双层0.618法在某力学问题中的应用

建立了一组平行移动荷载作用下,简支桥梁挠度的数学模型;利用双层0.618法搜索梁的绝对最大挠度对应的最危险截面位置以及移动荷载最不利位置,计算该位置相应的挠度得到梁的绝对最大挠度.本文算法以计算机为工具,适用于任意有限多个平行移动荷载,对于桥梁的设计计算与安全评估,有一定的实用价值.     

粘弹性梁的动力响应

本文利用Voigt力学模型对粘弹性简支梁进行动力分析,得到了梁的自由振动与强迫振动的若干解析解的表达式.并与S.Timoshenko给出的弹性简支梁的相应的结论进行了比较,指出了弹性动力分析的局限性.最后给出了二个数值例子.     

薄壳小挠度屈曲方程的加权解法

基于薄壳小挠度屈曲方程,提出了一种求临界载荷解析表达式的加权解法.在复杂边界条件下,小挠度屈曲方程的解析解仍然是一个难点.以轴对称屈曲问题为例,从方程中找出临界载荷的影响因素,加权平均得到临界载荷,再用特例解确定影响系数.这一方法利用特殊问题的已知解来求一般问题的解析解,简化了求解过程,拓宽了解决问题的范围;其计算结果与利用Algor有限元程序得到的数值解一致.     

复合材料多层板壳大挠度非线性问题的迭代解法

在王震鸣等人提出的各向异性多层扁壳的大挠度方程的基础上,提出了复合材料多层板壳大挠度非线性问题的迭代解法。分析了四边简支的复合材料多层矩形扁壳,与小挠度线性理论解析解及有限元非线性解进行了对比。结果表明,载荷较小并发生小挠度时,所得的大挠度解和小挠度解析解非常接近,载荷较大时,所得解和有限元非线性解非常接近。     

集中弯矩作用下箱梁剪力滞效应的解析解

以承受集中弯矩的简支梁结构为对象,基于能量变分法,获得了剪力滞效应计算的解析解通式.分别对仅跨内承受集中弯矩和单侧梁端承受集中弯矩简支梁,以及两侧梁端承受相反弯矩的纯弯梁,提出了剪力滞效应计算的理论公式,揭示了该类型结构的剪力滞规律.通过简支箱梁算例,研究了3种集中弯矩工况下的剪力滞效应,并和有限元板壳数值解进行对比分析.研究表明,该解析方法可以有效计算简支梁承受集中弯矩时的剪力滞效应.简支梁在集中弯矩作用部位存在较为突出的剪力滞效应.     

偏心圆柱薄壳的分析

本文推导了偏心圆柱薄壳小挠度时的近似方程，并利用解析方法求解了该方程，得出了偏心圆柱薄壳的应力、位移与偏心距之间的关系。     

双层网格圆底扁球壳的非线性稳定问题

从基于等效夹层壳思想的双层网格扁壳,非线性弯曲理论的变分方程出发,利用坐标变换方法和驻值余能原理,导出双层网格圆底扁球壳,在均布压力作用下的轴对称大挠度方程和边界条件．采用修正迭代法,求得了两类边界条件下双层网格圆底扁球壳的非线性载荷-位移关系式和临界屈曲载荷的解析表达式,并讨论了几何参数对临界屈曲载荷的影响．     

均布荷载作用下压电材料简支梁的解析解

采用逆解法求解了均布荷载作用下压电材料简支梁的解析解。首先给出应力函数和电位移函数的多项式表达式,进而根据相容方程以及应力和电位移、位移和电势的边界条件,求得了同时考虑材料弹性参数、密度参数和压电参数呈梯度变化时,简支梁在均布荷载作用下的解析解。作为特例还得到了常体力以及材料参数为常数时的解答。并对结果进行了讨论。     

粘弹性板动力稳定性分析中的两模态Galerkin逼近

利用最大Liapunov指数分析法以及其它数值和解析的动力学方法,研究了大挠度粘弹性薄板的动力稳定性。材料的行为由Boltzmann叠加原理描述。采用Galerkin方法将原积分-偏微分模型简化为两模态的近似积分模型,而通过引进新变量,该近似积分模型可进一步化为一个常微分模型。数值比较了1-模态和2-模态截断系统的动力学性质,讨论了面内周期激励下材料的粘弹性性质、加载的幅度和初值对板动力学行为的影响。     

正交异性简支矩形底双曲扁壳大挠度问题的解析解

本文在文献[1,2]的基础上,进一步研究了富里叶级数在求解板壳大挠度问题中的应用。文中导出了简支边界条件下正交异性矩底双曲扁壳大挠度微分方程组的解析解。这个解可通用于板与壳、大挠度与小挠度、各向同性与正交异性在直角坐标下的多种情况。其数值结果与实验数据和其它解法结果相吻合。     

一阶迭代微分方程的解析解

讨论了一阶迭代微分方程解析解的存在性,通过构造一个辅助方程的幂级数解给出该方程的解析解.     

变厚度圆薄板在均布载荷下大挠度问题

本文首先给出变厚度圆薄板大挠度方程,用小参数方法和修正迭代法联合求解此问题,得到三次近似解;给出特征曲线同线性理论进行了比较.     

Eisenstein series on quaternion half-space of degree N

In Kim [7], we studied an Eisenstein series on quaternion half-space of degree 2. By calculating the Siegel series using the method of Karel [5], we obtained the analytic continuation and functional equation of the Eisenstein series. In this note we study an Eisenstein series on quaternion half-space of degreen. By calculating the Siegel series in an analogous way as in Shimura [15] and Kitaoka [8], we obtain singular modular forms of weightk, k<2n and 4/k. Furthermore, we obtain the analytic continuation and functional equation of the Eisenstein series.     

On new analytic free vibration solutions of rectangular thin cantilever plates in the symplectic space

In this paper, we obtain accurate analytic free vibration solutions of rectangular thin cantilever plates by using an up-to-date rational superposition method in the symplectic space. To the authors’ knowledge, these solutions were not available in the literature due to the difficulty in handling the complex mathematical model. The Hamiltonian system-based governing equation is first constructed. The eigenvalue problems of two fundamental vibration problems are formed for a cantilever plate. By symplectic expansion, the fundamental solutions are obtained. Superposition of these solutions are equal to that of the cantilever plate, which yields the analytic frequency equation. The mode shapes are then readily obtained. The developed method yields the benchmark analytic solutions with fast convergence and satisfactory accuracy by rigorous derivation, without assuming any trial solutions; thus, it is regarded as rational, and its applicability to more boundary value problems of partial differential equations represented by plates’ vibration, bending and buckling may be expected.     

非线性强迫扰动Klein-Gordon方程的孤波渐近解法

研究了一类非线性强迫扰动Klein-Gordon方程.首先利用双曲正切待定系数法求得了典型的方程孤波解.然后利用泛函变分迭代原理得到了强迫扰动Klein-Gordon方程的一个近似解,并论述了解的一致有效性.所得到的近似解是一个解析式,它还可对近似解进行解析运算,而使用简单的模拟方法所得到的近似解是达不到这种效果的.     

The bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation

By using methods from dynamical systems theory, this paper researches the bifurcation and exact travelling wave solutions for the modified Benjamin-Bona-Mahoney (mBBM) equation. Implicit exact parametric representations of all travelling wave solutions as well as some explicit analytic solutions are given. Specially, breaking wave solutions are obtained, which KdV equation does not include.     

Septic B-spline method of the Korteweg-de Vries–Burger’s equation

In this paper, a numerical solution for the Korteweg-de Vries–Burger’s equation (KdVB) by using the collocation method using the septic splines is proposed. Applying the Von-Neumann stability analysis technique we show that the method is unconditionally stable. By conducting a comparison between the absolute error for the obtained numerical results and the analytic solution of the equation we will test the accuracy of the proposed method.     

Analytic invariant curves for a planar mapping

This paper is concerned with the existence of analytic invariant curves for a planar mapping. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained. In this paper, we discuss not only the general case, but also the critical cases as well, in particular, the case where β is a unit root is discussed.     

Solvability for Impulsive Neutral Integro-Differential Equations with State-Dependent Delay via Fractional Operators

This paper is mainly concerned with the existence of mild solutions for a first-order impulsive neutral integro-differential equation with state-dependent delay. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed-point theorem for condensing maps combined with theories of analytic resolvent operators, we prove some existence theorems. As an application of these main theorems, some practical consequences are derived.     

ANALYTIC SOLUTIONS OF AN ITERATIVE EQUATION WITH FIRST ORDER DERIVATIVE

This paper is concerned with a nonlinear iterative equation with first order derivative. By construction a convergent power series solution, analytic solutions for the original equation are obtained.