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1.
In the present paper, the geometric nonlinear formulation is developed for dynamic stiffening of a rectangular plate undergoing large overall motions. The dynamic equations, which take into account the stiffening terms, are derived based on the virtual power principle. Finite element method is employed for discretization of the plate. The simulation results of a rotating rectangular plate obtained by using such geometric nonlinear formulation are compared with those obtained by the conventional linear method without consideration of the stiffening effects. The application limit of the conventional linear method is clarified according to the frequency error. Furthermore, the accuracy of the assumed mode method is investigated by comparison of the results obtained by using the present finite element method and those obtained by using the assumed mode method.  相似文献   

2.
The previous low-order approximate nonlinear formulations succeeded in capturing the stiffening terms, but failed in simulation of mechanical systems with large deformation due to the neglect of the high-order deformation terms. In this paper, a new hybrid-coordinate formulation is proposed, which is suitable for flexible multibody systems with large deformation. On the basis of exact strain–displacement relation, equations of motion for flexible multibody system are derived by using virtual work principle. A matrix separation method is put forward to improve the efficiency of the calculation. Agreement of the present results with those obtained by absolute nodal coordinate formulation (ANCF) verifies the correctness of the proposed formulation. Furthermore, the present results are compared with those obtained by use of the linear model and the low-order approximate nonlinear model to show the suitability of the proposed models. The project supported by the National Natural Science Foundation of China (10472066, 50475021).  相似文献   

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4.
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   

5.
王剑  赵国忠  张洪武 《力学学报》2007,39(5):618-625
板壳结构作为航空、航天工程以及控制系统中的重要工作元件,在工作状态 中,要承受机械载荷、温度载荷、冲击载荷等各种负面影响, 而航空航天部件对结构形状变化非常敏感,如飞行器机翼、信息接收天线等结构, 微小的结构变形就会引起很大的性能改变,想要在设计初始阶段充分考虑所有不 利因素的影响显然是比较困难的. 利用压电材料控制结构变形往往是现代空间结 构开关控制中一个很好的选择. 基于一般壳体有限单元法, 推导了空间任意曲壳 压电单元, 利用约束方程连接主体壳元和压电壳元, 模型中约束方程的使用大大 减少了结构自由度, 使得计算速度有了明显的提升. 在此基础上, 重点研究了压 电曲壳结构的形状控制方法, 首先利用最小二乘法优化结构的电压分布, 控制结 构形状接近最优工作状态; 其次构建了以压电壳元厚度和电压联合作为设计变量 的优化控制模型, 采用非线性优化求解方法, 取得了更好的控制效果. 数值算例 表明了该文计算模型、 优化设计和控制方法的有效性.  相似文献   

6.
This paper aims the nonlinear aeroelastic analysis of slender wings using a nonlinear structural model coupled with the linear unsteady aerodynamic model. High aspect ratio and flexibility are the specific characteristic of this type of wings. Wing flexibility, coupled with long wingspan can lead to large deflections during normal flight operation of an aircraft; therefore, a wing in vertical/forward-afterward/torsional motion using a third-order form of nonlinear general flexible Euler–Bernoulli beam equations is used for structural modeling. Unsteady linear aerodynamic strip theory based on the Wagner function is used for determination of aerodynamic loading on the wing. Combining these two types of formulation yields nonlinear integro-differentials aeroelastic equations. Using the Galerkin’s method and a mode summation technique, the governing equations will be solved by introducing a numerical method without the need to adding any aerodynamic state space variables and the corresponding equations related to these variables of the problem. The obtained equations are solved to predict the aeroelastic response of the problem. The obtained results for a test case are compared with those of some other works and show a good agreement between results.  相似文献   

7.
The nonlinear deformation and atomization of a rotating column is considered using an axisymmetric boundary element formulation. Swirl has been considered by superposing a potential vortex to the bulk flow of the jet. The resulting model has been shown to reproduce the classical linear result due to Ponstein and parametric studies are conducted in the nonlinear regime to determine wave shapes and droplet sizes. As with prior nonlinear column breakup studies, results indicate that satellite drops are formed from the main wave under virtually all conditions. The ratio of the main drop to satellite drop diameter is shown to be remarkably constant over a variety of wave numbers/column lengths thereby providing a potential approach to produce tightly controlled bimodal sprays.  相似文献   

8.
A wide variety of mechanical and structural multibody systems consist ofvery flexible components subject to kinematic constraints. The widelyused floating frame of reference formulation that employs linear modelsto describe the local deformation leads to a highly nonlinear expressionfor the inertia forces and can be applied to only small deformationproblems. This paper is concerned with the formulation and computerimplementation of spatial joint constraints and forces using the largedeformation absolute nodal coordinate formulation. Unlike the floatingframe of reference formulation that employs a mixed set of absolutereference and local elastic coordinates, in the absolute nodalcoordinate formulation, global displacement and slope coordinates areused. The nonlinear kinematic constraint equations and generalized forceexpressions are expressed in terms of the absolute global displacementsand slopes. In particular, a new formulation for the sliding jointbetween two very flexible bodies is developed. A surface parameter isintroduced as an additional new variable in order to facilitate theformulation of this sliding joint. The constraint and force expressionsdeveloped in this paper are also expressed in terms of generalizedCholesky coordinates that lead to an identity inertia matrix. Severalexamples are presented in order to demonstrate the use of theformulations developed in the paper.  相似文献   

9.
This study focuses on the relative importance of two sources of nonlinearities affecting submerged cable response. The first of these is the added fluid damping offered by the surrounding medium while the second is the geometric stiffening offered by the cable through finite extensions of its centerline. The contribution of each nonlinear effect, taken separately and in tandem, is evaluated herein through the study of structural waves that form in the (out-of-plane) direction normal to the cable equilibrium plane.Numerical solutions are pursued herein using a finite difference algorithm which is brought to bear on two nonlinear cable/fluid models including: (1)~a nonlinear submerged cable model in which hydrodynamic drag is the sole nonlinear mechanism (referred to herein as the 'nonlinear drag model'); and (2)~a nonlinear submerged cable model in which hydrodynamic drag and geometric stiffening are both active nonlinear mechanisms (the 'nonlinear elastic-drag model'). Numerical solutions for propagating cable waves are developed for the case of a long suspension subjected to a concentrated harmonic excitation source. Conclusions are subsequently drawn regarding the spatial decay of the resulting out-of-plane waves and the dynamic cable tension induced by these waves. The effect of these two nonlinear mechanisms is further explored through the analysis of two additional, linear models: (3)~a simple linear taut string model without drag (the 'simple model'); and (4)~a linear taut string model with linear drag (the 'linear drag model'). The results of all models are critically compared and the range of validity of the linear/cable fluid models are assessed.  相似文献   

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