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Anharmonic 1D actuator model including electrostatic and Casimir forces with fractional damping perturbed by an external force

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Acta Mechanica Sinica 2018年第3期34卷 528-541页

作者： Maryam Mansoori Kermani Maryam Dehestani Department of Chemistry Shahid Bahonar University of Kerman

We modeled a one-dimensional actuator including the Casimir and electrostatic forces perturbed by an external force with fractional damping. The movable electrode was assumed to oscillate by an anharmonic elastic force originated from Murrell- Mottram or Lippincott potential. The nonlinear equations have been solved via the Adomian decomposition method. The behavior of the displacement of the electrode from equilibrium position, its velocity and acceleration were described versus time. Also, the changes of the displacement have been investigated according to the frequency of the external force and the voltage of the electrostatic force. The convergence of the Adomian method and the effect of the orders of expansion on the displacement versus time, frequency, and voltage were discussed. The pull-in parameter was obtained and compared with the other models in the literature. This parameter was described versus the equilibrium position and anharmonicity constant.

关键词： Murrell-Mottram potential Lippincott potential Casimir force fractional damping Pull-in parameter Adomian decomposition method

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Stochastic bifurcation analysis of a generalized Van der Pol oscillator with fractional derivative under Gaussian white noise

Stochastic bifurcation analysis of a generalized Van der Pol...

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第三十九届中国控制会议

作者： Yajie Li Qixun Lan School of Mathematics and Physics Henan University of Urban Construction

The stochastic P-bifurcation behavior of bi-stability in a generalized Van der Pol oscillator with a fractional damping under multiplicative Gaussian white noise excitation is ***,using the principle of minimal mean square error,the nonlinear stiffness terms can be equivalent to a linear stiffness which is a function of the system amplitude,and the original system is simplified to an equivalent integer order Van der Pol ***,the system amplitude’s stationary Probability Density Function（PDF） is obtained by stochastic *** then according to the singularity theory,the critical parametric conditions for the system amplitude’s stochastic P-bifurcation are ***,the types of the system’s stationary PDF curves of amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set *** consistency between the analytical results and the numerical results obtained from Monte Carlo simulation verifies the theoretical analysis in this paper and the method used in this paper can directly guide the design of the fractional order controller to adjust the response of the system.

关键词： stochastic P-bifurcation fractional damping Gaussian white noise transition set Monte Carlo simulation

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