过阻尼搓板势系统的随机共振

发布时间：2019-04-24 01:42

【摘要】：研究在周期信号和高斯白噪声共同作用下过阻尼搓板势系统的随机共振.由于用直接模拟法研究随机系统所用时间较多,考虑用半解析的方法对系统的随机共振现象进行研究.在弱周期信号极限下,结合线性响应理论和扰动展开法提出一种计算系统线性响应的矩方法.在此基础上,利用Floquet理论和非扰动展开法将矩方法扩展到系统非线性响应的计算.通过直接数值模拟结果和矩方法所得结果的比较展示了矩方法的有效性并采用均方差作为量化指标给出其适用的参数范围.研究结果表明,以系统的功率谱放大因子作为量化指标,发现在适当的参数条件下,系统的共振曲线有一个单峰出现,说明过阻尼搓板势系统存在随机共振现象.而且在一定范围内调节偏置参数时,共振曲线的峰值随偏置参数的增大而增大;在调节驱动幅值时,随机共振效应随驱动幅值的增大而增强.
[Abstract]:The stochastic resonance of overdamped rubbing plate potential system under the action of periodic signal and Gao Si white noise is studied. Because the direct simulation method takes a lot of time to study stochastic system, the semi-analytical method is considered to study the stochastic resonance phenomenon of the system. Under the weak periodic signal limit, a moment method for calculating the linear response of the system is proposed by combining the linear response theory and the perturbation expansion method. On this basis, the moment method is extended to calculate the nonlinear response of the system by using the Floquet theory and the undisturbed expansion method. The comparison between the direct numerical simulation results and the results obtained by the moment method shows the effectiveness of the moment method and uses the mean square error as the quantitative index to give its applicable parameter range. The results show that there is a single peak in the resonance curve of the system with the power spectrum amplification factor as the quantitative index, which indicates that there is a stochastic resonance phenomenon in the overdamped rubbing plate potential system. When the bias parameters are adjusted within a certain range, the peak value of the resonance curve increases with the increase of the bias parameters, and when the driving amplitude is adjusted, the stochastic resonance effect increases with the increase of the driving amplitude.
【作者单位】：西安交通大学航天航空学院机械结构强度与振动国家重点实验室;西安交通大学数学与统计学院;
【基金】：国家自然科学基金(批准号:11672219,11372233)资助的课题~~
【分类号】：O324

【相似文献】