弹簧螺旋摆系统非线性振动的理论研究

运用牛顿第二运动定律对弹簧螺旋摆系统建立了模型方程,该方程为一组非线性微分方程,表明该系统具有复杂的非线性特征.理论分析表明,当系统固有的振动频率和摆动频率之比为2时,自由振动的弹簧螺旋摆系统存在内共振现象,数值求解结果证实了这一结论.并认为在一般情况下,弹簧螺旋摆系统的自由振动可能是准周期的.     

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。     

Universality and hysteretic dynamics in rapid fracture

Experiments in the dynamic fracture of brittle polyacrylamide gels show that a single-crack state undergoes a hysteretic transition to the microbranching instability with a characteristic activation time. Quantitative measurements also indicate that features such as crack front inertia, self-focusing of microbranches, and the appearance of front waves are universal attributes of dynamic fracture.     

Coarsening dynamics of striped patterns in thin granular layers under vertical vibration

The process of pattern formation in granular layers was experimentally studied. Ten layers of granular materials inside a vacuum container were placed under a vertical vibration of A sin2pi f t. Control parameters were the dimensionless acceleration Gamma = A(2pi f)(2)/g and vibration frequency f. When the system was quenched from a flat pattern state to a striped pattern state by instantly increasing Gamma, there were more than 10(4) periods before a full steady striped pattern appeared. This nonequilibrium and nonsteady process showed dynamic scaling behavior. The growth exponent of the characteristic length scale of the ordered domain was 0.25, which agrees with that of the Swift-Hohenberg system.     

Influence of the diffusion current on the hysteretic behavior in the system of coupled Josephson junctions

The detailed investigation of the phase dynamics and the I–V curves in the system of coupled Josephson junctions have been carried out. The superconducting, quasiparticle, diffusion, and displacement currents have been calculated as functions of the total current through the system. The role of the diffusion current in the formation of the I–V curves has been studied and the influence of this quantity on the I–V curve branching and the magnitude of the return current has been revealed. The calculation results agree qualitatively with the experimental data.     

Research on performance indices of vibration isolation system

Power flow transmissibility is proposed as a performance index to evaluate the performance of isolation system. It is defined as the ratio of the power flow input into the equipment and the power flow transmitted into the receiver. Based on a simple vibration isolation system, its relationship with other performance indices is given by theoretical and numerical analysis. The results show that power flow transmissibility can reflect the response characteristics of the whole isolation system effectively. In addition, power flow transmissibility can be estimated easily according to vibration acceleration level difference and does not involve the measurement of power flow. Furthermore, the influences of several parameters such as the damping, loss factor and stiffness of isolator on power flow transmissibility are analyzed.     

Modelling the vertical grating-waveguide coupler for the description of its nonlinear symmetry-breaking dynamics

We propose a new scheme to observe the symmetry-breaking dynamics of two counter-propagating beams in a Kerr-type nonlinear waveguide coupler. Using a grating to couple light at normal incidence upon the waveguide allows for a single-beam geometry. The ability of the grating to couple light symmetrically is demonstrated on the basis of a linear coupled-mode approach especially adapted to vertical coupling. The nonlinear symmetry-breaking dynamics is studied analytically.     

A perspective on nonlinear dynamics

We present a brief report on the conference, a summary of the proceedings, and a discussion on the field of nonlinear science studies and its current frontiers.     

Some comments on nonlinear dynamics

I summarize here the remarks made at the closing of the Conference and Research Workshop: Perspectives on Nonlinear Dynamics, held in Trieste in July 2007.      

Two-dimensional front dynamics and spatial solitons in a nonlinear optical system

Two-dimensional fronts and coarsening dynamics with a t{1/2} power law are analyzed experimentally and theoretically in a nonlinear optical system of a sodium vapor cell with single-mirror feedback. Modifications of the t{1/2} power law are observed in the vicinity of a modulational instability leading to the formation of spatial solitons of different sizes. The experimental and numerical observations give direct evidence for the locking of fronts as the mechanism of soliton formation. A phenomenological equation for the dynamics of the domain radius explains the observed behavior.     

基于MATLAB的非线性振动系统临界阻尼的研究

用MATLAB研究了非线性振动系统临界阻尼的性质,提出了非线性振动系统临界阻尼的计算公式和临界阻尼状态下系统的运动方程,并与数值解进行了比较.     

The behavior of a periodically-forced nonlinear system subject to additive noise

We continue the study of a nonlinear first-order dynamical system first considered by Chen. This model is characterized by a multiplicative periodic forcing term and additive dichotomous noise in place of the white noise of Chen's analysis. Two parameters are used to characterize the qualitative properties of such a system, the mean first-passage time to the ends of the interval and the Fourier spectrum generated by the solution of the equation. We show that the mean first-passage time is monotonic in the amplitude of the periodic force and exhibits a resonant dependence on its frequency. In addition the substitution of dichotomous for white noise leads to a systematic change in the ability to smooth out the peaks in the Fourier spectrum of the solution.     

Effect of phase on discomfort caused by vertical whole-body vibration and shock--experimental investigation

An experimental study has investigated the effect of "phase" on the subjective responses of human subjects exposed to vertical whole-body vibration and shock. The stimuli were formed from two frequency components: 3 and 9 Hz for continuous vibrations and 3 and 12 Hz for shocks. The two frequency components, each having 1.0 ms(-2) peak acceleration, were combined to form various waveforms. The effects of the vibration magnitude on the discomfort caused by the input stimuli were also investigated with both the continuous vibrations and the shocks. Various objective measurements of acceleration and force at the seat surface, the effects of different frequency weightings and second and fourth power evaluations were compared with judgments of the discomfort of the stimuli. It was found that a 6% to 12% increase in magnitude produced a statistically significant increase in discomfort with both the continuous vibrations and the shocks. Judgments of discomfort caused by changes in vibration magnitude were highly correlated with all of the objective measurements used in the study. The effects on discomfort of the phase between components in the continuous vibrations were not statistically significant, as predicted using evaluation methods with a power of 2. However, small changes in discomfort were correlated with the vibration dose value (VDV) of the Wb frequency-weighted acceleration. The effect of phase between frequency components within the shocks was statistically significant, although no objective measurement method used in the study was correlated with the subjective judgments.     

Surface effect on the nonlinear forced vibration of cantilevered nanobeams

The nonlinear forced vibration behavior of a cantilevered nanobeam is investigated in this paper, essentially considering the effect due to the surface elastic layer. The governing equation of motion for the nano-cantilever is derived, with consideration of the geometrical nonlinearity and the effects of additional flexural rigidity and residual stress of the surface layer. Then, the nonlinear partial differential equation (PDE) is discretized into a set of nonlinear ordinary differential equations (ODEs) by means of the Galerkin’s technique. It is observed that surface effects on the natural frequency of the nanobeam is of significance, especially for the case when the aspect ratio of the nanobeam is large. The nonlinear resonant dynamics of the nanobeam system is evaluated by varying the excitation frequency around the fundamental resonance, showing that the nanobeam would display hardening-type behavior and hence the frequency-response curves bend to the right in the presence of positive residual surface stress. However, with the negative residual surface stress, this hardening-type behavior can be shifted to a softening-type one which becomes even more evident with increase of the aspect ratio parameter. It is also demonstrated that the combined effects of the residual stress and aspect ratio on the maximum amplitude of the nanobeam may be pronounced.