Broadband locally resonant beams containing multiple periodic arrays of attached resonators

The plane wave expansion method is extended to study the flexural wave propagation in locally resonant beams with multiple periodic arrays of attached spring-mass resonators. Complex Bloch wave vectors are calculated to quantify the wave attenuation performance of band gaps. It is shown that a locally resonant beam with multiple arrays of damped resonators can achieve much broader band gaps, at frequencies both below and around the Bragg condition, than a locally resonant beam with only a single array of resonators, although the two systems have the same total resonator masses.     

Dynamic stability of pretwisted columns under periodic axial loads

This paper deals with the parametric instability of pretwisted columns subjected to static and periodic axial loads. The governing equations of the problem are reduced to time domain by applying Galerkin's method. The instability regions are determined with the procedure proposed by Hsu. The analysis includes free vibration and static buckling of the column as special cases. Although the method is quite general, numerical calculations are carried out only for a simply supported column. Free vibration frequencies, static buckling loads and the coefficients of the instability regions are obtained for various values of the pretwisting angle and those of the cross sectional rigidity ratio of the column.     

一类非线性动力系统的稳定性及周期运动

根据“库仑扭秤”实验的原理提出了一个非线性动力系统模型,分析了其稳定性及其周期运动．     

高稳定线性调谐GaAs基波长可调谐共振腔增强型探测器

研制了一种GaAs基波长可调谐共振腔增强型探测器. 采用分子束外延设备生长In_0.25Ga_0.75As/GaAs量子阱作为器件的有源区, 无偏压时器件的响应峰波长在1071 nm,器件在21 V的直流调谐电压下,实现了波长大于23 nm的调谐. 统计结果表明,当调谐电压大于5 V时,调谐电压与响应波长之间具有稳定、精确的对应关系, 且近似线性调谐,同时对器件响应峰的特性进行了理论分析. 关键词： GaAs 共振腔增强型探测器 高稳定 线性调谐     

具有一般非线性弹性力和广义阻尼力的相对转动非线性系统的周期解问题

讨论了一类相对转动非线性动力系统的周期解问题.首先建立了一类具有一般非线性弹性力、广义阻尼力和强迫周期力项的相对转动非线性动力系统;其次得到了对应自治系统的周期解不存在性结果,以及运用Mawhin重合度理论得到了该模型的周期解存在性结果,推广了已有的结果;最后举例证明本文结果的正确性.     

余弦平方高斯光束通过无光栏透镜的梯度力

基于Collins公式推导了余弦平方高斯光束通过无光栏透镜光学系统聚焦后的光强分布及梯度力,采用数值模拟分析梯度力分布及光阱的数量、位置及尺度随光束参数、光束入射距离及系统菲涅耳数的变化。结果表明:光束相关参数b越大光阱的数量越多,光阱的位置随光束入射距离而改变,大小随系统菲涅耳数的增加而减小,但不影响其位置。     

Dynamic characteristics of resonant gyroscopes study based on the Mathieu equation approximate solution

Dynamic characteristics of the resonant gyroscope are studied based on the Mathieu equation approximate solution in this paper.The Mathieu equation is used to analyze the parametric resonant characteristics and the approximate output of the resonant gyroscope.The method of small parameter perturbation is used to analyze the approximate solution of the Mathieu equation.The theoretical analysis and the numerical simulations show that the approximate solution of the Mathieu equation is close to the dynamic output characteristics of the resonant gyroscope.The experimental analysis shows that the theoretical curve and the experimental data processing results coincide perfectly,which means that the approximate solution of the Mathieu equation can present the dynamic output characteristic of the resonant gyroscope.The theoretical approach and the experimental results of the Mathieu equation approximate solution are obtained,which provides a reference for the robust design of the resonant gyroscope.     

具有一般广义阻尼力和强迫周期力的相对转动非线性动力学模型的周期解

研究了一类具有一般广义阻尼力和强迫周期力项的相对转动非线性动力学模型的周期解问题.讨论了对应自治系统的周期解问题.运用Mawhin重合度理论,得到了该模型的周期解存在惟一性结果,推广了已有的结果,并且列举了具体的例子来说明结果的新颖性.     

The dynamic stability resonant cavity design of two rod Nd:YAG laser

The stability of the higher output power with high-quality beams is very important parameter in material processing. This paper presents using the S parameter and Gauss beam parameters matching to design efficient resonant cavity of two-rod Nd:YAG. The fundamental mode beam radius in rod, fundamental mode beam radius on the mirror, beam quality factor, and the value of the degree of the symmetry of the TEM00 mode volume as a function of the between neighbor rods distance, laser rod end face to mirror distance, and input power are simulated. The design method of resonant cavity is illustrated and compared with previously published experimental measurements for different pump power and the length of the cavity parameters and a good agreement has been found.     

原子力显微镜在轻敲模式下的动力学模型

基于Hamaker假设、Lennard-Jones势能定律及经典弹性理论建立了一种新型的球体与平面黏着接触的弹性模型，该模型显示黏着力在原子力显微镜(AFM)针尖趋近和撤离样品表面，即加载和卸载的两个过程中存在黏着滞后现象，表明了AFM在轻敲工作模式中存在能量耗散.同时，根据所建的黏着接触弹性模型，建立了AFM在轻敲工作模式下的动力学模型，研究了AFM在轻敲工作模式下的振动幅度、相位差及耗散功率随针尖与样品表面间距的变化规律，仿真结果与现有的实验结果相一致.     

基础激励下分数阶线性系统的响应特性分析

本文研究了基础激励下含分数阶阻尼的线性系统的响应特性. 当基础激励为简谐激励时, 通过待定系数方法求得系统的动力传递系数; 当基础激励为非简谐周期激励时, 首先将激励展开成傅里叶级数, 然后根据线性系统的叠加原理求得激励中各阶频率成分所引起的动力传递系数, 并根据展开的傅里叶级数解决了数值运算中的不可导问题. 用数值仿真的方法对解析结果进行了验证, 两者符合良好, 证明了解析分析的正确性. 研究表明, 基础激励引起的动力传递系数依赖于分数阶阻尼阶数的值, 通过调节阻尼阶数可以控制动力传递系数的大小. 对于基础激励为非简谐的周期激励情况, 当激励频率一定时, 激励中的高阶频率成分引起的动力传递系数可能大于激励中的低阶频率成分引起的动力传递系数. 因此, 激励中的高阶频率成分所起的作用是不可忽略的.     

Dynamic stability of linearly varying thickness viscoelastic rectangular plate with crack and subjected to tangential follower force

Based on the two-dimensional viscoelastic differential constitutive relation and the thin plate theory, the differential equations of linearly varying thickness viscoelastic plate with crack and subjected to uniformly distributed tangential follower force in the Laplace domain are established, and the expression of the additional rotation induced by the crack is given. The complex eigenvalue equations of linearly varying thickness viscoelastic plate constituted by elastic behavior in dilatation and the Kelvin-Voigt laws for distortion with crack and under the action of uniformly distributed tangential follower force are obtained by the differential quadrature method. The generalized eigenvalue under different boundary conditions is calculated, and the curves of real parts and imaginary parts of the first three order dimensionless complex frequencies versus uniformly distributed tangential follower force are obtained. The effects of the aspect ratio, the thickness ratio, the crack parameters and the dimensionless delay time on the dynamic stability of the viscoelastic plates are analyzed.     

高聚焦高斯光束对左手性材料球轴向力的光线模型计算

采用几何光线模型, 将基模高聚焦高斯光束对微米量级介电球和左手性材料球的轴向作用力进行了理论推导和数值模拟, 并对介电球和左手性小球的受力进行了比较. 对于介电球, 可以实现单光束陷阱捕陷介电球; 在右手性材料环境中的左手性材料小球, 受到的轴向作用力总是沿光传播的方向, 激光和左手性材料球的参数共同决定轴向力的最大值出现在光轴上的位置. 而在相对折射率较小时, 左手性材料小球的受力是介电球的百倍. 关键词： 基模高斯光束 几何光线模型 轴向作用力 左手性材料     

非共面多光束干涉及其在制作周期性微结构中的应用(Ⅰ)--一般分析及二维周期结构

非共面多光束干涉可以在空间形成二维或三维周期性强度分布,从而被用来制作二维或三维光子晶体.本文将对此课题的相关物理基础进行较为系统的分析和讨论,为沟通基础物理与近代物理的联系,理解光子晶体这一重要的前沿课题从一个侧面打下基础.本文第一部分首先简要介绍了此领域的相关背景,然后给出非共面多光束干涉的一般分析,最后着重讨论了非共面三光束干涉所形成的二维周期性空间结构,包括结构类型、光束设计及偏振最佳化等问题.     

非共面多光束干涉及其在制作周期性微结构中的应用(Ⅱ)--三维周期结构

分别在空域和倒格子空间介绍了非共面4光束干涉形成三维周期性微结构,即三维光子晶体的物理基础,证明了固体物理中的所有14种布拉维格均可用非共面4光束干涉来得到;给出了一些制作典型晶格的光束设计;并对相关问题,例如各光束振幅比、偏振态的选取及其对最终结构的影响进行了讨论.     

用纵横波声时比法测螺栓轴力精度研究

用纵横波测量螺栓轴力的技术已取得较大发展,本文介绍了纵横波比值法原理,通过理论推导,获得比值法计算的简易公式。建立试验平台,用现场用螺栓进行标定和测量,得出比值法在工程实践状态下的测量误差为10%以内,基本能满足工程应用的要求。此外,针对试验结果,本文还初步探讨了误差出现的原因以及提高精度的方法。本文介绍的比值法,无需精确测量标定螺栓长度和纵横波声速,现场应用更加简洁,具有较大的工程应用价值。     

On the stability of the three classes of Newtonian three-body planar periodic orbits

Currently,the fifteen new periodic orbits of Newtonian three-body problem with equal mass were found by Suvakov and Dmitra sinovi[Phys Rev Lett,2013,110:114301]using the gradient descent method with double precision.In this paper,these reported orbits are checked stringently by means of a reliable numerical approach(namely the"Clean Numerical Simulation",CNS),which is based on the arbitrary-order Taylor series method and data in arbitrary-digit precision with a procedure of solution verification.It is found that seven among these fifteen orbits greatly depart from the periodic ones within a long enough interval of time,and are thus most possibly unstable at least.It is suggested to carefully check whether or not these seven unstable orbits are the so-called"computational periodicity"mentioned by Lorenz in 2006.This work also illustrates the validity and great potential of the CNS for chaotic dynamic systems.     

Kirchhoff弹性直杆在力螺旋作用下的稳定性

研究受力螺旋作用的圆截面Kirchhoff弹性直杆在各种边界条件下的稳定性问题. 用直角坐标和Cardano角表示截面的形心位置和姿态. 由Kirchhoff方程得到弹性细杆的直线平衡特解,导出线性化扰动方程及其通解. 根据边界条件确定积分常数的非零解存在条件,讨论了各种边界条件,如两端铰支、两端固定、一端铰支一端固定以及一端固定一端自由的弹性细杆直线平衡状态的稳定性,导出了临界载荷的表达式,绘制了稳定域,将Greenhill公式推广到其他边界条件,并且使压杆的Euler 公式成为其特例. 关键词： Kirchhoff弹性杆 稳定性 力螺旋 Greenhill公式     

Temperature dependence of the stability of written bits in a magnetic hard-disk medium investigated by magnetic force microscopy

The thermal stability of written bits in a magnetic hard-disk medium has been investigated with a magnetic force microscope (MFM), which was equipped with an in situ heating system capable of heating the medium up to 300 °C. It is shown that both the annealing temperature and the duration have significant effect on the decay of the MFM signal. No signal decay is observed when annealing for 30 min up to temperatures of 200 °C. The MFM signal decays rapidly with increasing temperature, for temperatures over 200 °C. Repeated annealing at 280 °C with a duration below 10 min does not cause any signal decay.