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Smart Structures and Systems Volume 14, Number 5, November 2014 , pages 743-763 DOI: https://doi.org/10.12989/sss.2014.14.5.743 |
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Period doubling of the nonlinear dynamical system of an electrostatically actuated micro-cantilever |
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Y.M. Chen and J.K. Liu
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| Abstract | ||
| The paper presents an investigation of the nonlinear dynamical system of an electrostatically actuated micro-cantilever by the incremental harmonic balance (IHB) method. An efficient approach is proposed to tackle the difficulty in expanding the nonlinear terms into truncated Fourier series. With the help of this approach, periodic and multi-periodic solutions are obtained by the IHB method. Numerical examples show that the IHB solutions, provided as many as harmonics are taken into account, are in excellent agreement with numerical results. In addition, an iterative algorithm is suggested to accurately determine period doubling bifurcation points. The route to chaos via period doublings starting from the period-1 or period-3 solution are analyzed according to the Floquet and the Feigenbaum theories. | ||
| Key Words | ||
| micro-cantilever; incremental harmonic balance method; Floquet theory; period doubling; chao | ||
| Address | ||
| Y.M. Chen and J.K. Liu: Department of Mechanics, Sun Yat-sen University, 135 Xingang Road, Guangzhou 510275, China | ||