圆柱壳的轴对称平面应变弹性动力学解

给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法。首先通过引入一特定函数将非齐次边界条件化为齐次边界条件,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数,并由贝塞尔函数的正交性,导出时间函数的方程,容易求得此方程的解。将两者叠加可得弹性动力学问题的位移解。运用此方法,可以避免积分变换,并适宜于各种载荷。文中给出了各向同性和柱面各向同性圆柱壳内表面和实心圆柱外表面受冲击荷载作用以及内表面固定的柱面各向同性圆柱壳外表面受冲击荷载作用的数值结果。     

轴对称热冲击SIF过渡过程分析的热权函数法

热权函数法利用温度与热权函数的乘积的积分来直接计算热冲击过程中裂纹尖端的应力强度因子过渡过程。热权函数与时间τ无关,由于免除了对每一时刻τ所需作的有限元或边界元分析,计算过程大大简化,计算效率得到极大提高,本文将热权函数与有限元法直接耦合,给出了基于刚度阵导数法的轴对称问题的热权函数计算格式,实例计算表明,本文给出的热权函数计算格式具有满意的计算精度。     

基于Burton-Miller方程的轴对称结构声学边界元方法

提出了一种求取轴对称结构任意边界条件下声辐射特性的边界元方法。采用Burton和Miller改进型公式将高阶奇异项转化为弱奇异项之和,保证声辐射参数的唯一性,且计算简单精确。将结构表面声压与振速按照旋转轴角度进行Fourier级数展开,利用级数的正交性建立各项待定系数的求解公式;然后转化格林函数的法向偏导为切向偏导,方便直接计算各项积分,并将面积分公式表示为沿结构边界的线积分和沿旋转角度的积分;进一步采用二次等参单元离散结构边界线,建立声压与振速的关系矩阵,从而确定结构声辐射参数。以脉动球源和横向振动球源为例计算,与解析解和传统边界元法结果作对比,说明该方法的有效精确性。     

Free axisymmetric vibration of FGM circular plates

Based on the three-dimensional theory, this work presents a direct displacement method to investigate the free axisymmetric vibration of transversely isotropic circular plates, whose material is functionally graded and properties obey the exponential law along the thickness direction of the plate. Under two boundary conditions, the solution satisfies all basic equations and the Corresponding boundary condition at every point. Thus, it is three-dimensional exact. Numerical examples are presented and compared with previous works. The present method can also be extended to the case of arbitrary distribution of the material properties along the thickness direction of the plate.     

饱和粘弹性土层中端承桩纵向振动的轴对称解析解

基于弹性和饱和多孔介质理论,将桩和饱和土层分别视为单相弹性介质和饱和粘弹性介质,利用Helmholtz分解和变量分离法,在频率域研究了饱和粘弹性土层中端承桩纵向振动的动力特性,给出了饱和粘弹性土层中桩纵向振动时动力响应的轴对称解析解及桩头复刚度的解析表达式．通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了饱和土物性参数、桩土模量比、桩长径比、桩Poisson比等参数对桩头刚度因子和阻尼的影响．研究表明:由于考虑了桩的径向变形效应以及饱和粘弹性土层对桩的径向力作用,轴对称精确解的桩头动刚度因子和阻尼分别与经典Euler-Bernoulli杆模型桩的桩头动刚度因子和阻尼有较大的区别,特别是在若干激励频率处．因此,经典Euler-Bernoulli杆模型桩的适用性具有一定的局限,更加精确的分析应采用三维精确模型．     

Quasinormal modes of a stationary axisymmetric EMDA black hole

The massless scalar quasinormal modes (QNMs) of a stationary axisymmetric Einstein--Maxwell dilaton--axion (EMDA) black hole are calculated numerically using the continued fraction method first proposed by Leaver. The fundamental quasinormal frequencies (slowly damped QNMs) are obtained and the peculiar behaviours of them are studied. It is shown that these frequencies depend on the dilaton parameter $D$, the rotational parameter $a$, the multiple moment $l$ and the azimuthal number $m$, and have the same values with other authors at the Schwarzschild and Kerr limit.     

New infinite-dimensional symmetry groups for the stationary axisymmetric Einstein--Maxwell equations with multiple Abelian gauge fields

The so-called extended hyperbolic complex (EHC) function method is used to study further the stationary axisymmetric Einstein--Maxwell theory with $p$ Abelian gauge fields (EM-$p$ theory, for short). Two EHC structural Riemann--Hilbert (RH) transformations are constructed and are then shown to give an infinite-dimensional symmetry group of the EM-$p$ theory. This symmetry group is verified to have the structure of semidirect product of Kac--Moody group $\widehat{SU(p+1,1)}$ and Virasoro group. Moreover, the infinitesimal forms of these two RH transformations are calculated and found to give exactly the same infinitesimal transformations as in previous author's paper by a different scheme. This demonstrates that the results obtained in the present paper provide some exponentiations of all the infinitesimal symmetry transformations obtained before.     

一般夹层旋转壳在轴对称变形下的大挠度方程

应用最小势能原理建立了具有不同质不等厚薄表层和软夹心的一般夹层旋转壳在轴对称变形下的非线性理论,得到了一组相对简单的夹层壳大挠度方程和边界条件。在分析壳体的变形时,将表层视作薄膜,假设夹心沿厚度方向不可压缩且只能承受横向剪应力,参考面的法线在变形时保持为直线。为便于实际应用,给出几种特殊壳体情况下的大挠度方程。     

轴对称渗流中自由边界问题的近似解法

１．问题的提法 本文讨论各向异性非均匀介质的轴对称稳定渗流问题,我们延用［７］的记号。设有一水井（或油井）,其截面如图１所示,ｚ轴为对称轴,Ｄ为渗流区域,其边界为ＡＢＣＥＦＡ,Ｋ＝｛ｋｉｊ（ｒ,ｚ,ｈ,ｑ）｝为对称渗流张量,它依赖于柱坐标中的ｒ,ｚ,压头ｈ＝ｚ＋ｐ／ρｇ及渗流速率其中ｐ为点（ｒ,ｚ）处的压力,ρ为流体密度,ｇ为重力加速度．ｒ０为井的半径,Ｈ１为液面的高度,同时假设当ｒ≥Ｒ时,其渗流速度Ｖ＝０． 由渗流理论,有引入热函数,流函数 Ｄ中一点）,则满足下列一阶非线性方程组其中,若（ｉ＝ １…     

基于有限元轴对称分析的碳纳米管场增强因子建模与计算

通过采用二维建模而后旋转成为三维模型的轴对称分析,提出了一种基于有限元轴对称分析的碳纳米管建模方法,并计算了不同长径比的碳纳米管的场增强因子.通过对比轴对称模型与立体模型分析结果,证明轴对称模型在提高了网格划分精度的同时减小了计算量,提高了计算效率,并为类似的具有旋转对称特性的模型分析提供了一种切实可行的建模方法.相关计算表明,碳纳米管的场增强因子与其长径比的函数关系为β=h/ρ+2.00.