圆板非线性振动有限元分析的一种迭代方法

同时考虑横向振动和板平面内的运动,用3节点有限元研究均匀圆板的轴对称大振幅非线性振动,构造了一个避免发散加速收敛的平均迭代法,并将计算结果与文献的已有结果做了比较。     

二自由度结构受迫非线性振动响应的数值计算

本文研究了由飞机尾部简化而成的二自由度结构受迫非线性振动,由于对复杂的运动方程不作进一步简化,方程中含有强非线性耦合项,首先采用数字滤波技术对系统受确定性激励的响应进行了计算;然后在数字模拟计算的基础上用嫁接的ITO积分方法对系统受随机白噪音激励的响应进行了计算。结果表明,ITO积分的综合嫁接方法有更高的计算效率,结果并表明系统的非线性耦合部分对响应有重大影响,是不能加以忽略的,本文的研究为多自由度非线性结构的响应计算提供了有用的思想和方法。     

强非线性问题的一类能量迭代方法

基于能量原理，引进迭代及最小二乘，研究完全强非线性自治系统的周期解及其稳定性，算例表明，该法精度较高。     

带压电层的混合层合板的自由振动和动力响应

基于Reddy高阶剪切变形理论和广义Kármán型方程,用双重Fourier级数展开法求得了四边简支带压电层的混合层合剪切板的自由振动及动力响应的解析解,分析中考虑了热/机/电荷载共同作用,并讨论了温度变化、控制电压、铺层方式对固有频率及动力响应的影响。     

参数振动自由响应的指数三角级数逼近

研究了单自由度参数振动系统自由响应的指数三角级数逼近问题。根据系统调制反馈的概念,将自由振动响应表示为振荡频率与参数激励频率的线性组合。应用谐波平衡,将参数振动方程转化成无限阶线性代数方程组;从非零解条件给出特征方程,应用数值解得到振荡频率;采用逆矩阵运算,给出自由响应通解;结合初始条件确定自由响应。将文中的逼近方法与龙格-库塔法进行了对比,研究结果表明:两种算法的时域响应、响应相图具有较高的一致性,其中两种方法计算得到的均方根值误差为0.14%,可以忽略不计。本文提出的方法在以下方面具有优势:1与龙格-库塔法相比,本文用数学表达自由响应,有利于剖析参数振动自由响应的动力学性质,当参数指数为0.3的情况下,龙格-库塔法最大计算误差为1.5443,本文方法最大计算误差为9.911×10~(-9),计算精度上明显优于龙格-库塔法;2振动响应解的指数三角级数表达可以为工程应用,如为飞机机翼涡轮发动机的振颤运动提供方便的分析工具。     

圆柱壳的非线性自由振动分析

本文分析了各向同性封闭圆柱壳的非线性自由振动。文中采用经典的非线性弹性力学方法推导了圆柱壳的大振幅运动方程,这些方程的静态形式与冯·卡门的板理论方程具有同样的精度。文中讨论了四种基本振动模态,并且还以数学公式的形式给出了一般的最终结果,一些例子以曲线给出结果,并进行了比较。结果还表明线性振动可以作为非线性振动的一种特例。     

四边自由的矩形厚板的自由振动

由于要满足自由边的条件,使得本文所研究的板的分析相当困难。本文采用叠加法完满的解决了这个不易克服的困难,并使得边界条件能满足到任意精度,所取的位移解的每一项都严格满足控制微分方程。     

弹性体非线性振动多重共振的能量法

本论文以非线性振动理论的平均法为基础和力学的能量概念结合起来,找到了求解弹性体系非线性振动多重共振的能量法。应用本方法研究了电机轴系的双重共振等问题,证明了它是一个简易适用的方法。揭示了双重共振的一些新现象,理论得到了实验验证。     

折线型非线性振动响应计算的时域有限元分段求解

本文研究折线型非线性振动系统响应的求解,按分段线性性质建立了分段线性的时域有限元离散模型。在求解中先计算当前段的振动响应,根据转折条件判断是否存在转折点。当存在多个转折点时,以最早出现的转折点作为下一段的起始点,否则以本时间段终点作为下一段的起始点,然后进入下一段的计算。本文方法能在每一段较精确地求出转折点,并同时给出该转折点之前各结点的响应解。较有效地解决了这类问题的数值求解。文中算例给出了相当精确的计算结果,验证了本文方法的有效性。     

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.     

Stationary points iteration method for periodic solution to nonlinear system

The value method which is used to obtain the periodic solution to nonlinear system is mentioned in this article. Different point reflection is defined in the nonlinear autonomous and nonautonomous system firstly and then that linear reflection obtained from the inserting value of nonlinear reflection is asymptotic to original nonlinear reflection. The stationary points obtained by linear reflection are regarded as the asymptotic solution of the stationary points of original system. If this asymptotic solution of the stationary points is not satisfactorily accurate it can be used as the initial point of the next reflection. In addition, a corresponding method of researching the stability of periodic solution is put forward in this article.     

不确定非线性结构动力响应的区间分析方法

研究多自由度非线性不确定参数系统的动力响应问题. 以区间数学为基础,将不确定 性参数用区间进行定量化,借助一阶Taylor级数,给出了近似估计非线性振动系统动力响 应范围的区间分析方法. 从数学证明和数值算例两方面,将其与概率摄动有限元法进行了比 较,结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点.     

An efficient iteration algorithm of mixed boundary/finite element method and application to free torsional vibration analysis of bodies of revolution

In this paper,the general formulation of a new proposed iteration algorithm of mixedBEM/FEM for eigenvalue problems of elastodynamics is described.Approximatefundamental solutions of elastodynamics are adopted in the normal mixed BEM/FEMequations.The accuracy of solutions is progressively improved by the iteration procedure.Not only could the awkwar dness of non-algebraic eigenvalue equations be avoided but alsothe accuracy of numerical solutions is almost independent of the interior meshing.All thesegive many advantages in numerical calculation.The algorithm is applied to free torsionalvibration analysis of bodies of revolution.A few cases are studied.All of the numericalresults are very good.     

Quasi-Green’s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green’s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi-Green’s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob-lem. The mode shape differential equations of the free vibration problem of a simply-supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa-tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green’s function method.     

转子—非线性支承系统振动响应的优化计算

本文用一种新的优化方案计算装有非线性弹性支承－挤压油膜阻尼器的转子系统的振动响应。首先根据转子系统的结构特点，建立其无量纲形式的非线性运动微分方程；然后由微分方程构造－控制目标函数，最后对此目标函数进行优化计算，求得转子系统的振动响应。     

变截面欧拉梁自由振动分析的重采样微分求积法

采用重采样微分求积法求解了变截面欧拉梁的自由振动问题。推导了变截面梁的控制方程离散格式,采用重采样矩阵方法对边界条件进行处理,给出了变截面梁自由振动算法。采用本文方法对不同类型截面形式和不同边界条件的变截面梁进行自由振动分析,并和其他解法进行比较。计算结果表明,本文方法可以适用于不同变截面类型和不同边界条件,计算精度与解析解吻合良好,具有良好的收敛性能。在同等精度条件下网格点数少于现有计算方法。重采样转换矩阵边界处理方法相比于传统边界处理方法具有更快的收敛性能。     

The application of reduced space harmonic balance method for the nonlinear vibration problem in rotor dynamics

The reduced space harmonic balance method is demonstrated to find the maximum vibration responses of rotor systems. Within the reduced space SQP method, transition from the high dimensional optimization space to the desired reduced space is accomplished by resorting to the null space decomposition technique, resulting in the elimination of the harmonic balance constraints. Numerical examples of rotor systems are presented to show the applicability of the proposed methodology.     

Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam

The quadrature method (OM) has been used in structural analysis only in recent years. In this study, OM is applied to flexural vibration analysis of a geometrically nonlinear beam. The numerical results by OM agree with the results by the finite element method. It is believed that this is the first attempt to solve a nonlinear dynamic problem by the quadrature method.     

幂律全塑性罚函数随机有限元

用罚函数有限元方法解决平面应变下的体积下可压缩问题,应用摄动有限元理论发展幂律全塑性随机有限元,并以弹性模是E,泊松比u和节点坐标等的基本随机变量,推导有限元列式,给出单板受拉,梁受弯的算例。