基于初应力法的作大范围运动柔性梁动力学建模理论研究

研究了初应力法的作大范围运动柔性梁的建模理论.根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性梁进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性梁刚-柔耦合动力学方程.从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程.通过引入准静态概念,把其结构动力学方程转化为准静态方程.对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项.并对此非惯性系下作大范围运动柔性梁的结构动力学方程进行数值仿真,对零次近似模型、一次近似模型、初应力法动力学模型的仿真结果进行分析,揭示三种模型的动力学性质的差异.     

做大范围运动复合材料板的动力学建模研究

基于经典层合板理论建立了大范围运动复合材料板的动力学方程,考虑了传统建模方法忽略的二次耦合变形量。采用有限元法对复合材料板进行离散,利用Lagrange方法推导了大范围运动复合材料板的动力学方程。通过编制matlab程序计算了带中心刚体的旋转复合材料板的变形,将得到的结果分别与不计耦合变形量的传统方法的计算结果进行比较,随着转速的提高,本文方法收敛,而传统方法趋于发散。研究了铺层角度对作大范围运动复合材料板变形影响以及复合材料板和各向同性板在经历相同运动时角点最大变形的差异。     

作旋转运动功能梯度材料矩形Mindlin板的刚柔耦合动力学建模1)

研究了作大范围运动功能梯度材料矩形板的刚柔耦合动力学问题。从连续介质力学理论出发,基于Mindlin板理论,采用无网格径向基点插值法(radial point interpolation method,RPIM)对矩形板变形场进行离散,考虑柔性板变形位移中二阶非线性耦合变形量,即横向弯曲引起的纵向缩短量,运用第二类拉格朗日方程推导了大范围运动功能梯度材料板的刚柔耦合动力学方程。分别采用一次近似耦合模型和传统零次近似耦合模型对不同转速下的功能梯度悬臂板进行了仿真,结果说明随着转速的提高,传统零次模型将发散,而一次近似模型依然收敛。将仿真结果与假设模态法和有限元法对比,验证了本文基于RPIM建立的动力学模型的正确性及在同等计算条件下的优越性。研究了功能梯度指数对作旋转运动的功能梯度矩形板动力学特性的影响。结果表明,随着功能梯度指数的增大,板的横向变形增大,且固有频率随之减小,说明功能梯度指数的增大会使系统柔性增加。同时,对中心刚体-功能梯度悬臂板的自由振动频率转向现象进行了讨论。     

作大范围运动弹性梁刚—柔耦合动力学建模

利用弹性梁的变形理论和 Hamilton力学原理对作大范围运动弹性梁的刚 -柔耦合动力学建模理论进行了研究。分析了大范围运动对弹性梁的横向振动和纵向振动的影响 ,得到了大范围运动与弹性梁的中线耦合变形之间的耦合作用对该系统动力学性质有显著的影响 ,从而提出了作大范围运动弹性梁的刚柔耦合动力学模型     

活力板运动的动力学分析

作为一种特殊的滑板运动,活力板依靠乘员自身的摆动和扭动前进. 本文分析活力板运动的动力学原理. 当乘员的动作引起前后板的周期性摇摆时,地面对轮缘的摩擦力可产生向前的推动效应. 导出推力平均值的计算公式, 并解释蛇形轨迹的产生原因.     

作大范围回转运动柔性梁斜碰撞动力学研究

为正确估计由于碰撞引起的多柔体系统动力学特性的变化,针对作大范围回转运动的柔性梁与一固定斜面发生斜碰撞的情况,在考虑刚柔耦合效应的多柔体系统动力学建模理论的基础上,利用假设模态法建立起重力场作用下的柔性梁一致线性化动力法向碰撞过程中系统的动力行为。基于Ｈｅｒｔｚ接触理论和非线性阻尼项建立法向碰撞接触模型,基于线性切向接触刚度建立柔性梁切向碰撞接触模型,提出的数值算法保证了计算结果的合理性,给出的仿     

角支及多点支承矩形板的弯曲

本文取两对边简支另两对边自由的板为初始解,用迭加法在两边简支板上迭代消去板边上的剪力。为了简化消去板边剪力的复杂迭代过程,作者提出了高精度的简化方法,将无限迭代简化为一次计算,将角支板的求解化为计算两个对边简支矩形板的简单问题。对于多点支承矩形板,则可取角点支承板为基本结构用力法求解。文中还提出了一些实用经验公式,列出了典型算例,验证了方法的适用性和高精度。     

悬臂矩形板的对称弯曲与稳定性

运用弹性理论的里兹法,选择多项式和三角函数混合形式作为挠曲函数,讨论是悬臂形板的对称弯曲和稳定性问题,通过算例分析与比较,表明本文结果与文献基本吻合,且计算过程简单。     

功能梯度矩形板的非线性自由振动

研究了功能梯度矩形薄板的非线性自由振动问题.采用幂律分布规律描述功能梯度材料沿厚度的梯度性质,基于von Kámán理论,建立了功能梯度薄板的非线性振动控制方程.应用Bubnov-Galerkin法得到了功能梯度矩形薄板的单模态非线性振动的时域常微分方程,借助其势能函数分析了系统的周期振动状态.采用Lindstedt-Poincaré法和Runge-Kutta法分别获得了功能梯度矩形薄板单模态非线性周期振动的摄动解和数值解.研究表明:功能梯度薄板非线性振动控制方程中包含表征拉弯耦合效应的控制项,这导致其常微分方程中出现二次项;系统振幅在板横向的正负两个方向上是不相等的,其振动存在关于板中面的不对称性.     

Large deflection analysis of rectangular plates by combined perturbation and finite strip method

The perturbation method and finite strip method are combined to solve the largedeflection bending problems of rectangular plates.Perturbation method is used to reducethe nonlinear differential equations into a series of linear differential equations.The finitestrip method is then employed to tackle these linear equations.Some calculation examplesare compared with those got by other methods.     

EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES

IntroductionRecently,compositestructureshavereceivedwideapplicationsinmodernindustriesincludingastronavigation ,aviation ,petroleumandchemicalindustry ,etc.However,thiskindofmaterialsgenerallyhavethepropertiesofviscoelasticitywiththeapparentcreepphenomenonandrelaxationbehaviors.Moreover,variousdamagewillemergeinthestructuresundertheactionofloading ,temperatureandenvironment.Damagemakesthemechanicalbehaviorsdeteriorategraduallybeforethefailure .Damageeffectswillsoftenthestiffnessofthestructure…     

Effects of initial geometric imperfections on dynamic behavior of rectangular plates

The present work deals with the influence of initial geometric imperfections on the dynamic behavior of simply supported rectangular plates subjected to the action of periodic in-plane forces. The nonlinear large-deflection plate theory used in this analysis corresponds to the dynamic analog of von Karman's theory. The temporal response is analyzed by the first-order generalized asymptotic method. The solution for the temporal equations of motion takes into account the possibility of existence of simultaneous forced and parametric vibrations. The results indicate that the presence of initial imperfections may significantly raise the resonance frequencies, cause the plate to exhibit a soft spring behavior and improve slightly the stability of the plate by reducing the area of its instability zones. Furthermore, the presence of initial imperfections induces forced vibrations which interact with parametric vibrations in order to generate a competitive hesitation phenomenon in the transition zone.     

Geometric nonlinear formulation and discretization method for a rectangular plate undergoing large overall motions

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.     

Construction of rectangular displacement-based element for thick/thin plates

In this paper, a method of constructing displacement-based element for thick/thin plates is developed by using the technique of generalized compatibility, and a rectangular displacement based element with 12 degrees of freedom for thick/thin plates is presented. This method enjoys a good accuracy with simple formulation and is free of shear locking as the thickness of the plate approaches zero. The project supported by National Natural Science Foundation of China through Grant No. 59208075     

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

NONLINEAR BENDING OF SIMPLY SUPPORTED RECTANGULAR SANDWICH PLATES

In this paper,fundamental equations and boundary conditions of the nonlinearbending theory for a rectangular sandwicl plate with a soft core are derived by meansof the method of calculus of variations.Then the nonlinear bending for a simplysupported rectangular sandwich plate under the uniform lateral load is investigated byuse of the perturbation method and a quite accurate analytic solution is obtained.     

Formulation of a semi-analytical approach based on Gurtin variational principle for dynamic response of general thin plates

4 semi-analytical approach for the dynamic response of general thin plates which employes finite element discretization in space domain and a series of representation in time domain is developed on the basis of Gurtin variational principles. The formulation of time series is also investigated so that the dynamic response of plates with arbitrary shape and boundary constraints can be achieved with adequate accuracy.Project supported by the National Natural Science Foundation of China