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On resonances in a weakly nonlinear microbeam due to an electric actuation

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Abstract

In this paper, the oscillations of an actuated, simply supported microbeam are studied for which it is assumed that the electric load is composed of a small DC polarization voltage and a small, harmonic AC voltage. Bending stiffness and mid-plane stretching are taken into account as well as small viscous or structural damping. No tensile axial force is assumed to be present. By using a multiple time-scales perturbation method, approximations of the solutions of the initial-boundary value problem for the microbeam equation are constructed. This analysis is performed without truncating the infinite series representation in advance as is usually done in the existing literature. It is shown in which cases truncation is allowed for this problem. Moreover, accurate and explicit approximations of the natural frequencies up to order \(\varepsilon ^3\) of the actuated microbeam are also obtained. Intriguing and new modal vibrations are found when the frequency of the harmonic AC voltage is (near) half or twice a natural frequency of the microbeam, i.e., near a superharmonic or a subharmonic resonance.

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Acknowledgements

EH and JMT are supported by P3MI FMIPA ITB 2020 research grant. Part of this research was executed at the Department of Applied Mathematics, TU Delft. For that, EH and JMT acknowledge the hospitality and partial financial support from the Delft Institute of Applied Mathematics, TU Delft.

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Authors and Affiliations

  1. Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha no 10, Bandung, 40132, Indonesia

    Eric Harjanto & Johan M. Tuwankotta

  2. Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600, GA, Delft, The Netherlands

    Wim T. van Horssen

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  1. Eric Harjanto
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  2. Wim T. van Horssen
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  3. Johan M. Tuwankotta
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Correspondence to Eric Harjanto.

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Harjanto, E., van Horssen, W.T. & Tuwankotta, J.M. On resonances in a weakly nonlinear microbeam due to an electric actuation. Nonlinear Dyn 104, 3157–3185 (2021). https://doi.org/10.1007/s11071-021-06495-z

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