一类具有半线性多孔声学边界条件的变系数波方程的能量衰减性（英文）

研究一类具有半线性多孔声学边界条件的变系数波动方程.主要应用黎曼几何方法来处理这一变系数问题.通过使用黎曼流形上的能量乘子法,获得了该波动系统的能量衰减估计.     

一类高阶变系数线性非齐次微分方程的解

利用高阶变系数之间的关系,通过适当的线性变换,得到了五阶变系数线性非齐次方程常系数化的条件,给出了一类高阶变系数线性非齐次微分方程的新解法.     

具有变系数的偶数阶中立型差分方程的振动性

考虑了一类具有变系数的偶数阶中立型差分方程的振动性,通过建立一个比较定理,获得一些一类具有变系数的偶数阶中立型差分方程的振动性的充分条件.     

二元变系数递推数列的求解

运用矩阵理论给出一类二元变系数递推数列的求解公式,此方法适用于变系数分式递推式及m元变系数递推式的求解问题。     

一类变系数Boussinesq型方程的精确解

一类变系数Boussinesq型方程与变系数Broer-Kaup-Kupershmidt方程之间在某种约束下的关系.通过构造变系数Broer-Kaup-Kupershmidt方程的达布变换并应用达布变换得到这类变系数Boussinesq型方程的精确解.     

具有脉冲效应的分数阶p-Laplacian方程耦合系统的可解性（英文）

本文研究了一类具有脉冲效应的分数阶p-Laplacian方程耦合系统的问题.利用变分方法,获得了该系统解存在的一些新结果.在证明过程中,弱化了系统中变系数和非线性项的条件,推广了已有结果.     

微分方程的求解公式(Ⅰ)——高阶变系数常微分方程的求解公式

“常微分方程是工程技术、力学、物理等领域中常出现的一类数学问题,甚至更简单的吕卡提方程(变系数)也没有初等解”.由于这类问题较困难,因此这方面的研究较少,已知的有M.shoch和W.J.Coles等人就高阶变系数方程进行过研究.本文提出几种在原子物理、高能物理(如孤立子问题)、量子力学等许多领域内均有重要应用的高阶变系数方程,并给出了求通解的方法——解有退化核的第二类Volterra型积分方程法.本文是第一部分.第二部分是用本文的结果研究一类偏微分方程,给出其求解方法——“组     

一阶高次齐次微分方程的求解

详细地讨论了一类一阶变系数二次齐次微分方程的特征方程解法,并将其结果推广到同类型的一阶变系数n次齐次微分方程和一阶常系数n次齐次微分方程.     

变系数二阶线性微分方程的一个新的可解类型

通过双变换——未知函数的线性变换和自变量变换 ,将一类变系数线性微分方程化为二阶常系数线性微分方程 ,从而得到变系数二阶线性微分方程的一个新的可解类型 ,推广了著名的二阶 Euler方程 .     

带相依辅助信息的分位数自回归模型的经验似然估计

分位数自回归模型作为一类常用的变系数时间序列模型,在理论研究和实际问题中都有广泛的应用.考虑到这类模型具有自回归的结构属性,数据采集过程中产生的额外信息,以相依辅助信息函数的形式被引入到模型系数的估计中来.该文应用经验似然方法得到了模型系数的估计量,得到了模型系数的估计量,并论证了其渐近正态性.基于渐近正态性的理论结果,进一步讨论了模型系数线性约束性问题的Wald检验统计量的渐近性质.数值模拟和实例数据分析的结果均表明,利用经验似然估计处理带相依辅助信息函数的方法较传统的分位数回归估计更有效.因而,一般常系数线性分位数回归模型在独立假设下的结果,被推广至具有相依结构的一类变系数模型中去.     

斜拉桥拉索-阻尼器系统非线性瞬态响应分析

考虑索的抗弯刚度、垂度及几何非线性的影响,得出了索-阻尼器系统的空间非线性振动偏微分方程,用中心差分法将偏微分方程在空间内离散,导出了系统的非线性振动常微分方程组．结合Newmark法及虚拟力法提出了一种用于求解非线性振动瞬态响应的杂交分析算法．并以典型的斜拉桥拉索为研究对象,给出了数值算例,并与Runge-Kutta直接积分法进行了比较,说明了杂交算法的准确性及有效性．为大跨斜拉桥拉索的振动控制研究提供了一种简便、有效、快速的时程分析方法．     

Analysis of flow characteristics of granular material unloaded on nonlinear vibration inclined platform

In this study, the repeated discontinuous friction between granular material and contact platform and structural nonlinearity of inclined vibration platform giving rise to the vibration flow-aiding unloading is a complicated process, which has significant effects on the dynamic behaviors and flow characteristics of granular material. A simplified mathematical model of the inclined vibration platform and granular material is deduced by mechanical properties. Based on the equations of motion and a good degree of accuracy and applicability of the process with calculated data reported in the literature, the approximate analytical solution and flow properties are investigated by using the modified incremental harmonic balance method and numerical integration method. Moreover, the influences of friction coefficient, excitation amplitude, nonlinear stiffness and inclined angle on the complicated dynamic behaviors are explored and discussed. It is shown that the different motion paths of granular material on inclined vibration platform are observed depending on the different parameters. The increasing friction coefficient has complicated effects on the nonlinear dynamic behaviors of the granular material. The excitation amplitude and nonlinear stiffness can effectively control the flow characteristics of granular material at low excitation frequency but the inclined angle presents opposite property. The research may contribute to improve unloading efficiency, predict the motion state of granule and provide a theoretic foundation for further design the unloading system.     

Application of a revised cable theory to Rain-Wind-induced vibrations

Simultaneous occurrence of rain and wind can lead to vibrations with large amplitudes of inclined cables and hangers of arch bridges. These motion-induced vibrations are usually described with models based on the strip theory, or on the cable theory which is the best developed model [1]. The own solution concept derives complete nonlinear cable equations being mechanical equal to those known in literature but with a significant more simple structure by using longitudinal Green's strains and non-physical cable forces. The nonlinear effects of wind and rain forces are included. As an example of application a cable of the Erasmus bridge in Rotterdam (NL) will be analyzed. The own results are compared with the vibration amplitudes in the literature and with observations. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibration elimination in cable-stayed footbridges and bridges

In this paper, the problems of eliminating vibration in cable stayed footbridges and bridges by dynamically steering the tension in cables during construction vibration are considered. A physical and a mathematical model of cable stayed footbridges and bridges has been formulated. A damping model has been selected on the basis of an analysis of vibrations due to periodic excitation. Standard computer software and the author's own program, both leaning on Finite Element Method (FEM), have been used to analyze the eigenproblem and the forced vibration of bridges. On the basis of the formulated theory an efficient algorithm of forced vibration reduction analysis was established. The reduction is achieved by dynamically steering the tension in cables. A sensitivity analysis has been used. An example has been provided. The theory presented takes into account the new method in the elimination of vibration in cable stayed bridges and footbridges. It can therefore be applied to dynamic analysis of modern cable stayed bridges with typical structure systems. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling problems of steeply inclined cableway subjected to moving load

Problems of structural modeling of multi-span bicable ropeway systems due to significant inclination of a track are discussed in this paper with reference to the vibration analysis. The analytical continuous model of a cableway is formulated in a form which enables to describe in-plane vibrations of steeply inclined carrying cable subjected to traveling passenger carriers modeled by moving pendulums. The nonlinear interaction between carrying cable and moving carriers is taken into account in the moving load definition. Effects of a steep track slope are discussed on the basis of equations of motion of the system. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

任意变系数微分方程的精确解析法

工程中的许多问题归结为求解任意变系数微分方程的解.本文首次提出精确解析法,用以求解任意变系数微分方程在任意边界条件下的解.文中还给出精确解析法的一般计算格式,得到了一致收敛于精确解及其任意阶导数的解析表达式,并给出收敛性证明.文末给出四个算例,均得到较好的结果,证明了本文理论的正确性.     

Stress intensity factor for multiple cracks in bonded dissimilar materials using hypersingular integral equations

This paper deals with the multiple inclined or circular arc cracks in the upper half of bonded dissimilar materials subjected to shear stress. Using the complex variable function method, and with the help of the continuity conditions of the traction and displacement, the problem is formulated into the hypersingular integral equation (HSIE) with the crack opening displacement function as the unknown and the tractions along the crack as the right term. The obtained HSIE are solved numerically by utilising the appropriate quadrature formulas. Numerical results for multiple inclined or circular arc cracks problems in the upper half of bonded dissimilar materials are presented. It is found that the nondimensional stress intensity factors at the crack tips strongly depends on the elastic constants ratio, crack geometries, the distance between each crack and the distance between the crack and boundary.     

时滞影响下受控斜拉索的参数振动稳定性

研究了轴向激励作用下受控斜拉索系统主参数共振的时滞效应,考虑了拉索垂度和几何非线性的影响,基于Hamilton变分原理建立了受控斜拉索系统轴向激励下的非线性参数振动方程,利用Galerkin方法得到时滞动力系统,运用多尺度法对受控系统的主参数共振进行了分析,得到了不同时滞值、控制增益时参数振动稳定域和受控拉索的时程曲线.研究表明,时滞影响下斜拉索振动控制系统的效果变差,参数共振的稳定域发生偏移,对受控斜拉索系统的控制效果随着时滞的增大而变差,从而对控制系统的参数设计起到指导作用.     

任意边界条件下圆柱厚壳自由振动分析的空间变量变换法

本文提出一种一般解析方法——空间变量变换法,用以求解任意边界条件下圆柱厚壳自由振动问题.运用本文方法对悬臂圆柱厚壳的自振特性作了计算,计算结果与薄壳理论相应结果及试验值作了比较.理论分析和计算结果表明,本文方法具有很好的收敛性和精确性,可以推广用于分析梁、板、壳的自由振动.     

基于绳索作动器的大型太空望远镜桁架结构的振动主动控制

薄膜衍射是一种新型的太空望远镜的成像方式,它具有轻质、易折叠与展开、光学成像精度高等许多优点,是当今太空望远镜技术的研究热点.该文针对一类薄膜衍射太空望远镜桁架结构的振动主动控制进行了研究,提出了一种基于绳索作动器的振动主动控制策略.首先建立了望远镜桁架结构的动力学模型,然后采用粒子群优化算法研究了绳索作动器的优化布置...