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Some applications of stochastic averaging method for quasi Hamiltonian systems in physics

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Science china(Physics,mechanics & Astronomy) 2009年第8期52卷 1213-1222页

作者： deng maolin {2. weiqiu department of mechanics State Key Laboratory of Fluid Power Transmission and ControlZhejiang UniversityHangzhou 310027China

Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems can be applied to yield reasonable approximate response *** the present paper,the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly *** applications of the stochastic averaging method in studying the dynamics of active Brownian particles,the reaction rate theory,the dynamics of breathing and denaturation of DNA,and the Fermi resonance and its effect on the mean transition time are reviewed.

关键词： stochastic averaging method quasi Hamiltonian system Brownian motion reaction rate theory DNA denaturation Fermi resonance

Random vortex induced vibration response of suspended flexible cable to fluctuating wind

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Applied Mathematics and mechanics(English Edition) 2023年第12期44卷 2207-2226页

作者： Genjin MU weiqiu zhu {2. deng department of mechanics State Key Laboratory of Fluid Power and Mechatronic SystemsZhejiang UniversityHangzhou 310027China

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled *** first equation is a partial differential equation governing the cable *** second equation is a wake oscillator that models the lift coefficient acting on the *** incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic *** the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random *** the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating *** the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration *** on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant *** applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically ***,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal *** numerical simulation results confirm the obtained analytical *** is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal ***,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

关键词： vortex induced vibration(VIV) wake oscillator random response suspended flexible cable fluctuating wind

Optimal control strategies for stochastically excited quasi partially integrable Hamiltonian systems

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Acta Mechanica Sinica 2007年第3期23卷 311-319页

作者： Ronghua Huan maolin deng {2. zhu department of mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang UniversityHangzhou 310027 China

In this paper two different control strategies designed to alleviate the response of quasi partially integrable Hamiltonian systems subjected to stochastic excitation are proposed. First, by using the stochastic averaging method for quasi partially integrable Hamiltonian systems, an n-DOF controlled quasi partially integrable Hamiltonian system with stochastic excitation is converted into a set of partially averaged It^↑o stochastic differential equations. Then, the dynamical programming equation associated with the partially averaged It^↑o equations is formulated by applying the stochastic dynamical programming principle. In the first control strategy, the optimal control law is derived from the dynamical programming equation and the control constraints without solving the dynamical programming equation. In the second control strategy, the optimal control law is obtained by solving the dynamical programming equation. Finally, both the responses of controlled and uncontrolled systems are predicted through solving the Fokker-Plank-Kolmogorov equation associated with fully averaged It^↑o equations. An example is worked out to illustrate the application and effectiveness of the two proposed control strategies.

关键词： Nonlinear system Stochastic excitation Stochastic averaging Optimal control Dynamical programming