Stochastic Flutter And Vibrational Resonance In Two Different Nonlinear Systems

Airfoil flutter has always been a difficult point and hot issue in the aviation and aerospace fields. The airfoil flutter is a common aeroelasticity instability phenomenon in aircraft flight, which can lead to a catastrophe. Meanwhile, random disturbance is widespread in the airfoil vibration system. Thus, the investigation of stochastic stability of the airfoil flutter system has great applicable value and theoretical significance.For some kinds of nonlinear systems that driven by both low-frequency signal and high-frequency signal, along with the change of the amplitude of the high-frequency signal, the response amplitude of each system at the low-frequency will occur “resonance”, which is well known as vibrational resonance(VR). And the two-frequency signals are pervasive in many different fields, such as laser physics, brain dynamics, neuroscience, acoustics, etc. Therefore, the study of VR has important practical application value in a broad range of fields.In the present dissertation, besides the stochastic stability of binary airfoil driven by different kinds of noise, the VR in the Fitz Hugh-Nagumo(FHN) system with time-delay feedback are also investigated. The main research content are as following:(1) The stochastic stabilities of binary airfoil under the parametric excitation by white noise or non-Gausssian colored noise are investigated. Via the methods of singular perturbation and Fourier cosine series, the approximate analytic solution of the moment Lyapunov exponents are obtained, which agree with the results obtained using the Monte Carlo simulation well. In order to learn the random flutter mechanism more clearly, the relationships between the stochastic stability of the system and all parameters of the noise and system are obtained by the moment Lyapunov exponents. Finally, comparing the effect of different noise parameters and different noise on the stochastic stability, we realize that the different dynamic behaviors of binary airfoil are caused by different noise parameters or different noise.(2) The stochastic stabilities of binary airfoil under combined harmonic and white noise, or harmonic and real noise are studied. Firstly, the nonautonomous systems are translated into autonomous systems, and then applying the methods of singular perturbation and double Fourier series, the approximate analytic solution of the moment Lyapunov exponents and maximum Lyapunov exponents are obtained, which all agree with the results obtained using the Monte Carlo simulation well. The effect of parametric resonance and the influences of all parameters of the noise and system near the parametric resonance on the almost-sure stability and moment stability of binary airfoil are investigated. By comparing the stochastic stability of binary airfoil under the harmonic excitation or no, the effect of parametric resonance on the dynamic behavior of binary airfoil is understood more clearly.(3) The VR and the electrical activity of neuron in the FHN system with constant delay feedback or time-varying delay feedback are investigated. Via numerical simulation, we find that the periodic vibrational resonances in the system can be induced by the time-delay feedback, and the resonant behaviors appear with two periods which are the functions of the delay time, and the two periods equal to the periods of the low-frequency signal and the high-frequency signal, respectively. Moreover, the FHN systems with constant delay feedback or time-varying delay feedback have plentiful electrical activity, and the firing pattern of the neuron can be regulated by modulating the delay parameter. More interestingly, as soon as the resonance occurs, the neuron just fires.(4) The VR in the coupled FHN units with globally time-delay feedback is investigated. Via numerical simulation, it is found that the multiple VR is induced by modulating the delay time. Based on the mechanism of VR, the signal can be transmitted from the first neuron to all the others with a high efficiency and the weak low-frequency signal is enhanced significantly by adjusting the time-delay feedback.