theory is employed to obtain a general Kirchhoff micro-plate formulation. The von Karman strain tensor is used to capture the geometric non-linearity. The governing equations of motion and boundary conditions are obtained in a variational framework. The Homotopy analysis method is employed to obtain an accurate analytical expression for the non-linear natural frequency of vibration. For some specific values of the gradient-based material parameters, the general plate formulation can be reduced to those based on some special forms of strain gradient elasticity theory. Accordingly, three different micro-plate formulations are introduced, which are based on three special strain gradient elasticity theories. It is found that both geometric non-linearity and size effect increase the natural frequency of vibration. In a micro-plate having a thickness comparable with the material length scale parameter, the strain gradient effect on increasing the non-linear natural frequency is higher than that of the geometric non-linearity. By increasing the plate thickness, the strain gradient effect decreases or even diminishes. In this case, geometric non-linearity plays the main role on increasing the natural frequency of vibration. In addition, it is shown that for micro-plates with some specific thickness to length scale parameter ratios, both geometric non-linearity and size effect have significant role on increasing the frequency of non-linear vibration.  相似文献   

18.
采用基于小生镜技术的遗传算法,对半刚性连接钢框架进行优化设计,针对其早熟现象和局部搜索能力差的缺点改进遗传算法。使用自适应策略改进交叉与变异算子。建立半刚性连接钢框架优化设计数学模型,编制了基于遗传算法的优化设计程序。运用这一优化算法可以直接从型钢截面表中选取截面,并在优化设计过程中考虑了连接可变性和二阶效应的影响。通过几个设计实例表明,考虑几何非线性会使用钢量增加,有支撑的情况下,半刚性连接较刚接用钢量经济。  相似文献   

19.
蒲刚  章定国  黎亮 《力学学报》2019,51(6):1882-1896
基于修正偶应力理论, 研究了具有大范围旋转中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔柔性微梁系统的动力学特性.楔形梁是中间层为不完全功能梯度层, 两表层为均质材料的功能梯度夹层结构, 它可以减小传统夹层结构由于层与层之间材料属性的不同导致脱粘类型损伤的影响.采用假设模态法描述变形, 考虑具有捕捉动力刚化效应的非线性耦合项, 计及von Kármán几何非线性应变, 运用第二类Lagrange方程, 导出了适用于较大变形的高次刚柔耦合动力学方程.对在平面内做大范围运动的中心刚体-功能梯度夹层Euler-Bernoulli楔形多孔微梁的动力学特性进行了详细研究.研究表明: 功能梯度夹层楔形梁表层结构高度、旋转角速度、功能梯度幂指数、尺度参数、孔隙度以及各层结构的体积分数对系统的动力学特性都有很大的影响; 功能梯度夹层楔形梁综合了功能梯度直梁和楔形梁的特性, 其相对于功能梯度直梁的固有频率增大, 同时使得孔隙度对结构固有频率变化趋势的影响不再与功能梯度直梁相同; 由于柔性梁变形能中具有横向与轴向的耦合势能, 系统在稳态下的平衡位置发生了迁移现象; 系统随着尺度参数的变化发生了频率转向与振型转换.   相似文献   

20.
This paper develops geometric nonlinear hybrid formulation for flexible multibody system with large deformation considering thermal efect. Diferent from the conventional formulation, the heat flux is the function of the rotational angle and the elastic deformation, therefore, the coupling among the temperature, the large overall motion and the elastic deformation should be taken into account. Firstly,based on nonlinear strain–displacement relationship, variational dynamic equations and heat conduction equations for a flexible beam are derived by using virtual work approach,and then, Lagrange dynamics equations and heat conduction equations of the first kind of the flexible multibody system are obtained by leading into the vectors of Lagrange multiplier associated with kinematic and temperature constraint equations. This formulation is used to simulate the thermal included hub-beam system. Comparison of the response between the coupled system and the uncoupled system has revealed the thermal chattering phenomenon. Then, the key parameters for stability, including the moment of inertia of the central body, the incident angle, the damping ratio and the response time ratio, are analyzed. This formulation is also used to simulate a three-link system applied with heat flux. Comparison of the results obtained by the proposed formulation with those obtained by the approximate nonlinear model and the linear model shows the significance of considering all the nonlinear terms in the strain in case of large deformation. At last, applicability of the approximate nonlinear model and the linear model are clarified in detail.  相似文献   

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