中厚圆柱壳自由振动的动力刚度法分析

该文阐述了将动力刚度法应用于中厚圆柱壳的自由振动分析。从考虑横向剪切变形和转动惯量的中厚壳理论出发,将圆柱壳的振动分解为一系列确定环向波数下的一维振动问题。用常微分方程求解器COLSYS求解该一维问题的动力刚度,通过Wittrick-Williams算法及导护型牛顿法求得该环向波数下结构的频率和振型。由于求解动力刚度时使用COLSYS对控制方程进行了精确求解,所以该文方法是精确方法。数值算例验证了中厚圆柱壳壳段固端频率计数J0计算方法的可靠性。综合表明：应用动力刚度法对中厚圆柱壳自由振动进行分析是可靠、精确的。     

动力刚度法求解平面曲梁面外自由振动问题

该文将动力刚度法应用于平面曲梁面外自由振动的分析。通过建立单元动力刚度所满足的常微分方程边值问题,用具有自适应求解功能的常微分方程求解器COLSYS 进行求解,获得单元动力刚度的数值精确解。以COLSYS 求解单元动力刚度的网格作为单元上固端频率计数求解的子网格,由单元动力刚度的边值问题解答线性组合出该子网格下各子单元的动力刚度,由Wittrick-Williams 算法获得单元固端频率的计数。从而实现整体结构的Wittrick-Williams频率计数。通过建立单元动力刚度对频率的导数所满足的常微分方程边值问题,调用COLSYS求其数值精确解,并将其引入导护型牛顿法,可迅速求得结构精确的频率和振型。数值算例表明,该文方法准确、可靠、有效。     

求解杆系结构自由振动问题的力法

杆系结构的静力分析有两类方法——力法和位移法,而自由振动分析却仅有位移法。针对这一缺失,提出杆系结构自由振动的力法分析方法。通过放松某个位移约束并施加相应的动内力来建立力法的基本体系。当动内力的频率等于结构自振频率时被放松的约束位移重新得到满足,此时基本体系与原结构等价,由此建立力法的控制方程。该控制方程为频率的非线性方程,对该方程的求解建立了Newton法的迭代格式。数值算例表明该法是一个精确、高效、实用的方法。     

柱壳自由振动的渐近分析

本文应用奇异摄动原理,研究了闭合截面柱壳的自由振动问题。文中给出了闭合截面柱壳自振频率的一般计算渐近表达式。最后本文对椭园截面柱壳给出了具体的计算结果。     

复合材料纵横加筋圆柱壳自由振动分析

使用能力法分析了两端简支复合材料纵横加筋圆柱壳的自由振动特性,从Love’s理论出发,分别计算壳体面板和纵横加筋结构的应变能和动能,在计算加筋结构应变能和动能时,将加筋结构的作用影响平均在整个壳体区域。然后代入Lagrange方程得到频率方程。通过比较,计算方法所得到的结果与文献比较吻合。采用平均法计算的结果比采用离散方法计算的结果偏小。还研究了壳体和加筋结构参数的变化对圆柱壳自由振动频率的影响。     

带有弹簧-质量-圆柱壳耦合结构自由振动分析

采用子结构导纳法研究了简支边界条件下带有多根弹簧-集中质量-圆柱壳耦合结构的自由振动。根据已有结果,通过求解多根弹簧等效刚度的推导思路,采用柔度法得到各子结构矩阵元素的柔度系数,进而求得集中质量带有多根弹簧的圆柱壳耦合结构自振频率及模态理论公式,并与已有文献结果作对比,证明了本文理论推导的正确性。应用本文理论方法进一步求解了集中质量带有三根弹簧圆柱壳耦合结构的自振频率及振型,并与建立的ANSYS有限元模型分析结果作对比,二者结果误差很小,可以忽略,再次验证本文理论的合理性及正确性。     

壁厚不连续不对称圆柱壳和开口壳的自由振动分析

视壁厚不连续不对称的圆柱壳或开口壳为层合壳。以弹性力学中的Hamilton正则方程为基础,分别应用Hamilton正则方程的半解析法构建层合壳每一层的线性方程。考虑到每两层连接界面上应力和位移的连续性,联立各层的方程得到系统的控制方程和特征方程。主要的优点是系统的控制方程不限制圆柱壳的厚度,数学模型和数值方法也适应分析壁厚不连续且壁厚不对称的复合材料层合壳问题。     

变厚度旋转圆柱壳的自由振动研究

为了提高旋转圆柱壳结构的使用性能和工作效率,减轻其质量已成为有效方式之一,针对这一需求,旋转圆柱壳结构有设计为厚度沿轴向变化即变厚度的趋势。基于此,利用Chebyshev-Ritz方法,对厚度沿轴向有3种线性变化形式的变厚度旋转圆柱壳的自由振动进行研究。考虑科氏力与离心力的影响,基于Sanders壳理论,将圆柱壳的位移场近似展开为Chebyshev多项式与边界函数乘积的形式,计算变厚度旋转圆柱壳的动能与势能,再根据Ritz方法获得变厚度旋转圆柱壳的频率方程。在此基础上,将所得结果与已有文献中的结果进行比较,验证了建模方法的准确性,并对计算结果进行了收敛性研究。最后比较了不同厚度变化形式下旋转圆柱壳的自由振动,并讨论了转速、厚度变化参数、圆柱壳长径比等参数对变厚度旋转圆柱壳自由振动的影响。     

厚截锥壳结构的自由振动

本文对基于Mindlin理论所导出的厚截锥壳的一阶基本微分方程组采用了子结构离散变量法,求解了这类结构的固有频率和相应的振型。文中给出了算例,其结果与试验结果和有限无法计算结果相比是令人满意的。     

Free vibration analysis of sandwich beams using improved dynamic stiffness method

In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied.     

简支边界条件下超椭圆蜂窝夹芯板的自由振动

基于Reddy三阶剪切板理论,将铝基蜂窝芯层等效为一正交异性层,等效弹性参数由修正后的Gibson公式得出,对简支边界条件下超椭圆蜂窝夹芯板弯曲振动的固有频率进行了理论推导,应用具体算例与实验值和有限元计算结果进行了验证,结果表明本文方法具有较高的计算精度。研究了板宽、板厚和芯层胞元结构参数对简支边界条件下超椭圆蜂窝夹芯板固有频率的影响,并绘出相应的曲线图,该曲线图对超椭圆蜂窝夹芯板的工程应用具有指导意义。     

High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method

In this paper, high-order free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness method. The governing partial differential equations of motion for one element are derived using Hamilton’s principle. This formulation leads to seven partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are divided into two ordinary differential equations by considering the symmetrical sandwich beam. Closed form analytical solutions of these equations are determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. The element dynamic stiffness matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by use of numerical techniques and the known Wittrick–Williams algorithm. Finally, some numerical examples are discussed using dynamic stiffness method.     

两自由度椭圆柱体涡激振动的数值模拟

摘要：利用作者编制的基于松耦合方法求解气动弹性问题的程序,对高雷诺数条件下椭圆柱体的涡激振动进行了数值模拟。椭圆柱体的长短轴比接近2,来流和长轴垂直。数值结果表明：尽管椭圆柱体在横向和流向的动力参数不同,结构振动仍以横向振动为主;和圆柱以及方柱一样,两自由度椭圆柱体的涡激振动同样存在流向锁定和横向锁定,并且随着折减风速的增大,旋涡脱落模式从异相2S变化为同相2S。     

Free vibration analysis of thick laminated plates using a mixed finite element

Abstract

A mixed finite element scheme based on assumed local high‐order displacements is proposed for the free vibration of thick laminated plates. The effects of transverse shear deformation, transverse normal stress and rotary inertia are considered in the formulation. Cross‐ply laminates with simple supports and angle‐ply laminates with clamped edges are presented as examples. The three dimensional elasticity solutions of cross‐ply laminates with simple supports are used to assess the accuracy of the present scheme. The effects of the span‐to‐thickness, aspect and material anisotropy ratio on the fundamental natural frequency are investigated. The present results are compared with the results in the published literature, and agree closely with the 3‐D elasticity solutions.     

圆锥壳-圆柱壳-球壳组合结构自由振动分析

基于Reissner薄壳理论,采用区域分解法分析了不同边界条件下圆锥壳-圆柱壳-球壳组合结构的自由振动。首先在壳体连接处将组合壳体分为独立的圆锥壳、圆柱壳和球壳,并将各个子壳体沿旋转轴线分解为若干自由壳段;然后将所有壳段分区界面(包括边界界面)的位移协调方程通过分区广义变分和最小二乘加权残值法引入到组合壳体的能量泛函中;最后将壳段位移场变量的周向分量和轴向分量分别以Fourier级数和Chebyshev多项式展开,通过变分后得到整个组合壳体的离散动力学方程。将区域分解法计算结果与有限元软件ANSYS计算结果进行对比,验证了区域分解法在分析圆锥壳-圆柱壳-球壳组合结构自由振动的正确性和计算精度,并分析了组合壳体长径比及厚径比对自由振动频率的影响。     

Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method

This paper mainly Presents free vibration analyses of metal and ceramic functionally graded plates with the local Kriging meshless method. The Kriging technique is employed to construct shape functions which possess Kronecker delta function property and thus make it easy to implement essential boundary conditions. The eigenvalue equations of free vibration problems are based on the first-order shear deformation theory and the local Petrov–Galerkin formulation. The cubic spline function is used as the weight function which vanishes on internal boundaries of local quadrature domains and hence simplifies the implementation. Convergence studies are conducted to examine the stability of the present method. Three types of functionally graded plates – square, skew and quadrilateral plates – are considered as numerical examples to demonstrate the versatility of the present method for free vibration analyses.     

厚/薄板振动分析的样条无单元法

建立了厚/薄板振动分析的样条无单元法计算格式,对整个求解区域仅需少量的结点离散,无需单元分划,把挠度和剪应变作为全局的场变量,采用双向三次B样条基函数乘积的线性组合构造场函数,可以充分发挥无单元法及三次B样条基函数的优点。计算结果表明该方法适用于不同厚度,不同边界的板的动力特性分析,无剪切闭锁现象,且精度高,收敛快,未知量少,程序简便。