轴向运动薄板非线性振动及其稳定性研究

应用增量谐波平衡法(IHB法)研究轴向运动薄板横向非线性振动特性及其稳定性.通过Hamilton原理推导出了非惯性参考系下四边简支轴向运动薄板的横向振动微分方程,然后利用Galerkin方法离散运动方程.对离散后的非线性方程组应用IHB法进行非线性振动分析,研究了在固有频率之比ω20/ω10接近于3:1情况下,外激励频率ω在ω10附近的具有内部共振的基谐波响应.最后用多元Floquet理论分析了系统周期解的稳定性,其中采用Hsu方法来计算转移矩阵.通过对具体例子的数值计算,分别得到了自由振动和不同外激励下的频幅相应曲线,通过对比运动梁模型和运动薄板模型的计算结果,分析了各种模型的适用范围.     

采用人工神经网络求解薄板的自由振动问题

本文提出利用神经网络的非线性表示能力求解薄板的自由振动问题,分析了标准的ＢＰ算法及多种改进措施,采用动量法和自适应调整学习率的ＢＰ算法求解,比较几种计算方法的计算结果,表明采用人工神经网络计算薄板自由振动问题方法可行,结果令人满意     

四边简支矩形薄板的双Hopf分岔分析

基于奇异性理论,研究了主参数共振-1∶3内共振情形下参数激励与外激励联合作用下四边简支矩形薄板的双Hopf分岔问题.考虑弱阻尼和弱激励的情形,得到了四边简支矩形薄板的分岔方程,给出了四边简支矩形薄板在参数平面μ-σ1上的分岔图.对参数激励与外激励联合作用下四边简支矩形薄板的阻尼系数、外激励、参数激励以及调谐参数进行不同的取值,通过数值模拟得到了四边简支矩形薄板平衡解将发生Hopf分岔,并分岔出周期解,薄板系统的非线性振动形式为周期运动.当四边简支矩形薄板的参数满足给定条件时,我们得到薄板的1∶3共振双Hopf分岔.随后,四边简支矩形薄板将会呈现概周期振动.     

采用人工神经网络求解薄板的自动振动问题

本文提出利用神经网络的非线性表示能力求解薄板的自由振动问题,分析了标准的ＢＰ算法及多种改进措施,采用动量法和自适应调整学习率的ＢＰ算法求解,比较几种计算方法的计算结果,表明采用人工网络计算薄板振动问题方法可行,结果令人满意。     

参数激励和外激励联合作用下薄板的非线性动力学

研究了在参数激励和外激励联合作用下四边简支矩形薄板的非线性动力学.基于von Karman理论,推导出了在参数激励和外激励联合作用下四边简支矩形薄板的动力学方程.利用Galerkin法对偏微分方程进行三阶离散,得到一个三自由度的常微分方程.考虑1:2:4内共振-主参数共振-1/2亚谐共振的情况,利用多尺度法得到了薄板系统的六维的平均方程.最后,采用数值方法研究了薄板的周期和混沌运动.结果发现外激励对薄板的混沌运动是敏感的.     

非线性损伤粘弹性薄板准静态力学行为分析

基于损伤粘弹性材料的一种卷积型本构关系和大挠度薄板的yon Kdrman假设,给出了损伤粘弹性薄板准静态问题的数学模型,其控制方程为一组非线性积分-偏微分型方程．采用Galerkin截断技术,将原积分-偏微分系统化为积分系统．然后采用四阶的Runge-Kutta法在数值上得到了损伤粘弹性薄板的准静态问题的解．     

多数据项广播调度策略

多数据项广播是移动计算环境中一种重要的数据访问方式.为减少用户的平均访问时间和响应最多事务请求,提出了一种新的多数据项广播调度策略.调度策略分为两个阶段,第一阶段根据各事务包含的数据项数目和对重复申请数据项的处理选择事务请求;第二阶段对已选择的事务请求用QEM算法进行调度.实验结果表明,它比现有的QEM算法有更高事务调度成功率和更短的平均访问时间.     

子弹击穿飞机薄板结构的损伤预测研究

为对子弹击穿飞机薄板后的损伤尺寸进行预测.利用ANSYS/LS-DYNA建立了子弹击穿飞机薄板的有限元模型,仿真计算得到了薄板的损伤形貌及尺寸.根据实验结果对比验证了该模型的有效性.采用支持向量机回归算法构建损伤尺寸的预测模型,通过选择不同的核函数及参数.分析了薄板弹孔最大径向尺寸的预测精度,得到了较为理想和具有一定实际应用价值的预测模型.     

电磁与机械载荷作用下导电梁式板的超谐波共振

研究了电磁与机械载荷共同作用下梁式薄板的非线性超谐波共振问题．在给出薄板的电磁弹性运动基本方程及电磁力表达式的基础上,推得了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程;应用伽辽金积分法,进一步导出了相应的非线性振动控制微分方程．采用多尺度法进行求解,得到了稳态运动下的幅频响应方程．最后,通过算例,给出了相应的幅频响应曲线图和时间历程图,分析了板厚、磁场及激励幅值对系统振动的影响．     

弹性薄板绕轴转动时刚-柔耦合动力学非线性分析

从连续介质力学中关于弹性薄板的变形理论出发,讨论绕轴作大范围运动的弹性薄板的动力学性质.由于在无大范围运动的情况下,弹性薄板的变形对系统的动力学性质影响很小而被忽略,而其一旦与大范围运动耦合,对系统的动力学性质产生明显的影响.根据弹性薄板的应变-位移几何非线性关系,建立了作大范围运动弹性薄板的几何非线性动力学方程,然后利用Garlerkin模态截断方法建立了该系统的离散动力学方程,仿真计算验证了理论分析的正确性,从而表明了系统的横向振动是稳定的.     

Field/boundary element approach to the large deflection of thin flat plates

The problem of large deflections of thin flat plates is rederived here using a novel integral equation approach. These plate deformations are governed by the von Karman plate theory. The numerical solution that is implemented combines both boundary and interior elements in the discretization of the continuum. The formulation also illustrates the adaptability of the boundary element technique to nonlinear problems. Included in the examples here are static, dynamic and buckling applications.     

Lattice Boltzmann model for elastic thin plate with small deflection

In this paper, a lattice Boltzmann model for solving problems of elastic thin plate with small deflection is proposed. In order to recover the Sophie–Germain equation for elastic thin plate by lattice Boltzmann method, we transform the equation into a set of Poisson equations. Two sets of distribution functions are employed in the lattice Boltzmann equation to recover the Poisson equations. Based on this model, some problems on the rectangular elastic thin plate with small deflection are simulated. The comparisons between the numerical results and the analysis solutions are given in detail. The numerical examples show that the lattice Boltzmann model can be used to solve problems of the elastic thin plate with small deflection.     

Geometrically nonlinear analysis of a Reissner type plate by the boundary element method

The boundary element method is used in the geometrically nonlinear analysis of laterally loaded isotropic plates taking into account the effects of transverse shear deformation. This paper presents the general equations for finite deformation of a Reissner type plate, and also gives an integral formulation of the Von Kármán type nonlinear governing equations which involve coupling between in-plane and out-of-plane deformation. The boundary and the domain of the plate are discretized to solve nonlinear plate bending problems. All unknown variables are at the boundary. An iterative procedure is applied to achieve linearization of the nonlinear equations. Some numerical results of the computation are compared with the analytical solutions and other numerical techniques, and good agreement is obtained.     

基于塑性修正系数的矩形薄板屈曲计算方法

为探究薄板的屈曲破坏性能,以飞机机身设计中最常用的铝合金薄板结构为研究对象,利用金属材料塑性修正系数分析矩形薄板的屈曲失效,得到在均布压力和不同约束条件下矩形薄板的临界屈曲应力。数值仿真算例及其有限元计算结果对比,验证该方法的正确性。     

A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

The nonlinear sine-Gordon equation arises in various problems in science and engineering. In this paper, we propose a numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation. The proposed scheme is based on using collocation points and approximating the solution employing the thin plate splines (TPS) radial basis function (RBF). The new scheme works in a similar fashion as finite difference methods. Numerical results are obtained for various cases involving line and ring solitons.     

A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates

A simple displacement-based 3-node, 18-degree-of-freedom flat triangular plate/shell element LDT18 is proposed in this paper for linear and geometrically nonlinear finite element analysis of thin and thick laminated composite plates. The presented element is based on the first-order shear deformation theory (FSDT), and the total Lagrangian approach is employed to formulate the element for geometrically nonlinear analysis. The deflection and rotation functions of the element boundary are obtained from the Timoshenko’s laminated composite beam functions, hence convergence to the thin plate solution can be achieved theoretically and shear-locking problem is avoided naturally. The plane displacement interpolation functions of the Airman’s triangular membrane element with drilling degrees of freedom are taken as the in-plane displacements of the element. Numerical examples demonstrate that the present element is accurate and efficient for linear and geometrically nonlinear analysis of thin to moderately thick laminated composite plates.     

A finite element method for the free vibration of plates allowing for transverse shear deformation

An isoparametric quadrilateral plate bending element is introduced and its use for the free vibration analysis of both thick and thin plates is examined. Plates of rectangular planform and of orthotropic materials are analysed and excellent results are obtained. The element performance is assessed by comparison with well established analytical and numerical solutions based on Mindlin's thick plate theory, three dimensional elasticity solutions and solutions based on thin plate theory. The ease with which the element may be implemented is stressed. The use of an eigenvalue economiser which produces considerable economy in the computer solution is demonstrated. Various mass lumping schemes and numerical integration rules used in the construction of the element mass matrix are also examined.     

Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

An asymptotic perturbation method is presented based on the Fourier expansion and temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported angle-ply composite laminated rectangular thin plate with parametric and external excitations.According to the Reddy's third-order plate theory,the governing equations of motion for the angle-ply composite laminated rectangular thin plate are derived by using the Hamilton's principle.Then,the Galerkin procedure is applied to...