具有涨落质量的线性谐振子的共振行为

The resonant behavior of a linear harmonic oscillator with fluctuating mass

Brown运动中,环境分子的吸附能力使Brown粒子的质量存在涨落.本文将这一质量涨落建模为对称双态噪声,以考察其对系统共振行为的影响.首先,利用Shapiro-Loginov公式和Laplace变换推导系统稳态响应振幅的解析表达式,并根据相应数值结果,研究系统的共振行为;然后,通过仿真实验对理论与实际的符合情况进行对比分析,验证理论结果的可靠性及其对实际应用的指导意义.理论结果和仿真实验均表明:1)系统稳态响应为频率与外部驱动相同的简谐振动;2)稳态响应振幅随外部驱动频率、振子质量、噪声强度及相关率的变化分别相应出现真实共振、参数诱导共振、随机共振现象;3)质量涨落噪声导致系统共振形式出现多样化现象,包括单峰共振、单峰单谷共振、双峰共振等.

The mass of Brownian particle is fluctuant in a viscous medium, because the molecules of surrounding medium may randomly stick on it. This mass fluctuation influence on the system resonant behavior is studied by modeling it as a symmetric dichotomous noise. Using Shapiro-Loginov formula and Laplace transformation, the analytical expression of system steady response amplitude is presented. The corresponding numerical results are used to discuss system resonant behavior. Furthermore, the reliability of theoretical results is tested by simulation experiments. All the research results show that： 1） the system steady response is a simple harmonic vibration which has the same frequency as the driving signal; 2） with the variations of driving frequency, oscillator mass and noise parameters, the system presents real resonance, parameter induced resonance and stochastic resonance phenomenon, respectively; 3） because of the mass fluctuation, some new resonant forms are observed, such as one-peak and one-valley resonance, two-peak resonance, etc.