用线化和校正法近似求解一种非谐振动

利用拉格朗日方程建立了单质点弹簧振子非线性振动方程,作出了回复力、势能随坐标的变化曲线以及相图.应用第一类完全椭圆积分求出了非线性振动周期的精确解.应用线化和校正法对单质点弹簧振子的周期和近似解进行了求解.利用Maple计算机绘图,分别作出了它们的周期近似解与周期精确解随振幅的变化曲线以及近似解与数值解的变化曲线.利用线化和校正法所求得的近似解与数值解比较,具有简单实用、精度高、相对误差低等优点,在求解非线性振动中具有一定的实用价值.     

对称圆环状多原子分子的自由振动

考虑对称的圆环状多原子分子的振动问题,给出了该振动系统简正频率的数学表达式和自由振动的一般解.     

输电线非线性振动问题的同伦映射近似解

研究了一类输电线非线性振动的动力学模.利用同伦映射方法,得到了该模型的任意次精度的近似解. 关键词： 输电线 非线性振动 同伦映射 近似解     

弹簧振子振动的探讨

对于弹簧振子的振动,通常只讨论其纵向振动,横向振动由于其恢复力与位移不成正比,不是简谐振动,并且难以求得其振动规律的解析解.通过数值计算的方法可以得到在玩具弹簧和小振动条件下,横向振动的规律.     

一维分子链中激子与声子的相互作用和呼吸子解

运用连续极限近似，求解声子与激子相互作用的运动方程，得到了简谐分子链和 非简谐分子链中晶格振动的孤子解，在考虑三次非简谐势的情况下，一维分子链晶格振动具 有扭结孤子解，在考虑具有四次非简谐势的情况下，得到一维分子链晶格振动具有呼吸子解 . 关键词： 一维分子链 激子 声子 孤子 呼吸子 非线性效应     

利用线化和校正法求非线性单摆运动的周期

应用线化和校正方法,研究了单摆的非线性振动,作出了周期比和相对误差随摆角的变化曲线.将所得近似解与精确解比较可知,该方法具有简单实用,精度高,相对误差低等优点,对于求解非线性振动问题具有一定的实用价值.     

矩形薄膜受迫横振动问题的求解及可视化

膜的横振动分析在乐器膜、耳膜以及植物细胞膜中有着广泛的应用价值.相比自由振动,受迫膜振动问题的研究更符合应用实际.本文采用数学物理定解问题的傅里叶级数法与冲量定理法,对四周固定的均匀矩形薄膜振动问题进行了研究,得到了此类问题在受迫振动下的解析解,并对其振动状态进行了可视化分析.研究发现：一维弦振动解法同样可为二维有界膜振动问题提供简便的求解途径,且膜振动将呈现更加丰富的特点.本文的二维非齐次振动问题的冲量定理解法还可推广到二维有源(汇)输运问题中去.     

具有在位势的一维双原子链中杂质引起的对称局域模

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解,给出了在位势对局域振动影响的基本特征,并简要讨论了对称局域模的存在形式.     

具有在位势的一维双原子链中杂质引起的局域振动

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解, 给出了在位势对局域振动影响的基本特征,并简要讨论了局域模的存在形式.     

垂直悬挂质点弹簧系统的振动

讨论了振动的振幅与周期的变化规律,给出了当质点质量m0与弹簧质量m之比趋于零与趋于无穷大以及系统水平放置时的振动解.     

High-frequency ultrasonic wire bonding systems

The vibration characteristics of longitudinal-complex transverse vibration systems with multiple resonance frequencies of 350-980 kHz for ultrasonic wire bonding of IC, LSI or electronic devices were studied. The complex vibration systems can be applied for direct welding of semiconductor tips (face-down bonding, flip-chip bonding) and packaging of electronic devices. A longitudinal-complex transverse vibration bonding system consists of a complex transverse vibration rod, two driving longitudinal transducers 7.0 mm in diameter and a transverse vibration welding tip. The vibration distributions along ceramic and stainless-steel welding tips were measured at up to 980 kHz. A high-frequency vibration system with a height of 20.7 mm and a weight of less than 15 g was obtained.     

Nonlinear free transverse vibration of an axially moving beam: Comparison of two models

Nonlinear free transverse vibration of an axially moving beam is investigated. A partial-differential equation governing the transverse vibration is derived from the Newton's second law. Under the assumption that the tension of beam can be replaced by the averaged tension over the beam, the partial-differential reduces to a widely used integro-partial-differential equation for nonlinear free transverse vibration. The method of multiple scales is applied directly to two equations to evaluate nonlinear natural frequencies. Numerical examples are presented to demonstrate the analytical results and to highlight the difference between two models. Two models yield the essentially same results for the weak nonlinearity, the small axial speed and the low mode, while the difference between two models increases with the nonlinear term, the axial speed, and the order of mode.     

Vibration of edge reinforced annular plates

The free transverse vibration of annular plates reinforced by circular rings along the simply supported outer and free inner boundaries is analyzed. A closed form solution is obtained by applying the appropriate forces, moments and motions of the circular edge-beams as boundary conditions on the differential equation for the free transverse vibration of plates. A study of the resulting natural frequencies compared with previous results for unreinforced edges indicates that edge-beams with even a relatively small stiffness have a significant effect upon the natural frequencies of the system.     

船舶轴系振动教学演示实验台架设计与实验分析

通过船舶轴系振动理论和实践特点的分析,设计和制作了船舶轴系振动教学演示实验台架.同时,在教学演示实验台架与实船之间开展了比对实验,在船舶轴系振动信号、轴系扭振频谱、横振频谱、纵振频谱等关键实验环节进行了比对分析和讨论,得出了船舶轴系振动教学演示实验台架的可用性和可比性.     

Configurations of high-frequency ultrasonics complex vibration systems for packaging in microelectronics

Ultrasonic high-frequency complex vibrations are effective for various ultrasonic high-power applications. Three types of ultrasonic complex vibration system with a welding tip vibrating elliptical to circular locus for packaging in microelectronics were studied. The complex vibration sources are using (1) a longitudinal-torsional vibration converter with diagonal slits that is driven only by a longitudinal vibration source, (2) a complex transverse vibration rod with several stepped parts that is driven by two longitudinal vibration source crossed at a right angle and (3) a longitudinal vibration circular disk and three longitudinal transducers that are installed at the circumference of the disk.     

Shear and rotatory inertia effects on large amplitude vibration of skew plates

The large amplitude free flexural vibration of elastic, isotropic skew plates is investigated, the effects of transverse shear and rotatory inertia being included. By use of Galerkin's method and the extended Berger approximation, solutions are obtained on the basis of an assumed vibration mode. The non-linear period vs. amplitude behavior is of the hardening type and the non-linear period is found to increase when the effects of transverse shear and rotatory inertia are considered in the analysis. The influence of these effects on aspect ratios and skew angles of thin and moderately thick skew plates is investigated both at small and large amplitudes.     

Vibrational response of a moving suspension-slider loading system exciting a rotating flexible disk

To investigate the vibrational response of the magnetic read/write head in hard disk drives this paper models a rotating flexible disk excited by a moving suspension-slider system which is considered to be a mass-dashpot-spring loading system, with the initial unstressed transverse runout integrated into the rotating disk dynamic model. The slider motion on the disk surface is driven by the suspension rotating at a constant speed. By subtracting the steady-state deflection component from the instantaneous deflection response of the rotating disk system, the relative vibration transverse deflection of the slider caused by the motion of the suspension-slider loading system is obtained. The effects of the slider initial and final positions, speed of movement, the disk rotational speed, and the disk mode of the initial transverse runout on the maximum amplitude of the relative vibration deflection are analyzed.     

Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: A nonlocal elasticity approach

The magnetic properties of carbon nanotubes and their mechanical behaviour in a magnetic field have attracted considerable attention among the scientific and engineering communities. This paper reports an analytical approach to study the effect of a longitudinal magnetic field on the transverse vibration of a magnetically sensitive double-walled carbon nanotube (DWCNT). The study is based on nonlocal elasticity theory. Equivalent analytical nonlocal double-beam theory is utilised. Governing equations for nonlocal transverse vibration of the DWCNT under a longitudinal magnetic field are derived considering the Lorentz magnetic force obtained from Maxwell's relation. Numerical results from the model show that the longitudinal magnetic field increases the natural frequencies of the DWCNT. Both synchronous and asynchronous vibration phases of the tubes are studied in detail. Synchronous vibration phases of DWCNT are more affected by nonlocal effects than asynchronous vibration phases. The effects of a longitudinal magnetic field on higher natural frequencies are also presented. Vibration response of DWCNT with outer-wall stationary and single-walled carbon nanotube under the effect of longitudinal magnetic field are also discussed in the paper.     

关于由薄膜振动产生李萨如图形的研究

在声波演示实验中,可以利用薄膜的受迫振动演示稳定的李萨如图形.在声波驱动下,薄膜的振动可以分为垂直于薄膜表面的横向振动及平行于薄膜表面的纵向振动,本文对理想状态的简化模型的力学原理进行了分析和探讨.     

纳米氮化镓的拉曼光谱研究

纳米氮化镓的拉曼光谱研究罗薇邹广田崔启良赵永年崔田李红东韩杰（吉林大学超硬材料国家重点实验室长春１３００２３）ＳｔｕｄｙｏｆＲａｍａｎＳｐｅｃｔｒａｏｎＧａＮＮａｎｏｃｒｙｓｔａｌＬｕｏＷｅｉ，ＺｏｕＧｕａｎｇｔｉａｎ，ＣｕｉＱｉｌｉａｎｇ，Ｚｈａｏ...