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Updated: Nov 18, 2025

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators
Published on: August 15, 2014
Duffing-type oscillator under harmonic excitation with a variable value of excitation amplitude and time-dependent
1Department of Ship Operation, Faculty of Navigation, Gdynia Maritime University, Aleja Jana Pawła II 3, 81-345, Gdynia, Poland. w.wawrzynski@wn.umg.edu.pl.
Abstract:
For more complex nonlinear systems, where the amplitude of excitation can vary in time or where time-dependent external disturbances appear, an analysis based on the frequency response curve may be insufficient. In this paper, a new tool to analyze nonlinear dynamical systems is proposed as an extension to the frequency response curve. A new tool can be defined as the chart of bistability areas and area of unstable solutions of the analyzed system. In the paper, this tool is discussed on the basis of the classic Duffing equation. The numerical approach was used, and two systems were tested. Both systems are softening, but the values of the coefficient of nonlinearity are significantly different. Relationships between both considered systems are presented, and problems of the nonlinearity coefficient and damping influence are discussed.
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