低频振动管外流动与传热特性研究

采用数值模拟与实验相结合的方法,研究了低频振动管外的流动与传热特性,分析了不同参数对换热性能的影响.数值计算结果的场协同理论分析与实验表明:振动有利于强化传热,且其强化传热的效果随着振动频率与振幅升高而增强.在半周期内,时相位为90°时管外的换热性能最好,在一定范围内协同角余弦值随振动频率的变化与振幅基本无关.对比不同管型,沿椭圆管短轴方向振动的协同角余弦值最高,传热效果最好.     

复摆的振动分析

研究复摆的非线性振动，从能量和摆角两个方面来分析它们对复摆运动的影响，用第一类完全椭圆积分求出了复摆振动的解和周期，对非线性特征进行了分析。     

离散余弦型线圈结构的二极场应用研究

介绍了粒子加速器中超导二极试验磁体中离散余弦型(DCT)超导线圈的电磁设计、线圈制作和验证测试过程。     

椭圆曲面摆参数振动的数值计算及仿真

为研究变摆长参数振动的规律,以椭圆曲面摆装置为对象,根据刚体定轴转动定律及椭圆曲线方程,构建了椭圆曲面摆的二阶变系数齐次微分动力学方程.运用四阶龙格-库达法对方程进行数值求解,并结合MATLAB软件绘制了椭圆曲面摆振动不同的图像,给出椭圆曲面摆在无阻尼状态时的方程通解形式,在此基础上,讨论了不同参数对椭圆曲面摆振动特性的影响情况.研究表明,椭圆曲面摆与单摆振动类似,在无阻尼状态时小球摆动符合正弦函数变化规律,小球摆动周期受到阻尼系数、椭圆曲面几何尺寸、振幅等参数影响.研究结论丰富了关于变摆长单摆参数振动教学内容.     

超声马达中夹紧压电环的非轴对称振动

应用环形压电板振子的超声马达具有厚度小的优点,能满足很多工程上的要求。其工作原理和其他类型的超声马达一样,也是通过摩擦力把振子表面质点的椭圆运动变换为转子的运动。因此,为要开发出性能优良的超声马达,必须清楚了解作为超声马达定子的环形板的振动特征。过去对环形板或圆盘的分析均仅考虑自由振动的情形,本文则分析了在环的内缘或外缘夹紧的情况下,环形压电板的非轴对称振动。内容包括振动时的位移分布图样,自由边缘上质点的椭圆运动,表面上感应电荷的分布及机电耦合因数等。还进行了数字计算,并从应用于超声马达的角度出发,对几种不同的振动模式作了评估。     

强非局域介质中高斯型损耗空间光孤子

 利用变分法研究了1+1维傍轴高斯光束在含有小损耗的强非局域非线性介质中的传输特性，得到了光束各参量的演化方程、束宽的演化规律和一个临界功率。在介质损耗足够小的前提下，当光束初始功率等于临界功率时，得到了一个束宽随传输距离缓慢展宽的准空间光孤子——损耗空间光孤子；当光束初始功率小于临界功率时，光束束宽则按雅可比椭圆正弦函数和椭圆余弦函数作准周期展宽变化；当光束初始功率大于临界功率时，光束束宽将从按雅可比椭圆正弦函数和椭圆余弦函数作准周期压缩变化过渡到按雅可比椭圆正弦函数和椭圆余弦函数准周期展宽变化。     

太阳辐射观测仪余弦误差修正方法

为了提高太阳辐射观测仪测量准确度,针对余弦校正器自身漫射特性和菲涅耳反射引起的余弦误差,研究了不同安装形式、不同结构下修正余弦误差的方法.结合太阳辐射特性和余弦误差的产生因素,提出了余弦校正器外露、余弦器外露配合挡光环两种安装形式下的余弦误差修正方法,以及余弦校正器、积分腔两种结构形式下的余弦误差修正方法.根据太阳辐射观测仪的使用要求,利用TracePro对不同安装方式下的余弦误差进行建模仿真,利用高准直性太阳模拟器配合转台和转臂模拟不同方向的准直太阳光,并实测余弦误差.实测结果表明,余弦器外露配合挡光环形式下,入射角小于±80°,余弦误差可优于±6%.该修正方法可有效地减小太阳辐射光大入射角情况下的余弦误差,提高太阳辐射观测准确度.     

部分相干余弦-高斯光束

引入部分相干余弦-高斯光束,推导出部分相干余弦-高斯光束通过近轴ABCD光学系统的传输公式和M2因子,研究了部分相干余弦-高斯光束通过像散透镜的传输特性.结果表明,部分相干余弦-高斯光束的M2因子与部分相干余弦-高斯光束的空间相干参量和离心参量有关,但与透镜的像散系数无关.适当选取空间相干参量,离心参量或像散系数,在几何焦面处可得到类高斯、平顶和空心等不同的光强剖面,实现部分相干余弦-高斯光束的空间整形.     

部分相干余弦-高斯光束

引入部分相干余弦-高斯光束,推导出部分相干余弦-高斯光束通过近轴ABCD光学系统的传输公式和M2因子,研究了部分相干余弦-高斯光束通过像散透镜的传输特性.结果表明,部分相干余弦-高斯光束的M2因子与部分相干余弦-高斯光束的空间相干参量和离心参量有关,但与透镜的像散系数无关.适当选取空间相干参量,离心参量或像散系数,在几何焦面处可得到类高斯、平顶和空心等不同的光强剖面,实现部分相干余弦-高斯光束的空间整形.     

余弦分布球面电荷的电场

用电场的迭加原理及等效变换法则，可给出真空中具有余弦分布球面电荷的电场公式． 若在匀强电场的无限大介质中引入另一均质介质球（包括挖成一个球形空腔），或引入一个导体球，则球面上的束缚电荷或自由电荷均属于余弦型分布．运用静电场边值条件（Ｄ１ｎ＝Ｄ２ｎ），可决定相应的电荷面密度的最大值σ０；从而求出相应情况下的电场分布．     

A pendulum on a rotating and vibrating foundation

The motion of a pendulum is investigated in a uniform gravity field. The foundation of the pendulum is assumed to rotate around the vertical simultaneously accomplishing harmonic vibrations along it with a high frequency and small amplitude. With use of the classical perturbation theory and modern methods of analysis of nonlinear dynamical sets, the problem on the existence and stability of periodic motions of a pendulum with the period equal to that of the vibrations of the foundation is solved.     

An autoparametric energy harvester

This paper presents a numerical study of an autoparametric system composed of two elements: a pendulum and an excited nonlinear oscillator. Owing to an inertial coupling between the two elements, different types of motion are possible, from periodic to chaotic. This study examines a linear induction of an energy harvester depending on the pendulum motion. The harvester consists of a cylindrical permanent magnet mounted on a rotor and of four windings fixed to the housing as a stator. When the pendulum is rotating or swinging, the converter is generating energy due to magnetic induction. In this paper, a method utilizing parametrical resonance for harvesting energy from low frequency vibrations is studied. The authors compare energy induced by different types of pendulum motion: swinging, rotation and chaotic dynamics. Additionally, voltage values for different parameters of excitation are estimated.     

扭摆振动实验

为了丰富“非线性系统实验”课程的教学内容,开设了扭摆振动实验,将力学中的非线性现象引入到教学中.在实验内容的设计上,采取线性振动和非线性振动相结合的方式,即:首先研究扭摆的线性振动,如阻尼振动、受迫振动等,先对振动问题有基本的理解,然后再研究扭摆的非线性振动,分别固定驱动频率、改变励磁电流和固定励磁电流、改变驱动频率,观察非线性摆的运动情况.     

Tautochronic centrifugal pendulum vibration absorbers: General design and analysis

Since the 1930s, centrifugal pendulum vibration absorbers have been used in rotating and reciprocating machinery for the attenuation of torsional vibrations. A large variety of absorber types were suggested and the design was done by linearization theory until the introduction of the tautochronic bifilar pendulum absorbers. Since then, the performance and dynamic stability of this specific absorber type have been considered in analytical and numerical investigations. Different perturbations, e.g. nonlinear mistuning, were considered in order to optimize the system performance, but the characteristic bifilar design remained unchanged. In this paper, a general approach for the design of tautochronic pendulum vibration absorbers is proposed. As a result, it is possible to deal with a large variety of non-bifilar centrifugal vibration absorber designs which provide application-related optimal performance and resolve some of the existing design limitations.     

非线性单摆的Jacobi椭圆函数解

对非线性单摆运动进行了数值分析,用Matlab绘出其运动相图,并求出了它在一定条件下的Jacobi椭圆函数解.     

Kapitza pendulum effect in an amorphous magnet with a weak disorder

The mechanism of magnetization orientation in an amorphous ferromagnet under the effect of a weak anisotropic disorder of the random anisotropy type is considered. The disorder orients the magnetization so as to minimize the transverse magnetization fluctuations. The effect of the disorder is found to be analogous to the effect of vibrations of the suspension point on the orientation of a mechanical pendulum (the Kapitza pendulum). The disorder types ensuring the presence of the orienting effect are specified; simultaneously with the effect, the continuous degeneracy is lifted and the Larkin-Imry-Ma mechanism of long-range order collapse is suppressed.     

Dynamics of an anharmonic oscillator with a periodic perturbation

We study the features of the stochastic dynamics of a Hamiltonian system with the potential x ²ⁿ subjected to an external monochromatic perturbation. Three regimes of stochastic diffusion, which differ in the value of the amplitude of the external perturbation, are detected. We demonstrate the possibility of chaotic regimes manifesting themselves in pendulum vibrations of the well of a water-moderated and-cooled nuclear power reactor as an application of the model being investigated. Finally, we propose a method of simple proportional control, which makes it possible to control the chaotic vibrations of the anharmonic oscillator. Zh. éksp. Teor. Fiz. 115, 361–377 (January 1999)     

用局部常化三倍角公式研究单摆周期

应用局部常化方法对三倍角公式进行局部常化处理,对一类非线性动力学方程进行了一种简洁的近似修正,得到精确度较高的大摆角单摆运动周期的两个新结论,同时用此结论推导出一个简洁的推论,并且用3种方法进行了具体比较.     

求大摆角单摆周期近似解的"局部常化"方法

建构“局部常化”的近似处理方法,对一类非线性动力学方程进行了一种简洁的近似修正,得到大摆角单摆运动周期的一个新结论,并且给出了精确度很高的三个推论,同时得到了第一类完全椭圆积分的一种简洁的近似公式．