非线性恢复力耦合的振动系统广义同步与参数识别

对于一类非线性恢复力无法精确解析表达的简谐激励振动系统,建立了由原系统非线性恢复力激振的派生系统.证明了派生系统与原系统可以达到广义同步.派生系统可以自动与激励力频率、大小变化的原非线性振动系统保持广义同步.证明了由派生系统的广义同步,可以识别出原系统的阻尼系数、激振力幅值与频率.由Duffing系统的仿真计算结果可以看出,这种方法是有效的,而且识别精度较高. 关键词： 非线性恢复力 广义同步 混沌     

Approximations for motion of the oscillators with a non-negative real-power restoring force

Oscillators with a non-negative real-power restoring force are considered in this paper. This type of restoring force is related to systems with a quasi-zero stiffness characteristic or those in which the restoring force is purely nonlinear in nature. Examples of these types of restoring force are grounded in real physical and engineering systems. Periodic motion of such conservative oscillators is described first in a novel way by means of the elliptic function the parameters of which are obtained from the energy conservation law and Hamilton's variational principle. Then, the approach is extended to non-conservative oscillators by adjusting the elliptic Krylov-Bogoliubov method. The methods proposed for the conservative and non-conservative systems under consideration have wider applications than the existing one with respect to the power of the restoring force. Several examples, the majority of which are so far unsolved, are given to illustrate the methods proposed and to demonstrate their generality, which permits unforeseen solutions for motion, containing higher harmonics and assuring consistent accuracy regardless of the value of the power of the restoring force. The results obtained are compared with numerical results and have excellent accuracy.     

Bifurcations and chaotic threshold for a nonlinear system with an irrational restoring force

Nonlinear dynamical systems with an irrational restoring force often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational nonlinearity avoiding the conventional Taylor's expansion to retain the natural characteristics of the system. A series of transformations are proposed to convert the homoclinic orbits of the unperturbed system to the heteroclinic orbits in the new coordinate, which can be transformed back to the analytical expressions of the homoclinic orbits. Melnikov's method is employed to obtain the criteria for chaotic motion, which implies that the existence of homoclinic orbits to chaos arose from the breaking of homoclinic orbits under the perturbation of damping and external forcing. The efficiency of the criteria for chaotic motion obtained in this paper is verified via bifurcation diagrams, Lyapunov exponents, and numerical simulations. It is worthwhile noting that our study is an attempt to make a step toward the solution of the problem proposed by Cao Q J et al. (Cao Q J, Wiercigroch M, Pavlovskaia E E, Thompson J M T and Grebogi C 2008 Phil. Trans. R. Soc. A 366 635).     

分数阶时滞反馈对Duffing振子动力学特性的影响

研究了含分数阶时滞耦合反馈的Duffing自治系统, 通过平均法得到了系统周期解的一阶近似解析形式, 定义了以反馈系数、分数阶阶次、时滞参数表示的等效刚度和等效阻尼系数, 发现分数阶时滞耦合反馈同时具有速度时滞反馈和位移时滞反馈的作用. 比较了三种参数条件下近似解析解与数值积分的结果, 二者的吻合精度都很高, 证明了近似解析解的正确性和准确性. 分析了反馈系数、分数阶阶次和非线性刚度系数等参数对系统分岔点、周期解稳定性、周期解的存在范围、零解的稳定性以及稳定性切换次数等系统动力学特性的影响.     

变质量完整力学系统的高阶运动微分方程

从Мещерский方程出发,建立变质量力学系统的高阶D'Alembert-Lagrange原理,导出变质量完整力学系统的各类高阶运动微分方程.结果表明,它们扩充和优化了完整力学的相关理论. 关键词： 变质量完整力学系统 高阶力变率 高阶D'Alembert-Lagrange原理 高阶运动微分方程     

Stability of a linear oscillator with damping force of the fractional-order derivative

It begins with the study of damping representation of a linear vibration system of single degree of freedom (SDOF),from the view point of fractional calculus. By using the idea of stability switch,it shows that the linear term involving the fractional-order derivative of an order between 0 and 2 always acts as a damping force,so that the unique equilibrium is asymp-totically stable. Further,based on the idea of stability switch again,the paper proposes a scheme for determining the stable gain region of a li...     

On the tunneling time of arbitrary continuous potentials and the Hartman effect

This paper obtains a generalized tunneling time of one-dimensional potentials via time reversal invariance.It also proposes a simple explanation for the Hartman effect using the useful concept of the scattered subwaves.     

论恒力作用下质点的相对论运动

在相对论情况下，讨论了受恒力作用的质点的运动规律。     

Equations of motion from field equations and a gauge-invariant variational principle for the motion of charged particles

New, gauge-independent, second-order Lagrangian for the motion of classical, charged test particles is proposed. It differs from the standard, gauge-dependent, first-order Lagrangian by boundary terms only. A new method of deriving equations of motion from field equations is developed. When applied to classical electrodynamics, this method enables us to obtain unambiguously the above, second-order Lagrangian from the general energy-momentum conservation principle.     

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。     

虚功原理与义坐标

指出所选广义坐标使平衡点成为虚位移,进而成为广义力的奇点是导致“广义力”在平衡点上不为零的原因,而不是虚功原理本身的问题。     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

On the symmetry of three identical interacting particles in a one-dimensional box

We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D_3d$D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh–Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.     

新型AFM探针的制备及应用

采用熔拉 -腐蚀复合方法 ,将普通单模石英光纤制成直锥形光纤探针。利用自制工具将探针打弯 ,制成悬臂式光纤探针 ,在AFM上取得了较理想的测试结果。将自制光纤探针和商用硅材料探针获得的两种扫描图像进行了对比 ,分析了悬臂式光纤探针的特点     

板式电势差计测量电动势及内阻实验的改进

通过对原板式电势差计测量电池电动势及内阻实验的分析，得出 Rs-R关系图，从而求出电动势和内阻。     

On the generalized Kadomtsev-Petviashvili equation with generalized evolution and variable coefficients

In this Letter, the existence of the solitary wave solution of the Kadomtsev-Petviashvili equation with generalized evolution and time-dependent coefficients will be studied. We use the solitary wave ansätze-method to derive these solutions. A couple of conserved quantities are also computed. Moreover, some figures are plotted to see the effects of the coefficient functions on the propagation and asymptotic characteristics of the solitary waves.     

变悬点变摆长单摆运动分析

用两种方法导出了变悬点变摆长单摆的加速度和运动微分方程，分析了小球作周期振动的条件，讨论了角速度最大值的位置，并通过计算机数值计算，画出了小球作周期振动时的相图。     

Characterization of a SiC/SiC composite by X-ray diffraction, atomic force microscopy and positron spectroscopies

A SiC/SiC composite is characterized by X-ray diffraction, atomic force microscopy and various positron spectroscopies (slow positron implantation, positron lifetime and re-emission). It is found that besides its main constituent 3C-SiC the composite still must contain some graphite. In order to better interpret the experimental findings of the composite, a pyrolytic graphite sample was also investigated by slow positron implantation and positron lifetime spectroscopies. In addition, theoretical calculations of positron properties of graphite are presented.