轴对称薄壁结构自由振动的边界元分析

采用双互易法分析薄壁轴对称结构自由振动的特征频率以及特征模态.首先,采用径向基函数插值域积分里的位移,利用双互易法将域积分转化为子午面边界的积分.然后,将边界物理量、基本解和特解展开为傅里叶级数,沿环向积分后得到的边界积分方程可用于轴对称结构带体积力问题和受非对称载荷的动力学分析,其积分域为轴对称结构子午面边界上的线积分,进一步降低了问题的维度和离散的难度.文章详细探讨了源点处于对称轴的特殊情况,根据基本解和特解的退化形式,针对无体积力和有体积力分别给出了处理奇异矩阵的方案.对于薄壁结构,采用双曲正弦变换处理近奇异积分有效提高积分精度.最后将双互易法和双曲正弦变化应用于薄壁轴对称结构带体积力的静力学和自由振动分析.数值结果表明,文章提出的处理奇异矩阵的方法能够有效处理源点处于对称轴的情况;当圆筒厚高比为$10^{-3}$,边界元计算的特征频率的相对误差为$10^{-3}$,且优于有限元的结果.      

求解二维结构-声耦合问题的一种半数值半解析方法

基于传递矩阵法和虚拟源强模拟技术提出了一种求解在谐激励作用下二维结构-声相互作用问题的半数值半解析法．在足够小的积分步长内，文中对任意形状弹性环沿周向曲线坐标的非齐次状态微分方程组，建立了一种齐次扩容方法．对于外声场，采用多圆形虚拟源强配置方案。并在每一条圆形配置曲线上将源强密度函数用Fourier级数展开，同时结合快速Fourier变换法，提出了一种高精度、高效率求解任意形状二维孔穴Helmholtz外问题的快速算法．在耦合方程的求解方面，根据叠加原理，将外激励和虚拟源强的Fourier级数展开项作为广义力分别作用在弹性环上，借助齐次扩容方法和精细积分法求得弹性环的状态向量，再利用流固交接条件和最小二乘法直接建立了耦合系统的求解方程．文中给出了二个典型弹性环在集中谐激励力作用下声辐射算例，计算结果表明该文方法较通常采用的混合FE-BE法更为有效．     

On damping coefficient due to phase transformation

The damping coefficient of capillary waves due to the evaporation-condensation process at the interface of the two phases of a fluid is evaluated. To highlight the mechanism of the effect of heat and mass transfer across the interface between regions of liquid and vapor, potential flow of incompressible fluids are assumed. Thus other mechanisms of damping are neglected. To fascilitate the analysis, the method of multiple-scale is employed in the analysis, even though the problem is linear.     

Normal Forms for High Co-Dimension Bifurcations of Nonlinear Time-Periodic Systems with Nonsemisimple Eigenvalues

The normal forms for time-periodic nonlinear variational equations witharbitrary linear Jordan form undergoing bifurcations of highco-dimension are found. First, the equations are transformed via theLyapunov–Floquet (L–F) transformation into an equivalent form in whichthe linear matrix is constant with degenerate nonsemisimple lineareigenvalues while the nonlinear monomials have periodic coefficients. Byconsidering the resulting coupling of the bases of the near identitytransformation, the solvability condition for an arbitrary Jordan matrixis then derived. It is shown that time-independent and/or time-dependentnonlinear resonance terms remain in the normal form for various Jordanmatrices. Specifically, the normal forms for quadratic and cubicnonlinearities with the following linear Jordan forms are explicitlyderived: double zero eigenvalues (co-dimension two bifurcation), triplezero eigenvalues (co-dimension three bifurcation), and two repeatedpairs of purely imaginary eigenvalues (co-dimension two bifurcation). Acommutative system with cubic nonlinearities and a double inverted pendulum with a periodicfollower force are used as illustrative examples.     

The step-wise martensite to austenite reversible transformation

The step-wise martensite to austenite reversible transformation (SMART) in shape memory alloys (SMA) is a martensitic thermoelastic transformation where a step-wise kinetics is induced by a partial cycling procedure within the hysteresis cycle (incomplete cycle on heating (ICH) procedure). The ICH procedure has been proved effective in inducing a reversible microstructural modification of the martensitic phase. Results till now obtained both on the SMART behaviour and on the effects of the ICH procedure are reviewed here: the hypotheses advanced till now are discussed to explain experimental evidences.

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Sommario Con l'acronimo di SMART (step-wise martensite to austenite reversible transformation) si indica una trasformazione martensitica termoelastica in cui la cinetica di trasformazione risulta modificata dall'esecuzione di un'appropriata procedura di ciclaggio termico parziale (procedura ICH — Incomplete Cycle on Heating) nell'intervallo di temperatura in cui ha luogo la trasformazione martensitica inversa. Vengono qui presentati i risultati sperimentali relativi sia alla SMART sia agli effetti indotti dalla procedure ICH e responsabili delle modifiche della cinetica di trasformazione. Vengono inoltre discusse le ipotesi sino ad ora avanzate per spiegare i risultati sperimentali.

     

完全变换法在无网格伽辽金方法中的应用

由于移动最小二乘形函数一般不具有常规有限元或边界元形函数所具有的插值特征，本质边界条件的处理成为无网格伽辽金法实施中的一个难点。本文通过建立节点位移和广义位移之间的关系对移动最小二乘形函数进行修正，给出了修正的移动最小二乘形函数；以二维问题为例，对完全交换法在无网格伽辽金方法中的应用进行了研究，实现了本质边界条件在节点处的精确施加。数值计算结果表明该方法不仅简单合理，而且具有较高的精度、收敛性和稳定性。     

Molecular-dynamics of a 2D model of the shape memory effect

A 2-dimensional molecular-dynamic model is presented for the investigation of crystalline phase transitions. The model is based on potential functions of the Lennard-Jones type. By use of two types of particles a stable square crystalline lattice may be created. It may transform into sheared variants, which represent martensitic phases. It turns out that the phase stability is dependent on the temperature of the body. In numerical experiments it is shown that the austenite appears to be stable at high temperature, while martensite is stable at lower temperature. The present article - being the first part of a work on the subject - explains the used model in detail. In several examples it is shown, how the model is capable to cover temperature-induced transitions between austenite and martensite. It turns out that the presented molecular dynamic experiments exhibit important characteristics as they are known from shape memory alloys.Received: 15 April 2002, Accepted: 18 March 2003, Published online: 27 June 2003 Dedicated to Professor Ingo Müller on the occasion of his 65th birthday     

动脉中非平稳流动壁面剪切力及其Hilbert-Huang变换

本文通过数值方法求解均匀动脉中的非平稳脉动流,给出了通过测量非平稳脉动血流量确定壁面切应力的方法.作为算例,采用实测的大鼠颈总动脉流量信号,求出了均匀动脉壁面切应力波形.进一步对求得的切应力波形进行经验模态分解(EMD),得到了切应力波形的各内在模态(IMF),以及Hilbert幅值谱.从切应力波形经Hilbert-Huang变换得到的IMF和Hilbert谱图可以明显地看出切应力各频率成分的物理意义.所得结果为进一步深入研究非平稳脉动切应力与血管重建的关系提供了一种方法学基础.     

Analysis of periodic-quasiperiodic nonlinear systems via Lyapunov-Floquet transformation and normal forms

In this paper a general technique for the analysis of nonlinear dynamical systems with periodic-quasiperiodic coefficients is developed. For such systems the coefficients of the linear terms are periodic with frequency ω while the coefficients of the nonlinear terms contain frequencies that are incommensurate with ω. No restrictions are placed on the size of the periodic terms appearing in the linear part of system equation. Application of Lyapunov-Floquet transformation produces a dynamically equivalent system in which the linear part is time-invariant and the time varying coefficients of the nonlinear terms are quasiperiodic. Then a series of quasiperiodic near-identity transformations are applied to reduce the system equation to a normal form. In the process a quasiperiodic homological equation and the corresponding ‘solvability condition’ are obtained. Various resonance conditions are discussed and examples are included to show practical significance of the method. Results obtained from the quasiperiodic time-dependent normal form theory are compared with the numerical solutions. A close agreement is found.     

二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射

利用复变函数法、多极坐标及傅立叶级数展开技术求解了二维直角平面内固定圆形夹杂对稳态入射反平面剪切（shearing horizontal, SH）波的散射问题。首先构造出介质内不存在夹杂时的入射波场和反射波场,然后建立介质内存在夹杂时由夹杂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，从而利用叠加原理写出介质内的总波场。利用夹杂边界处位移条件和傅立叶级数展开方法列出求解散射波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了二维直角平面水平边界点的位移幅度比和相位随量纲一波数、入射波入射角及夹杂位置的不同而变化的情况，结果表明了算法的有效实用性。