R-函数理论及准Green函数方法在正交各向异性板振动问题中的应用

首次将R-函数理论及准Green函数方法应用于求解固支正交各向异性薄板的自由振动问题。首先引入参数变换,将正交各向异性薄板的自由振动微分方程转化为双调和算子的边值问题,并应用R-函数理论,以解析函数形式描述复杂边界形状;利用问题的基本解和边界方程构造了一个准Green函数,该函数满足了问题的齐次边界条件;通过R-函数理论构造适当的边界方程,消除了积分方程核的奇异性;再采用Green公式将其化为第二类Fredholm积分方程。数值算例表明:该方法减少了理论计算量,精度较高。本文还证明了其优越性和正确性,是一种新型的数学方法。     

三角形分形网络电阻上的电流分布

中点三角形和相似缩小正三角形的无限叠代,形成三角形电阻分形网络.自相似性要求节点上电流分配和比例系数不变.利用基尔霍夫定律,得到了这些系数的值.利用电阻电路的线性关系,得到了分形网络节点之间的等效电阻.     

Quasi-Green＇s function method for free vibration of simply-supported trapezoidal shallow spherical shell

The idea of quasi-Green＇s function method is clarified by considering a free vibration problem of the simply-supported trapezoidal shallow spherical shell. A quasi- Green＇s function is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the prob- lem. The mode shape differential equations of the free vibration problem of a simply- supported trapezoidal shallow spherical shell are reduced to two simultaneous Fredholm integral equations of the second kind by the Green formula. There are multiple choices for the normalized boundary equation. Based on a chosen normalized boundary equa- tion, a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome. Finally, natural frequency is obtained by the condition that there exists a nontrivial solution to the numerically discrete algebraic equations derived from the integral equations. Numerical results show high accuracy of the quasi-Green＇s function method.     

Green quasifunction method for vibration of simply-supported thin polygonic plates on Pasternak foundation

A new numerical method—Green quasifunction is proposed.The idea of Green quasifunction method is clarified in detail by considering a vibration problem of simply-supported thin polygonic plates on Pasternak foundation.A Green quasifunction is established by using the fundamental solution and boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem.The mode shape differential equation of the vibration problem of simply-supported thin plates on Pasternak foundation is reduced to two simultaneous Fredholm integral equations of the second kind by Green formula.There are multiple choices for the normalized boundary equation.Based on a chosen normalized boundary equation,a new normalized boundary equation can be established such that the irregularity of the kernel of integral equations is overcome.Finally,natural frequency is obtained by the condition that there exists a nontrivial solution in the numerically discrete algebraic equations derived from the integral equations.Numerical results show high accuracy of the Green quasifunction method.     

Quasi-Green’s function method for free vibration of clamped thin plates on Winkler foundation

The quasi-Green’s function method is used to solve the free vibration problem of clamped thin plates on the Winkler foundation. Quasi-Green’s function is established by the fundamental solution and the boundary equation of the problem. The function satisfies the homogeneous boundary condition of the problem. The mode-shape differential equation of the free vibration problem of clamped thin plates on the Winkler foundation is reduced to the Fredholm integral equation of the second kind by Green’s formula. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The numerical results show the high accuracy of the proposed method.     

单模光纤中基于暗孤子交叉相位调制的亮脉冲压缩

对单模光纤正群速色散区中基于暗孤子交叉相位调制的亮脉冲压缩进行了定量计算和详细分析，结果表明，亮脉冲的压缩程度与昱孤子相对于亮脉冲的初始峰值功率有关，初始相对峰值功率愈高，亮脉冲的压缩比和压后的峰值功率愈高，同时所需的光纤长度愈短，对于给定的初始条件，光纤长度存在一最佳值，在最佳长度处，压缩后的亮脉冲峰值功率最高，宽度最窄。     

Pasternak地基上简支板振动问题的准格林函数方法

提出一种新的数值方法——准格林函数方法．以Pasternak地基上简支多边形薄板的振动问题为例,详细阐明了准格林函数方法的思想．即利用问题的基本解和边界方程构造一个准格林函数,这个函数满足了问题的齐次边界条件,采用格林公式将Pasternak地基上薄板自由振动问题的振型控制微分方程化为两个耦合的第二类Fredholm积分方程．边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程来表示问题的边界,以克服积分核的奇异性,最后由积分方程的离散化方程组有非平凡解的条件,求得固有频率．数值方法表明,该方法具有较高的精度．     

简支梯形底扁球壳自由振动问题的准Green函数方法

以简支梯形底扁球壳的自由振动问题为例,详细阐明了准Green函数方法的思想.即利用问题的基本解和边界方程构造一个准Green函数,此函数满足了问题的齐次边界条件,采用Green公式,将简支梯形底扁球壳自由振动问题的振形控制微分方程化为两个耦合的第二类Fredholm积分方程.边界方程有多种选择,在选定一种边界方程的基础上,可以通过建立一个新的边界方程来表示问题的边界,以克服积分核的奇异性.最后由积分方程的离散化方程组有非平凡解的条件,求得固有频率.数值结果表明,该方法具有较高的精度.     

一种新型快速检测半胱氨酸的荧光探针EI北大核心CSCD

基于三苯胺母体的强供电子能力,设计合成了一种共轭性良好的新型半胱氨酸(Cys)荧光探针。采用荧光光谱法和紫外-可见光谱法研究了目标探针T-Probe对半胱氨酸(Cys)的光谱响应。结果表明:目标探针分子与Cys作用后,荧光发射波长有约20 nm红移,荧光强度发生明显的增强,在365 nm紫外灯下,溶液由青色变为蓝色;探针分子选择性识别Cys的检测限为98.4 nmol/L,且灵敏度较高。     

电化学法合成荧光碳纳米粒子及性能表征

介绍了一种通过电化学氧化-还原循环的方法的制备碳纳米粒子并对其相关性质进行了表征.透射电镜结果表明,制备的纳米粒子粒径大小分布在(2.5±0.3)nm区间,而且其晶格间距为0.33nm左右,完全符合石墨的晶体特征.荧光光谱显示,该粒子在456nm具有稳定的可见光发射,其荧光量子效率达到了0.11.此外还考察了纳米碳颗粒的电化学发光性质,结果表明,该粒子在电化学发光检测方面具有潜在的应用价值.