Experimentally Modeling Stochastic Resonance in the Duffing Oscillator
Grade Level at Time of Presentation
Secondary School
Institution
Western Kentucky University
KY House District #
20
KY Senate District #
32
Faculty Advisor/ Mentor
Ivan Novikov
Department
Physics and Astronomy
Abstract
Stochastic Resonance (SR) is a phenomenon that has been observed in various disciplines including climate science, mechanical and electrical engineering, optics, and various chemical and sociological models. Because it has been shown that energy harvesting is possible using a nonlinear system, it was proposed that SR can be used to increase the amount of collected energy. SR occurs when the optimal amount of white noise is added to a bistable or nonlinear system such that the signal to noise ratio is maximized. Energy harvesters rely mainly on ambient energy sources such as temperature fluctuations or electromagnetic waves as their source of power, so it is possible random fluctuations in these can be controlled to cause SR. The Damped Driven Duffing Oscillator (DDDO) is a bistable system with a damping force, which exhibits chaotic behavior when a periodic external force is applied. To observe SR in the DDDO an external random force or white noise is introduced into the system. The goals of this project are to build a DDDO system experimental setup controlled by LabVIEW modules and to experimentally study SR. As the first step, numerical methods have been used to calculate analytical solutions of the DDDO. These solutions were visualized as phase portraits and Poincaré maps were plotted. The phase portrait shows both the position and velocity in an intuitive way; the Poincaré map of the DDDO shows the periodic recurrence of the oscillator, a result that cannot be observed in the phase portrait due to the chaotic nature of the oscillator. Data analysis and visualization was done in the Jupyter Notebook environment, which allows our work to be easily shared and worked with by other researchers. The project is supported by The Gatton Academy at Western Kentucky University.
Experimentally Modeling Stochastic Resonance in the Duffing Oscillator
Stochastic Resonance (SR) is a phenomenon that has been observed in various disciplines including climate science, mechanical and electrical engineering, optics, and various chemical and sociological models. Because it has been shown that energy harvesting is possible using a nonlinear system, it was proposed that SR can be used to increase the amount of collected energy. SR occurs when the optimal amount of white noise is added to a bistable or nonlinear system such that the signal to noise ratio is maximized. Energy harvesters rely mainly on ambient energy sources such as temperature fluctuations or electromagnetic waves as their source of power, so it is possible random fluctuations in these can be controlled to cause SR. The Damped Driven Duffing Oscillator (DDDO) is a bistable system with a damping force, which exhibits chaotic behavior when a periodic external force is applied. To observe SR in the DDDO an external random force or white noise is introduced into the system. The goals of this project are to build a DDDO system experimental setup controlled by LabVIEW modules and to experimentally study SR. As the first step, numerical methods have been used to calculate analytical solutions of the DDDO. These solutions were visualized as phase portraits and Poincaré maps were plotted. The phase portrait shows both the position and velocity in an intuitive way; the Poincaré map of the DDDO shows the periodic recurrence of the oscillator, a result that cannot be observed in the phase portrait due to the chaotic nature of the oscillator. Data analysis and visualization was done in the Jupyter Notebook environment, which allows our work to be easily shared and worked with by other researchers. The project is supported by The Gatton Academy at Western Kentucky University.