用于变厚度圆盘振动分析的动态环形元

本文利用动态位移的回转周期变化规律,将变厚度圆板弯曲振动的二维问题化为一维形式.并将环形单元的位移函数以频率的升幂形式展开,作为动态形状函数,进而推导了动态环形元的质量和刚度矩阵及其一次动态修正矩阵,并以简洁的形式给出.最后作为本文方法的直接应用,计算了叶盘组合件的固有特性与实验值及其它方法进行了比较,说明动态的变厚度环板元的优越性.     

应用4变量精确平板理论分析FG复合板的自由振动

应用4变量的精确平板理论,对矩形功能梯度材料(FGM)复合板进行自由振动分析.与其它的理论不同,该理论的未知函数数量只有4个,而别的剪变形理论的未知函数为5个.提出的4变量精确平板理论,协调条件有了改变,与经典的薄板理论相比,许多方面有着惊人的相似,无需引入剪切修正因数——当横向剪应力越过板厚后,为了满足剪应力自由表面条件,出现抛物线状的改变,导致横向剪应力的变化.考虑了两种常见类型的FGM复合板,即,FGM表面层和各向同性夹芯层的复合板,以及各向同性表面层和FGM夹芯层的复合板.通过Hamilton原理,得到了FGM复合板的运动方程.得到闭式的Navier解,然后求解特征值问题,得到自由振动的基本频率.将该理论得到的结果,与经典理论,一阶的及其它更高阶的理论所得到的结果进行比较,检验了该理论的有效性.研究发现,该理论在求解FGM复合板自由振动性能方面,既精确又简单.     

缓变系数动力系统的运动稳定性

本文举例说明“冻结”系统稳定性与原变系数系统稳定性之间的各种关系,用函数的方法给出了变系数动力系统运动稳定性的充分条件,用显式确定系数缓变的界限,非线性附加项的界限,带有时滞的系统的时滞的界限.     

用线法分析中厚板的振动与稳定性问题

发展了基于胡海昌中厚板的振动与稳定性理论等特征值问题的线法.利用常微分方程(ODE)技巧给出求解固有频率及临界荷载的标准非线性ODE体系,并采用所谓初始特征函数法通过ODE求解器(Solver)直接解出指定的任一特征值,而不依赖于振型正交性等条件.算例表明,本文方法是有效和可靠的.     

矩形厚板的自由振动分析

出了一种新方法来对基于 Mindlin剪切变形理论的矩形厚板进行自由振动分析 .此方法采用了一种新的基函数并结合 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .数值结果表明此方法相当精确有效 .     

一类缓变 KdV 方程的精确求解

<正> [1]讨论了缓变 KdV 方程U_t+α(T)UU_x+β(T)U_(xxx)=0,(1)其中α(T),β(T)>0,T=εt,ε(?)1.这种方程对于渠道截面和流动介质有缓慢变化的弱非线性弱色散系统是一种近似度相当好的数学描述.这里只讨论α(T)>0,实际上作适当变换,已包含α(T)<0的情况.文[1]运用摄动法给出了此方程的首项近似解,这些结果与文[2,3]是相同的.本文则指出在一定条件下,缓变 KdV 方程(1)可以转换到通常的常系数 KdV 方程.我们考虑变换     

等腰三角形Mindlin板的自由振动分析

提出了一种新方法来对基于 Mindlin剪切变形理论的等腰三角形板进行自由振动分析 .此方法采用了一种新的基函数并利用 pb-2 Rayleigh-Ritz边界函数得到了一种新型的 Ritz方法 .这种方法的有效性通过收敛性和对比性分析得到了证实 .数值结果表明此方法相当精确有效 .     

无界弦自由振动问题的算法

探讨了无界弦自由振动问题的两种算法：行波法和积分变换法,主要就积分变换法利用富里叶变换和matlab软件使得计算更简单,并给出了积分变换法的一般算法．     

膜自由振动的多辛方法

基于Hamilton空间体系的多辛理论研究了膜自由振动问题,讨论了构造复合离散多辛格式的方法,并构造了一种典型的9×3点半隐式的多辛复合离散格式,该格式满足多辛守恒律、能量守恒律和动量守恒律．数值算例结果表明该多辛离散格式具有较好的长时间数值稳定性．     

一维六方准晶简支梁的自由振动

采用不同高阶剪切变形理论研究一维六方准晶梁的自由振动问题,应用哈密顿原理,推导了一维六方准晶梁的自由振动控制微分方程.采用Navier法获得了一维六方准晶简支梁自由振动的精确解,并将不考虑相位子场所求解结果与已有解进行比较,验证求解结果的有效性.最后研究材料尺度对一维六方准晶梁固有频率的影响.     

电磁场中变厚度载流圆板的非线问题

本文建立了在非定常电磁场和机械场作用下变厚度载流弹性圆板在非线性变形状态下的磁弹性二维关系方程和运动方程，给出了弹性圆板在轴对称条件下的数值解．     

Linearly Coupled,Slowly Varying Oscillators

A dynamical system is considered whose normal frequencies and normal modes vary slowly with time in such a way that two frequencies come into close coincidence. When this occurs the corresponding normal modes undergo a drastic change in their physical properties. Away from coincidence, each normal mode conserves its action. A multiple-time-scale asymptotic procedure is employed to derive equations which describe the mode coupling at coincidence. These equations are solved exactly using parabolic cylinder functions. It is found that in general, action is exchanged between modes at coincidence, but that except for very strong coupling the amount of action exchanged is quite small.     

慢变线性切换系统的镇定(英文)

The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.     

具有随厚度变化膨胀特征应变的弹性层的分析

提出了含随厚度变化膨胀特征应变的弹性层在任意载荷作用下的一般分析步骤。该研究基于状态空间方法和一种渐近展开技巧。如果外载均匀,则展开式系数自前几项后为零,从而可得弹性层力学场量封闭形式的表达式。这一表达式仅依赖于中面的位移分量,后者由一组类似于经典板理论的二维微分方程控制。因此,获得二维方程的解便可立即给出弹性层的三维响应。作为例子,还详细分析了均匀分布载荷作用下的夹支椭圆层。     

Dynamics of a Delay Logistic Equation with Slowly Varying Coefficients

Computational Mathematics and Mathematical Physics - The existence, stability, and asymptotic behavior of steady modes for a delay logistic equation with slowly varying coefficients are analyzed.     

Weighted Polynomial Approximation for Weights with Slowly Varying Extremal Density

Polynomial approximation by weighted polynomials of the form wⁿ(x) P_n(x) is investigated on closed subsets of the real line. It is known that the possibility of approximation is closely related to the density of an extremal measure associated with w via a weighted energy problem. It is also known that if in a neighborhood of a point x₀ this density is continuous and positive, then, in that neighborhood, any continuous function can be approximated. The aim of the present paper is twofold. On the one hand it is shown that the same approximation theorem is true if in a neighborhood of x₀ the density is slowly varying and is bounded away from 0. This allows singularities of logarithmic types. On the other hand, we also show that under some mild conditions, if the density at x₀ is slowly varying, then approximation is still possible even if the density vanishes at x₀ . This is the first positive result for approximation with a vanishing density.     

Slowly Varying Phase Planes and Boundary-Layer Theory

A method is presented that combines phase-plane techniques with the ideas of multiple scale and matched asymptotic expansions to explain the behavior of solutions to second-order, nonlinear, nonautonomous, singular boundary-value problems. It is shown that if one is willing to give up the detailed information provided by a procedure such as matched asymptotic expansions, then complete qualitative information can be obtained by the much simpler method given here. (“Complete” here means that the method provides a way of categorizing all possible solutions of such problems.) In addition, the similarities and differences between the present method and that of Melnikov, which has been useful in the study of dynamical systems, are noted.     

Resonance in a Weakly Nonlinear System with Slowly Varying Parameters

We survey multiple-variable expansion procedures appropriate for nonlinear systems in resonance using the model of two coupled weakly nonlinear oscillators with either constant or slowly varying frequencies. In the autonomous problem we show that an n-variable expansion (where n depends on the order of accuracy desired) yields uniformly valid results. We also consider the problem of passage through resonance for the nonautonomous problem and describe the solution by constructing a sequence of three expansions. The solution before resonance is developed as a generalized multiple-variable expansion and is matched with an inner expansion valid during resonance. This latter is then matched with a postresonance solution and determines it completely. Numerical integrations are used to substantiate the theoretical results. The dominant effect of passage through resonance is shown to be the excitation of a higher-order oscillation beyond resonance. Contrary to the claim in a recent work, the total action of the system does not remain constant if one accounts for the leading perturbation terms in the postresonance solution. Instead, the total action goes from one constant value to another.     

Applications of Slowly Varying Nonlinear Dispersive Wave Theories

Previous theories for the slow dispersion of singly periodic and multiply periodic nonlinear wavetrains are applied to various examples. Stability of the solution with respect to large scale variations and possible shocks in the wave properties (frequency, wavenumber, and amplitude) are discussed. The general approach is also used to analyze certain aperiodic waves.     

The Critical Conditions in a Reactive Slab with Slowly Varying Surface Temperature

Liouville's non-linear partial differential equation is consideredfor an infinite rectangular strip domain with a slowly varyingboundary condition. The equation describes a layer of chemicallyreactive material under conditions where the resistance to surfaceheat transfer is negligible and the ambient temperature variesslowly along the surface. Symmetrical heating by a zero orderexothermic reaction is assumed. If is a small dimensionlesstemperature difference between regions where the surface temperatureis effectively constant, a perturbation series solution in may be determined provided the Frank-Kamenetskii parameter satisfies _c(). It is shown that a plausible value for thecritical parameter is _c() = _c(0) e^–e,where _c(0) = 0.878.The corresponding critical temperature distribution is shownto have a dependence on different from that for subcriticalcases.