单摆非线性特征的研究

通过实验精准地测量了大摆角情况下单摆的摆角与周期,同时利用Matlab软件,求解了非线性的单摆动力学方程.理论模拟与实验测量的结果进行对比分析,证明了大摆角单摆具有典型的非线性特征.     

基于P A S CO系统的单摆相图研究

利用PASCO系统测量单摆角位置-角速度运动状态相图,通过相图法研究该系统所包含的力学线性和非线性运动行为.     

基于LabVIEW的单摆振动图像的探究实验

针对传统实验的不足,结合数据采集和虚拟仪器测量技术,开发了基于LabVIEW的单摆振动图像的探究实验装置,实现了单摆振动图像的绘制、单摆周期的测量和当地重力加速度的计算,直观地展示了单摆振动图像,提高了可视化效果和测量精度,降低操作难度,并将单摆振动图像演示实验和用单摆测定重力加速度实验进行了整合,提高了测量效率.     

用单摆测重力加速度实验中单摆周期的测定

对用单摆测重力加速度实验中单摆周期的测定进行了研究,给出了一种基于电子秒表的自动测量单摆周期的可靠装置,改进了传统单摆周期测量的不足,提高了测量单摆周期的精度.     

大摆角单摆运动周期的三个公式

建构出一类非线性动力学方程的近似处理方法 ,对单摆的动力学方程进行了修正 ,得到单摆运动周期的三个新结论。     

用力传感器测量单摆的周期

在研究单摆的实验中，测量单摆的周期是一个重要环节。传统的方法是用秒表直接测量，如今， DIS 系统在物理实验中得到了广泛应用，许多实验的方法都得到了革新。本文将介绍用DIS系统的力传感器测量单摆周期的方法，以供大家参考。     

用双线摆测重力加速度

在应用单摆测量重力加速度时, 造成误差的主要因素有实验仪器引起的系统误差和实际测量引起的随 机误差. 文中针对单摆做圆锥摆引起的系统误差, 采用了双线摆代替单摆的方法来改进实验装置, 巧用万能板来固 定双线摆, 并使其与D I S L a b通用软件相结合, 能更精确地测量出重力加速度     

用微机自动测量重力加速度

用微机自动测量重力加速度程志惠（中国人民解放军军需工业学校邢台０５４０３５）用普通单摆测量重力加速度一般精度仅能达到千分之几，而且测量比较繁琐．为提高测量精度和简化测量过程，本人对单摆装置作了改进，并采用２８６微机，实现了高精度自动测量．相对误差仅为...     

单摆运动的非线性求解

本文给出了单摆运动非线性微分方程的精确解,并得到了单摆运动周期与初始条件的关系。当初始条件满足一定关系时,单摆的运动状态并不由初始条件唯一确定,而有两种可能,因此状态空间出现分支点,这是非线性方程解的特征.     

红外微位移传感器在测重力加速度实验中的应用

用单摆测量重力加速度是大学普通物理实验中的一个基础实验,测量的核心问题是如何精确的测量单摆周期,常有秒表法、光电探测器、霍耳位置传感器等方法.这些方法各有优缺点,但无法测出单摆在摆动过程中的运动情况.本文设计的基于红外微位移传感器的精密测量装置,不仅可以对单摆周期进行精确测     

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.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,拓展非线性振动教学内容.     

高功率超声脉冲激励下金属板的非线性振动现象研究

对高功率超声脉冲作用下金属板中的超谐波、次谐波、准次谐波以及混沌等非线性振动现象进行了实验和理论研究.在实验中,高功率超声换能器产生脉冲调制的高频振动激励金属板产生非线性振动,利用激光测振技术测量不同尺寸和不同固定方式下金属板复杂的非线性振动情况,并对其进行了时序分析、频谱分析以及相空间分析.根据实验条件,提出包含非线性接触阻尼的振动-碰撞动力学模型,用以研究强超声振动-碰撞作用下的板非线性振动机制,并进行了相应的理论计算.计算结果表明,超声换能器的变幅杆与金属板之间的间歇性高频碰撞作用是金属板强非线性振 关键词： 非线性板振动 强超声脉冲激发 振动-碰撞动力学     

Nonlinear free vibrations of curved double walled carbon nanotubes using differential quadrature method

Nonlinear free vibration analysis of curved double-walled carbon nanotubes (DWNTs) embedded in an elastic medium is studied in this study. Nonlinearities considered are due to large deflection of carbon nanotubes (geometric nonlinearity) and nonlinear interlayer van der Waals forces between inner and outer tubes. The differential quadrature method (DQM) is utilized to discretize the partial differential equations of motion in spatial domain, which resulted in a nonlinear set of algebraic equations of motion. The effect of nonlinearities, different end conditions, initial curvature, and stiffness of the surrounding elastic medium, and vibrational modes on the nonlinear free vibration of DWCNTs is studied. Results show that it is possible to detect different vibration modes occurring at a single vibration frequency when CNTs vibrate in the out-of-phase vibration mode. Moreover, it is observed that boundary conditions have significant effect on the nonlinear natural frequencies of the DWCNT including multiple solutions.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

三质点单自由度非线性振动特性分析

设计一个非线性振动实验装置，建立系统的动力学方程，用计算机数值计算并画出相图和运动图，对非线性振动的性质进行了分析。     

Large amplitude vibration of an initially stressed cross ply laminated plates

In this paper, nonlinear equations of large amplitude vibration for a laminated plate in a general state of nonuniform initial stress are derived. The equations include the effects of transverse shear and rotary inertia. Using these derived governing equations, the large amplitude vibration behaviour of an initially stressed cross-ply laminated plate is studied. The initial stress is taken to be a combination of pure bending stress plus an extensional stress in the plane of the plate. The Galerkin method is used to reduce the governing nonlinear partial differential equations to ordinary nonlinear differential equations and the Runge-Kutta method is used to obtain the nonlinear to linear frequencies. The frequency responses of nonlinear vibration are sensitive of the vibration amplitude, aspect ratio, thickness ratio, modulus ratio, stack sequence, layer number and state of initial stresses. The effects of various parameters on the large amplitude free vibrations are presented.     

Method of Green’s function of nonlinear vibration of corrugated shallow shells

Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations became nonlinear ordinary differential equations with regard to time. The amplitude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.     

试样激励下轻敲模式原子力声显微镜的非线性动力学特性

利用Euler-Bernoulli梁理论和DMT针尖-样品作用力模型建立了试样激励下轻敲模式原子力声显微镜(AFAM)系统的动力学方程,并应用非线性动力学分析方法对AFAM微悬臂梁的振动特性进行研究。通过合理改变超声激励幅值、超声激励频率和针尖-样品初始间距等模型参数模拟得到微悬臂梁的超谐波、次谐波、准周期和混沌振动现象,采用时间序列、频谱、相空间、Poincare截面和Lyapunov指数等方法对不同非线性振动特性进行表征。通过分析不同模型参数条件下微悬臂梁针尖-样品作用力特性,探索了微悬臂梁不同非线性振动现象的产生机制。此外,研究了AFAM微悬臂梁运动的分岔特性,发现当超声激励幅值和针尖-样品初始间隙连续变化时,周期、准周期和混沌运动交替出现。研究结果对AFAM系统非线性动力学行为分析和混沌振动控制提供了理论参考。      

Spectral transformation of the energy in Fröhlich systems

Spectral energy transformation is one of the general properties of nonlinear systems. We examined the Fröhlich vibration system as a model nonlinear system. Energy is transferred down towards low frequency vibration modes with considerable damping.