双稳杜芬振子的随机共振及其动力学机制  

STOCHASTIC RESONANCE IN BISTABLE DUFFING OSCILLATORS AND ITS DYNAMICAL MECHANISMS

作　　者：康艳梅[1] 徐健学[1] 谢勇[1] 

机构地区：[1]西安交通大学机械结构强度与振动国家重点实验室,西安710049

出　　处：《力学学报》2004年第2期247-253,共7页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(19972051;10172067)~~

摘　　要：把矩方法应用于高斯白噪声和弱周期信号驱动的双稳杜芬振子,发现矩方法的收敛快慢与阻尼系数的大小有关,即在固定非线性参数的前提下,阻尼系数越大,收敛速度越快。在阻尼系数较大的情形,对于不同频率的弱周期输入信号,系统输出功率谱增益因子的演化防噪声强度呈单峰或双峰结构,亦即对于不同的激励频率,系统可表现出单峰或者重峰随机共振结构。为了解释这些共振结构,通过考察由波动谱密度定义的非零频率峰对噪声强度依赖性,发现重峰随机共振的发生在于噪声一方面抑制了井内运动,另一方面诱发了势垒上振动。研究结果为已有结论的修正,在统计力学等方面具有显著意义。The method of moments is applied to the bistable Duffing oscillators driven by Gaussian white noise and weak periodic force,and the converging rate of the method is found dependent on the damping size,namely,with the same nonlinear parameter,it converges quicker if the damping coefficient is larger.Since the method of moments can make us disclose more general characteristic than only using numerical simulations,the results derived from the method of moments along with the numerical simulation results can make us to find relations between stochastic resonance and stochastic dynamical behavior.With the method of moments,the mono-peak and double-peak resonant structures in the system are disclosed with the spectral amplification factor for different drive frequencies for the case of the larger damping coefficient.To explain the derived resonant structure,the dependence of nonzero frequency peaks peaked out from fluctuating spectral density on noise intensity is investigated,and the double-peaked resonance is found to be resulted from the intrawell vibrations and the above potential barrier vibrations,which is a modification to the previous result.The study confirms there are three possible resonant sources,i.e.interwell jump,intrawell vibration and above-barrier vibration in the considered system,and the results have importance in statistical mechanics.

关 键 词：振动理论 双稳杜芬振子 随机共振 矩方法 线性响应 功率谱增益因子 波动谱密度 

分 类 号：O324[理学—一般力学与力学基础]