受任意个同心弹性环支圆板横向自由振动的一个新的解析解法

本文研究受任意个同心弹性环支图板的横向自由振动问题，给出了一个新的解析解法。对弹性环支反力表示为作用于圆板上的待定外力，在求得圆板受迫振动的解析式后，由圆板的边界条件决定积分常数，利用环支处板位移与环支反力之间的线性关系得环支反力，并得频率方程。它是一阶数等于环支个数的行列式，可由行列式搜根法数值计算各阶固有频率，而振型函数则用一解析式表示，本文最后给出了一个算例，并与已有结果进行了比较。     

均匀热载荷作用下功能梯度圆板的非线性振动

基于经典板理论,研究了热载荷作用下功能梯度圆板的大幅振动问题。在经典板理论下利用物理中面概念,导出了功能梯度圆板的非线性运动方程。利用Ritz-Kantorovich方法消去时间变量,将非线性运动方程转换成了一组关于空间变量的非线性常微分方程。采用打靶法数值求解所得方程,并利用数值结果研究了热载荷作用下功能梯度圆板静态响应的影响和振幅、材料梯度参数、热载荷以及边界条件等对功能梯度圆板振动行为的影响。研究表明:热变形的存在使周边夹紧与简支FGM圆板的振动响应及线性振动与非线性振动行为均有显著不同。热过屈曲变形板的硬化是有限度的,过大的热过屈曲变形也会降低FGM圆板的刚度。     

磁场环境下导电圆形薄板的磁弹性强迫振动

研究了电磁场环境下机械载荷作用圆形导电薄板的磁弹性强迫振动问题。首先给出了圆形薄板的磁弹性轴对称振动方程,并依据麦克斯韦方程,得到了相应的电磁场方程和电磁力表达式,在此基础上,对横向恒定磁场中周边固支和周边简支边界约束圆板的振动问题进行了分析。基于位移函数的设定,应用伽辽金法,推得了导电圆板的磁弹性强迫振动微分方程。通过数值计算,得到了两种边界约束条件下圆板磁弹性振动的幅频和相频曲线图,并对结果进行了分析,讨论了磁感应强度和板厚等参数对系统振动特性的影响。     

热环境下混凝土矩形薄板在弹性地基上的振动

基于刚性板的小挠度理论，考虑混凝土的材料非线性，推导了双参数弹性地基上混凝土矩形薄板热弹性问题的动力方程。采用级数法，导出了热环境下双参数弹性地基上四边简支混凝土矩形薄板的固有频率计算公式和强迫振动下的挠度函数。为便于工程应用，给出了双参数弹性地基上四边简支混凝土矩形薄板在恒向变温和温度均匀变化时的固有频率和均布荷载作用下的挠度函数。针对Winlder弹性地基的情况，讨论了板的材料弹性常数、几何尺寸（长宽比）、相对厚度、刚度系数k和温度对薄板固有频率和挠度函数的影响，从而为工程结构中热环境下弹性地基上混凝土矩形薄板的振动计算提供了理论依据。     

一维六方准晶复合材料界面层中螺型位错分析

本文研究了一维六方准晶复合材料夹杂界面层中螺型位错与夹杂以及无限大基体的干涉效应。运用复变函数方法,得了该问题的解析解答,所得退化结果与已有文献结果一致,并得到了作用在圆环形界面层中螺型位错的位错力的精确表达式。讨论了一维六方准晶材料弹性常数对位错运动以及位错力的影响规律。结果表明,一维六方准晶中的材料弹性常数对位错力的变化影响是显著的。随着相位子场弹性常数或者声子场-相位子场耦合弹性常数的增大,其相应区域对位错的排斥或者吸引作用也分别增强。在夹杂界面或者基体界面附近,随着相位子场弹性常数和声子场-相位子场耦合弹性常数同时增大,夹杂或者基体对位错的吸引作用增强,但是并不改变位错平衡点的位置。     

弹性地基扇形板弯曲问题的复Bessel函数级数解

本文对于在Ｗｉｎｋｌｅｒ型弹性地基上的扇形板弯曲问题给出了一种级数解法。对于沿径向简单支撑的扇形板,在周向采用正纪三角函数展开后,将于关径向待定函数的Ｂｅｓｓｅｌ方程用复Ｂｅｓｓｅｌ函数表示其解。然后,将其变换成实解形式,从而得到原问题齐次方程的实能解。在此基础上,对于扇形板受集中力或沿周向线分布载荷作用下的弯曲解给出了一般设计方法以及任意横向载荷作用下挠曲函数的表达式,并给出沿径向和周向都为简单     

随从力作用下功能梯度矩形板的非线性振动

本文研究了切向均布随从力作用下简支FGM矩形板的非线性振动问题。按照材料组份体积分数的简单幂率分布规律,FGM板的材料常数仅沿厚度连续变化。由大挠度的von Karman理论建立了以应力函数和挠度函数表示的运动偏微分方程组,再由Galerkin法转化成非线性常微分方程。对随从力作用下的四边简支陶瓷/金属矩形板,讨论了随从力、梯度指标和边长比对板的动力特性的影响,得到了各种条件下板中心振幅与非线性基频的关系。     

具有初挠度夹层圆板非线性振动与解的稳定性

基于均布载荷作用下夹层圆板大幅度振动的基本方程和四种边界条件,利用空间模态假设和变分法,将初挠度设成空间函数的形式,动挠度设为时间和空间函数的分离形式,并将其代入各非线性振动方程,得出应力和转角用设定的挠度函数表示的形式,再将假定模态函数代入本问题的非线性振动方程,利用伽辽金法推导出时间模态的控制方程,并在相平面上讨论了解的稳定性。     

弹性地基扇形权弯曲问题的复Bessel函数级数解

本文对于在Winkler型弹性地基上的扇形板弯曲问题给出了一种级数解法。对于沿径向简单支撑的扇形板,在周向采用正弦三角函数展开后,将关于径向待定函数的Bessel方程用复Bessel函数表示其解。然后,将其变换成实解形式,从而得到原问题齐次方程的实通解。在此基础上,对于扇形板受集中力或沿周向线分布载荷作用下的弯曲解给出了一般计算方法以及任意横向载荷作用下挠曲函数的表达式,并给出了沿径向和周向都为简单支撑情形的算例。     

拉压模量不同圆板的非线性弯曲计算

拉压弹性模量不同的圆板在均布外载荷作用下,会形成拉压弹性模量不相同的拉伸区和压缩区,把拉压弹性模量不同的圆板看成两种材料组成的层合板,采用弹性力学理论建立了拉压模量不同圆板在均布外载荷作用下的静力平衡方程,利用静力平衡方程确定了拉压弹性模量不同圆板的中性面位置.在此基础上,建立了拉压弹性模量不同圆板的非线性弯曲微分方程...     

简支圆板非线性热弹耦合振动问题的研究

对温度场中周边简支圆板的轴对称非线性热弹耦合自由振动问题,运用伽辽金法求解, 得出一个关于时间的非线性常微分方程组,求出振幅随时间变化的数值解。将热弹耦合与非 热弹耦合情况进行对比,发现振幅较小时,热弹耦合效应使板的固有频率相对于无热弹耦合 情形提高：振幅较大时,热弹耦合效应使固有频率降低。本文还比较了不同热弹耦合参数对 应的振动情况。     

A point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material

We use the compact mono-harmonic general solutions of transversely isotropic electro-magneto-thermo-elastic material to construct the three-dimensional Green’s function for a steady point heat source on the surface of a semi-infinite transversely isotropic electro-magneto-thermo-elastic material by five newly introduced mono-harmonic functions. All components of coupled field are expressed in terms of elementary functions and are convenient to use. Numerical results are given graphically by contours.     

横向常磁场中铁磁圆板的主共振特性与静载效应

针对横向常磁场中铁磁圆板的主共振问题进行研究。基于电磁基本理论,得到薄板在常磁场中所受的磁体力和洛伦兹力,应用哈密顿变分原理,推导出磁场中铁磁圆板磁弹性耦合横向振动微分方程。常磁场中铁磁圆板受到的磁体力为静载荷,根据伽辽金法得到周边夹支边界条件下铁磁圆板在静载荷作用下的初挠度,进一步应用多尺度法对周期载荷作用下的非线性方程进行一阶和二阶近似求解,得到主共振下系统幅频响应方程。通过算例,给出了系统幅频特性曲线图、振幅随磁场强度和激励力变化的曲线图,分析了板厚、磁场强度、激励力对系统共振振幅的影响,并对比了一阶近似和二阶近似计算结果的不同。结果表明,共振区域内振幅显著增加,磁场强度较小时一阶近似与二阶近似计算结果相近,而磁场强度较大时,二阶近似计算结果更加准确。     

Three-Dimensional Thermo-Electro-Elastic Field in a Circular Plate of Functional Graded Materials with Transverse Isotropy

This article presents a set of axisymmetric solutions for a circular plate of functional graded materials with transverse isotropy subjected to uniform thermal loadings on the upper and lower surfaces. The temperature field in the plate is obtained as a prior, by integration. A direct displacement method is then employed to explicitly derive the thermo-electro-elastic field induced by the thermal loadings. Numerical calculations are carried out to validate the present results and to show the effect of material heterogeneity on the distributions of the coupled field. Some interesting phenomena have been observed.     

环形均布荷载作用下简支圆板的塑性极限分析

本文采用双剪统一屈服准则首次对受环形均布荷载作用下的简支圆板进行了塑性极限分析,得出了相应的统一解形式。已有的Tresca准则、Mises准则、双剪应力准则的解答是文中解答的特例或逼近,它可以适用于不同性状的拉压同性材料。用本文的解还可以推出多种荷载作用下简支圆板的塑性极限荷载。     

A 3-D Ritz solution for free vibration of circular/annular functionally graded plates integrated with piezoelectric layers

This paper addresses three-dimensional (3-D) free vibration characteristic of thick circular/annular functionally graded (FG) plates with surface-bonded piezoelectric layers on the basis of 3-D Ritz solution. Three displacement components along with electrical potential field of the plate are expressed by a set of Chebyshev polynomials multiplied by geometry boundary functions. Both open-circuit and closed-circuit surface conditions are taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness of the plate and obey either exponent or power law distribution of the volume fraction of the constituents. The effect of thickness-to-radius ratio, inner-to-outer radius ratio, piezo-to-host thickness ratio and gradient index on the natural frequencies of coupled piezoelectric FG circular/annular plates is investigated for different electrical and mechanical boundary conditions. It is observed that, unlike isotropic homogeneous circular/annular plates, frequency parameters of their piezoelectric coupled FG counterparts significantly increase with an enhancement in the host plate thickness to radius ratio. Results also show that the frequency parameters for open-circuit condition are higher than those for closed-circuit condition.     

CLASSICAL SOLUTION SHAPE FUNCTIONS IN THE FINITE ELEMENT ANALYSIS OF CIRCULAR AND ANNULAR PLATES

The objective of this work is to present a new method for the dynamic and static analysis of thin, elastic, isotropic, non-uniform circular and annular plates. The method is a combination of plate theory and finite element analysis. The plate is divided into one circular and many annular finite elements. The displacement functions are derived from Sanders' classical plate theory. These displacement functions satisfy the convergence criteria of the finite element method. The matrices for mass and stiffness are determined by precise analytical integration. A computer programme has been developed, the convergence criteria have been established, and the natural frequencies and vibration modes have been computed for different cases. The results obtained reveal that the frequencies calculated by this method are in good agreement with those obtained by other authors. © 1997 by John Wiley & Sons, Ltd.     

Thermo elasticity solution of functionally graded,solid, circular,and annular plates integrated with piezoelectric layers using the differential quadrature method

Static analysis of functionally graded (FG) solid circular/annular plates imbedded in piezoelectric layers under thermo-electro mechanical load is investigated using the differential quadrature method. The plate has various edge boundary conditions and its material properties are assumed to vary in an exponential law with the Poisson ratio to be constant. The method is validated by comparing numerical results with the results obtained in the literature. The effects of the gradient index, thickness to radius ratio, and edges boundary conditions on the thermoelastic behavior of FG solid circular and annular plates are investigated.