重复型相同分段多自由度振动系统分析

构造了一种单摆和弹簧组成的重复型相同分段多自由度振动系统,导出了计算振动系统固有圆频率和振型矢量的简单公式,并对公式进行了证明和验证,同时导出了计算系统运动学方程中待定常数的公式.     

两质点两滑轮组成的两自由度问题研究

利用拉格朗日方程导出了两质点和两滑轮组成的两自由度系统的运动微分方程并通过计算机数值解，给出无摩擦时系统的运动图像，指出系统能在平衡位置附近运动，摩擦的作用不可忽略。     

对称型三原子分子振动的弹簧质量模型

给出了对称型三原子分子振动的一个模型。以键角变化和两个键长变化为广义坐标建立了微幅振动微分方程,得到了该模型的3个本征振动频率和对应的振动模式。利用文献数据对上述模型进行了检验。结果表明模型预测的分子振动频率与实验数据吻合良好。     

弹簧振子在光滑水平面内的运动规律

在非线性双自由度运动的弹簧振子中,光滑水平面内运动的模型具有运动微分方程简单、变量可分离的特点.本文通过极坐标描述法,建立了弹簧振子在光滑水平面内的运动微分方程.将与径向运动有关的变量分离出来,建立了径向运动微分方程,并基于其非线性的特点进行了定性分析和近似求解.使用MATLAB数值求解,模拟弹簧振子的运动轨迹,验证了本文的定性分析结论和两种特殊情形下的近似解的精度.     

窄带随机噪声作用下单自由度非线性干摩擦系统的响应

研究了单自由度非线性干摩擦系统在窄带随机噪声参数激励下的主共振响应问题.用Krylov-Bogoliubov平均法得到了关于慢变量的随机微分方程.在没有随机扰动情形,得到了系统响应幅值满足的代数方程.在有随机扰动情形,用线性化方法和矩方法给出了系统响应稳态矩计算的近似计算公式.讨论了系统阻尼项、非线性项、随机扰动项和干摩擦项等参数对于系统响应的影响.理论计算和数值模拟表明,当非线性强度增大时系统的响应显著变小,系统分岔点滞后;随着激励频率的增大系统响应变大,而当激励频率小于一定的值时,系统响应为零;增加干 关键词： 单自由度非线性干摩擦系统 主共振响应 Krylov-Bogoliubov平均法     

两电子人造分子的能级结构

给出了相距为d的两个单电子圆盘量子点构成的人造分子的能级结构,讨论了能级随d,ω0(谐振子圆频率)及B(外磁场强度)变化的情况。     

光子两自由度超并行量子计算与超纠缠态操控

光子系统在量子信息处理和传输过程中有非常重要的应用. 譬如, 利用光子与原子(或人工原子)之间的相互作用, 可以完成信息的安全传输、存储和快速的并行计算处理等任务. 光子系统具有多个自由度, 如极化、空间模式、轨道角动量、时间-能量、频率等自由度. 光子系统的多个自由度可以同时应用于量子信息处理过程. 超并行量子计算利用光子系统多个自由度的光量子态同时进行量子并行计算, 使量子计算具有更强的并行性, 且需要的量子资源少, 更能抵抗光子数损耗等噪声的影响. 多个自由度同时存在纠缠的光子系统量子态称为超纠缠态, 它能够提高量子通信的容量与安全性, 辅助完成一些重要的量子通信任务. 在本综述中, 我们简要介绍了光子系统两自由度量子态在量子信息中的一些新应用, 包括超并行量子计算、超纠缠态分析、超纠缠浓缩和纯化三个部分.     

人造氦分子能谱的近似计算

给出了均匀磁场中相距为d的两个双电子园盘量子点构成的人造氦分子的能级结构,讨论了能级随d,ω0(谐振圆频率)及B(外磁场强度)变化的情况.     

利用计算机辅助装调检测矩形大口径离轴非球面的方法研究

通过非球面的零位补偿法,完成了对矩形大口径离轴非球面镜的检测。先用光学设计软件Zemax从理论上分析了在检测中会出现的现象,并结合计算机辅助装调技术,确定在检测过程中相对敏感的自由度,然后控制这些量,使补偿器和非球面的相对关系与理论设计相吻合,在Zygo相位干涉仪上测得最终结果。在λ=632.8nm时,中心圆口径与两个边缘圆口径面形误差RMS分别为0.022λ,0.037λ,0.032λ。检测结果,达到预期目的。     

二能级原子玻色-爱因斯坦凝聚体与双模光场相互作用系统中原子激光的压缩性质

利用格子液体方法对二能级原子玻色-爱因斯坦凝聚体与双模光场相互作用系统的哈密顿量进行了改进,并且研究了系统中原子激光的压缩性质.结果表明:原子激光的两个正交分量均可被周期性压缩,其最大压缩深度主要依赖于光场初始压缩因子,而崩塌-回复振荡频率和量子Rabi振荡频率主要分别由光场与原子间的相互作用强度和光场圆频率决定.     

三线摆的运动方程、周期及角位置概率分布

基于保守系统拉格朗日方程给出三线摆在大摆角运动时的微分方程,以及小摆角线性振动近似处理方法,在考虑三线摆的结构尺寸取相应近似条件下,讨论了三线摆在大摆角和小摆角两种不同情况下的运动微分方程、周期及角位置概率密度分布情况及其在实验中的应用.     

On radially symmetric vibrations of orthotropic non-uniform disks including shear deformation

This paper deals with the free axisymmetric vibrations of orthotropic circular plates with linear variation in thickness. The analysis is based on a set of two differential equations derived by an extension of Mindlin's shear theory for plates. On simplification and algebraic manipulation, one of the dependent variables is eliminated from the governing equations of motion, giving rise to a fourth order linear differential equation with variable coefficients. The resulting differential equation is solved numerically by the Chebyshev collocation technique. Frequencies and mode shapes for the first five modes of vibration are computed for different plates.     

An analogy between free vibration of a plate and of a particle of mass

In this paper, the free flexural vibration of an elastic circular thin plate with an initial imperfection is investigated. Approximate solution of the problem for the fundamental frequency of vibration, of large amplitude and with the plate imperfection, leads to a non-linear ordinary differential equation with time as the independent variable. It is shown that this equation also represents the free vibration of a particle of mass on a shallow curve of fourth degree.. With this similarity in view, it is possible to draw an analogy between these two vibrations. A numerical analysis is made with particular reference to this analogy and the results are given in various figures which represent the vibratory motion and the period of vibration versus the initial amplitude of the plate or of the particle of mass.     

Free vibration analysis of the completely free rectangular plate by the method of superposition

While the subject of free vibration analysis of the completely free rectangular plate has a history which goes back nearly two centuries it remains a fact that most theoretical solutions to this classical problem are considered to be at best approximate in nature. This is because of the difficulties which have been encountered in trying to obtain solutions which satisfy the free edge conditions as well as the governing differential equation. In a new approach to this problem, by using the method of superposition, it is shown that solutions which satisfy identically the differential equation and which satisfy the boundary conditions with any desired degree of accuracy are obtained. Eigenvalues of four digit accuracy are provided for a wide range of plate aspect ratios and modal shapes. Exact delineation is made between the three families of modes which are characteristic of this plate vibration problem. Accurate modal shapes are provided for the response of completely free square plates.     

Transverse Vibration and Stability Analysis of Circular Plate Subjected to Follower Force and Thermal Load

Transverse vibration and stability analysis of circular plate subjected to follower force and thermal load are analyzed . B ased on the thin plate theory in involving the variable temperature, the differential equation of transverse vibration for the axisymmetric circular plate subjected to follower force and thermal load is established. Then, the differential equation of vibration and corresponding boundary conditions are discretized by the differential quadrature method. Meanwhile, the generalized eigenvalue under three different boundary conditions are calculated. In this case, the change curve of the first order dimensionless complex frequency of the circular plate subjected to the follower force in the different conditions with the variable temperature coefficient and temperature load is analyzed. The stability and corresponding critical loads of the circular plate subjected to follower force and thermal load with simply supported edge, clamped edge and free edge are discussed. The results provide theoretical basis for improving the dynamic stability of the circular plate.     

Residual vibration reduction of a flexible beam deploying from a translating hub

This paper presents a method for reducing the residual vibration of a flexible beam deployed from a translating hub. Whereas previous studies have discussed reducing vibration in translating constant-length beams, this study investigates a vibration reduction method for translating beams of variable length. The partial differential equation of motion for a translating beam is derived and transformed into a variational equation. Based on the discretized equations from the variational equation, the dynamic responses of the flexible beam under translation are analyzed. A vibration reduction method is proposed that is effective for both constant- and variable-length deploying translating beams.     

一般阻尼随机微分方程的拟局部振荡算法

提出了一种模拟随机微分方程的拟局部振荡算法,即利用算符劈裂方法和势函数的泰勒展开,对噪声作用下耗散粒子的时间演化算符进行分解,得到了对应涨落行为的扩散算符和对应确定轨迹的漂移算符.其中局部简谐势场的涨落过程可获得解析解,而剩余的确定项则利用简单的Euler算法积分.应用到几个算例并与常用的两种算法相比较,结果表明:本算法随时间步长最稳定,可使用较大的时间步长.     

对称双弹簧振子横向振动的椭圆函数解

通过分析对称双弹簧振子横向振动的特点,在立方非线性振动精确解的基础上提出振动方程的椭圆函数型近似解析解,并与数值解结果进行了比较.     

Free vibration of non-circular cylindrical shells with variable circumferential profile

An analysis is presented of the free vibration of non-circular cylindrical shells with a variable circumferential profile expressed as an arbitrary function. The applicability of thin-shell theory is assumed and the governing equations of vibration of a non-circular cylindrical shell are written in a matrix differential equation by using the transfer matrix of the shell. Once the transfer matrix has been determined by numerical integration of the matrix equation, the natural frequencies and mode shapes of vibration are calculated numerically in terms of the matrix elements. The method is applied to cylindrical shells of three or four-lobed cross-section, and the effects of the length of the shell and the radius at the lobed corners on the vibration are studied.     

Vibrations of non-uniform rectangular plates: A spline technique method of solution

The fourth order differential equation governing the transverse motion of an elastic rectangular plate of variable thickness has been solved, by using the quintic spline interpolation technique. An algorithm for computing the solution of this differential equation is presented, for the case of equal intervals. Frequencies, mode shapes and moments for doubly symmetric, antisymmetric-symmetric and second symmetric-symmetric modes of vibration are presented for various cases of boundary conditions.