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The resonant behavior of a linear harmonic oscillator with fluctuating mass

Yu Tao Zhang Lu Luo Mao-Kang

The resonant behavior of a linear harmonic oscillator with fluctuating mass

Yu Tao, Zhang Lu, Luo Mao-Kang
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  • Abstract views:  920
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  • Received Date:  12 January 2013
  • Accepted Date:  12 January 2013
  • Published Online:  20 June 2013

The resonant behavior of a linear harmonic oscillator with fluctuating mass

  • 1. Department of Mathematics, Sichuan University, Chengdu 610064, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11171238) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 11221101).

Abstract: 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.

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