<p>The present paper investigates the nonlinear modal interactions arising in a hybrid-shaped MEMS device. Simulations are focused on the vicinity of the veering zone between the second (first antisymmetric) and third (second symmetric) modes, by taking into account the first five mode dynamics. After analyzing a combination resonance of the first and second modes, the same combination relationship is activated again, while internally resonating with the third mode, yielding a combination internal resonance. The additional internal resonance coupling is able to switch the bending dominance. Four distinct branches are generated, which experience both quasi-periodic, periodic, and chaotic response, all of them sharing the same signature of combination relationship. The diverse Fast Fourier Transform spectra are examined. Modulated quasi-periodic dynamics draw asymmetric frequency combs driven by the nonlinearity, whose main aspects are retained as the system routes into the chaotic behavior. Focus is placed on the frequency trend curves evolving from the softening combination resonance to the hardening combination internal resonance branches, as they present a unified specific underlying path.</p>

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Signature of combination resonance in chaotic dynamics and diverse quasi-periodic patterns of a hybrid-shaped MEMS

  • Laura Ruzziconi,
  • Amal Z. Hajjaj

摘要

The present paper investigates the nonlinear modal interactions arising in a hybrid-shaped MEMS device. Simulations are focused on the vicinity of the veering zone between the second (first antisymmetric) and third (second symmetric) modes, by taking into account the first five mode dynamics. After analyzing a combination resonance of the first and second modes, the same combination relationship is activated again, while internally resonating with the third mode, yielding a combination internal resonance. The additional internal resonance coupling is able to switch the bending dominance. Four distinct branches are generated, which experience both quasi-periodic, periodic, and chaotic response, all of them sharing the same signature of combination relationship. The diverse Fast Fourier Transform spectra are examined. Modulated quasi-periodic dynamics draw asymmetric frequency combs driven by the nonlinearity, whose main aspects are retained as the system routes into the chaotic behavior. Focus is placed on the frequency trend curves evolving from the softening combination resonance to the hardening combination internal resonance branches, as they present a unified specific underlying path.