矩形板结构的振动响应分析

为了建立矩形板在弹性约束边界条件下的振动模型,采用横向位移弹簧、旋转约束弹簧和扭转约束弹簧三种类型的弹簧对模拟边界条件。矩形板结构的振动位移函数采用二维Fourier余弦级数加辅助级数的形式来描述,通过引入辅助项使矩形板结构的振动位移函数适用于任意弹性边界条件。结合Rayleigh-Ritz法和Mindlin理论得到矩形板结构在任意边界条件下振动响应的矩阵表达式。最后进行了数值仿真计算,研究了弹簧刚度变化时矩形板结构的响应规律。     

基于改进傅里叶级数法的环扇形板三维自由振动分析

基于三维弹性理论,采用改进傅里叶级数法(Improved Fourier Series Method,IFSM)对环扇形板三维自由振动进行了数值分析。环扇形板的位移函数表示为一种改进的三角级数形式,而边界条件则通过均匀分布在各边界面的线性弹簧来模拟,通过改变边界约束弹簧的刚度值来实现不同的边界条件。将位移函数的未知级数展开系数看作广义坐标,并采用瑞利-里兹法进行求解,得到一个关于未知系数的标准特征值问题。环扇形板结构的三维自由振动特性可以通过求解标准特征值问题简单获得。数值计算结果充分表明,文中采用改进傅里叶级数法分析环扇形板三维自由振动问题的有效性和正确性。     

载流线圈中导电圆板的磁弹性固有振动

针对处于平行共轴三线圈和球形载流线圈产生磁场中的导电圆板,基于Kirchhoff薄板理论,给出磁场中圆板的磁弹性横向振动基本方程。根据电磁理论,导出线圈产生均匀磁场区域中圆板所受电磁力的表达式。通过位移函数的设定并应用伽辽金法,得到圆板的磁弹性轴对称振动微分方程及固有频率的表达式。通过算例,绘制了周边夹支和简支两种边界条件下圆板的磁弹性固有振动特性曲线图,分析了两种边界条件下固有频率、阻尼比、电磁力矩随线圈载流强度、线圈匝数和板厚等参数的变化规律。     

正交各向异性矩形板面内自由振动分析

以正交各向异性矩形板结构为研究对象,采用改进傅里叶级数方法(Improved Fourier Series Method,IFSM)构建了任意边界条件下正交各向异性矩形板面内自由振动分析模型。面内振动位移容许函数被不变地描述为包含正弦项的改进三角级数形式,并能够有效解决在边界处存在的不连续或者跳跃现象。将未知级数展开系数看作广义坐标,基于Rayleigh-Ritz法推导了板结构面内振动特征方程,并通过求解一个标准特征值问题来获得面内自由振动特征参数。通过大量的数值算例,并与现有文献解和有限元方法结果对比来验证文中方法的正确性。     

弹性地基上转动功能梯度材料Timoshenko梁自由振动的微分变换法求解

基于Timoshenko梁理论研究弹性地基上转动功能梯度材料（FGM）梁的自由振动。首先确定功能梯度材料Timoshenko梁的物理中面,利用广义Hamilton原理推导出该梁在弹性地基上转动时横向自由振动的两个控制微分方程。其次采用微分变换法（DTM）对控制微分方程及其边界条件进行变换,计算了弹性地基上转动功能梯度材料Timoshenko梁在夹紧-夹紧、夹紧-简支和夹紧-自由三种不同边界条件下横向自由振动的量纲一固有频率,与已有文献的计算结果进行比较,退化后结果一致。最后讨论了不同边界条件、转速、弹性地基模量和梯度指数对功能梯度材料Timoshenko梁自振频率的影响。结果表明：功能梯度材料Timoshenko梁的量纲一固有频率随量纲一转速和量纲一弹性地基模量的增大而增大;在量纲一转速和量纲一弹性地基模量一定的情况下,梁的量纲一固有频率随着功能梯度材料梯度指数的增大而减小。     

旋转运动导电圆板磁气弹性横向振动分析

基于Kirchhoff薄板理论并应用哈密顿原理,建立旋转运动导电圆板的磁气弹性横向振动基本方程。根据电磁场基本原理并结合一种简化的气动模型,给出旋转运动圆板所受电磁力和气动载荷的表达式。运用伽辽金法进行积分,得到圆板的磁气弹性轴对称自由振动微分方程。通过算例,得到两种边界约束条件下圆板的固有振动特性曲线图,分析了固有频率随磁感应强度、板厚、气动力、旋转速度的变化规律,给出了临界阻尼下磁感应强度与板厚、气动力、旋转速度之间的关系曲线图并进行了分析。     

四边固支矩形薄板固有振动的理论计算和有限元分析

基于理论计算有限元方法分析了四边固支矩形板结构的自由振动问题,求得了四边固支矩形板的振动固有频率和振型。利用双向梁函数构造了四边固支矩形板的振型函数,并根据位移变分原理求得了矩形板的固有振动特性。在板单元理论的基础上,利用有限元法推导了薄板振动的质量矩阵和刚度矩阵。由于工程实际中只关心板结构振动的横向位移幅值,利用静力凝聚法将质量矩阵和刚度矩阵中转动自由度上的质量和刚度凝聚到横向振动自由度上,以达到降低模型阶目的,为板结构振动主动控制奠定基础。     

振动磨机环扇形激振板的横向振动与稳定性分析

振动磨机的磨粉效果与激振系统动力学响应有较大关系,其激振系统的横向振动和稳定性研究具有重要的理论意义.根据弹性薄板小挠度理论和哈密顿原理,建立振动磨机环扇形激振板的运动微分方程.采用微分求积法离散方程和边界条件,计算得到环扇形板前三(四)阶无量纲复频率随无量纲角速度的变化情况,分析半径比和扇形角对环扇形板横向振动的影响.结果 显示在不同的旋转角速度情况下,环扇形板会发生发散失稳和颤振耦合失稳现象.该结论为振动磨机的设计与研究提供了一定的理论基础.     

机械载荷作用下梯度多孔材料圆板非线性力学行为的研究

基于一阶剪切变形圆板理论,应用最小势能原理,推导了梯度多孔材料圆板在径向载荷与横向载荷共同作用时的控制微分方程及边界条件,并将其退化为经典板理论下的结果。利用打靶法求解圆板非线性力学行为的数值解,并根据结果分析了梯度多孔材料的性质、机械载荷及边界条件等因素对圆板非线性力学行为的影响。     

含附加结构的圆形和环形板振动的积分方程方法

为了分析任意位置含附加结构的圆形和环形板结构的振动特性,运用特殊函数论、傅里叶级数和积分方程理论,采用由第1类和第2类贝塞尔函数组成的平方可积空间L2[a,b]上的完备正交函数系构造圆形和环形板结构的静力学格林函数,将任意位置带有附加结构的圆形和环形板结构的自由振动问题转化为积分方程特征值问题,进而将积分方程特征值问题转化为无穷阶矩阵的标准特征值问题,给出分析这类结构振动特性的积分方程方法。典型算例计算结果表明,该方法不仅算法简捷、收敛速度快,而且能从整体上对带有附加结构的圆形和环形板的非轴对称振动进行研究,为这类结构的优化设计和安全性评估提供了有效的途径。     

直角平面内圆形弹性夹杂对稳态入射平面SH波的模糊散射

用多极坐标移动技术、格拉夫(Graf)加法公式和扩张原理研究含模糊波数直角平面内圆形弹性夹杂对稳态入射平面SH(shearing horizontal)波的模糊散射问题。首先利用直角平面两直角边界应力自由条件写出介质内的自由波场和散射波场;其次,利用圆形弹性夹杂边界处的应力和位移连续条件、傅里叶级数展开和Graf加法公式得到确定散射波函数中未知系数的无穷线性代数方程组。为了利用模糊波数的模糊信息,将模糊波数理解为模糊参数,将其支集等距划分,利用扩张原理通过确定性方法间接得到划分节点处的模糊波场值及其隶属度。实际计算表明,该算法收敛速度快,计算精度高,数值结果稳定,且能克服求解模糊波响应隶属度信息的困难。     

半空间内圆孔对稳态入射平面SH波的散射

利用复变函数方法、多极坐标移动技术和Graf加法公式讨论半空间内圆孔对稳态入射平面SH( shearing horizontal)波的散射问题.首先写出介质内的自由波场和散射波场,它们能够预先满足半空间边界自由应力条件;其次,利用Graf(格喇夫)加法公式,将虚源波函数进行数学变换,使之与圆孔产生的波函数共同表示为同一个无穷正交函数级数的形式;最后利用圆孔边界处的应力自由条件,得出确定散射波函数中未知系数的无穷线性代数方程组,该方法避免了散射波函数傅里叶级数展开中积分的数值计算,因而显著地提高收敛速度和计算精度.算例结果表明方法的可行性.     

二维直角平面内偏心圆形衬砌对稳态入射平面SH波的散射

利用复变函数法、多极坐标变换及傅里叶级数展开技术求解二维直角平面内偏心圆形衬砌对稳态入射平面SH(shearing horizontal)波的散射问题.首先构造出介质内不存在偏心圆形衬砌时的入射波场和反射波场;其次建立介质内存在偏心圆形衬砌时由衬砌外边界产生的能够自动满足直角边应力自由条件的散射波解和衬砌外边界向衬砌介质内的折射波解以及衬砌内边界的散射波解,从而利用叠加原理可写出衬砌介质内外的总波场.利用衬砌外边界处应力位移的连续条件和内边界处应力自由条件以及傅里叶级数展开方法列出求解波解中未知系数的无穷代数方程组,在满足计算精度的前提下通过有限项截断,得到相应有限代数方程组的解,最后通过算例具体讨论衬砌内边界处的动应力集中系数和水平直边界位移幅度比及其相位随无量纲波数、入射波入射角、衬砌位置及其偏心度的不同而变化的情况,结果表明文中算法的有效实用性.     

基于十四面体模型的开孔泡沫材料弹性模量的有限元分析

利用十四面体模型描述开孔泡沫材料的胞体结构,并用有限元方法确定开孔泡沫材料的弹性模量。计算中使用相同尺寸的十四面体胞体模型,并考虑两种不同支柱截面（圆截面和Plateau截面）形状对弹性模量计算的影响。此外,通过数值方法研究开孔泡沫材料的弹性模量随模型尺寸的变化规律。同时,讨论边界条件处理对开孔泡沫材料弹性模量计算的影响。结果表明,支柱为Plateau截面形状的模型,其弹性模量明显高十具有圆截面支柱模型的结果。且两种模型的弹性模量均随模型尺度的增加而增加,最终趋于一个稳定值,并与Warren和Kraynik的理论预测较为一致。此外,边界条件对模型刚度的影响随着模型尺度的增加而逐渐减小。     

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bernoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method (DTM) has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.     

导电板上方涡流检测探头阻抗的快速计算与仿真

采用一种基于Maxwell方程组、矢量磁位和空间解域截取的级数展开快速计算方法,导出级数形式的导电板上方通电线圈阻抗变化表达式;通过设定适当的解域截取半径和级数求和项数,可以在保证计算精度的同时提高计算速度。在多种线圈激励频率下,分别采用级数展开法与有限元仿真法,对线圈的阻抗变化进行了计算,两种方法的计算结果非常吻合,相互验证了两种涡流检测计算模型的正确性。     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

Creative approach for the deflection formula according to relative length of supporting edge in a partially supported circular plate

The purpose of this investigation is to derive the maximum deflection formula of the circular plate with nonaxisymmetric boundary condition, such as chalk valves for vessel and artificial heart valves, with respect to the length ratio of supporting edge using elastic beam theory. To evaluate the deflection characteristics of this plate, we assumed the circular plate to have a cross-section that varies in the longitudinal direction, and derived the maximum deflection formula of this circular plate with a radius of ‘r’ in four boundary conditions. Then to verify the deflection formula that is derived from elastic beam theory, five different relative lengths of the supporting edge were adopted as the design parameter, and finite element analysis was carried out for each model.     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

弹性波散射反演的一种新思路

针对半空间界面半圆形凹陷和介质内圆孔对SH(shearing horizontal)波散射的反演问题提出一种优化求解方法.具体分析两种情况下弹性波散射反演问题的模型和特点,给出反演目标函数和反演数学模型,利用黄金分割法或对分法进行寻优求解.算例结果表明方法的可行性.文中方法对研究得比较成熟的弹性波散射正演问题对应的反演问题的求解具有应用价值和理论指导意义.