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Nonlinear dynamic modeling of a micro-plate resonator considering damage accumulation

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Abstract

One of the prominent issues regards MEMS structures is their reliability in the presence of damage accumulation that can limit their usage in various applications. Damage accumulation could be happened due to slow growth of the existing submicron or sub-nano cracks, where its effect on the system behavior could be considered through a slowly decreasing in the equivalent stiffness of the structure over time, and as result, it can lead to an unpredictable collapse due to a fracture failure as well as due to experiencing instability in the structure. Therefore, in the current study, a mathematical model with slow and fast time variables is proposed to show the effect of accumulated damage on the stability of capacitive micro and nanostructures by considering a slowly decreasing system equivalent stiffness. As a case study, nonlinear dynamic behavior of a micro circular plate under DC and AC voltage has been investigated. The governing nonlinear coupled radial (in-plane) and transversal (out-of-plane) vibrations considering nonlinear von-Karman strains have been derived and they have been simplified for low-frequency actuation ignoring radial motions inertial forces. The governing nonlinear integrodifferential equation has been discretized over the spatial domain using the Galerkin-based reduce order model and the effect of the damage accumulation has been shown on the dynamic behavior of the micro circular plate. The obtained results show that a MEMS capacitive structure experiences the pull-in phenomenon in very low applied voltages when it experiences cyclic loads over time. It also has been shown when the system is subjected to an excitation frequency different from its natural frequency, due to the decreasing stiffness of the system it experiences primary resonance as well as secondary resonances by increasing the load cycles.

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Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales, Canberra, Australia

    Zaher Rahimi

  2. Mechanical Engineering Department, Urmia University, Urmia, Iran

    Ghader Rezazadeh

  3. South Ural State University, Chelyabinsk, Russian Federation

    Ghader Rezazadeh

  4. Mechanical Engineering Department, University of Tabriz, Tabriz, Iran

    Mohammad Asadi

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  1. Zaher Rahimi
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Correspondence to Zaher Rahimi.

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Rahimi, Z., Rezazadeh, G. & Asadi, M. Nonlinear dynamic modeling of a micro-plate resonator considering damage accumulation. Acta Mech 234, 2933–2946 (2023). https://doi.org/10.1007/s00707-023-03542-1

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  • DOI: https://doi.org/10.1007/s00707-023-03542-1

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