<p>Micro-electro-mechanical system (MEMS) is a key component in modern sensing and RF front-ends, playing a central role in numerous engineering applications. In this paper, we analyse the dynamic complexity of a symmetrically coupled pair of comb-drive MEMS resonators, and focus on the linear stability, static bifurcation structure, and weakly forced quasi-periodic and chaotic dynamics. First, we perform a modal decomposition of the linearized system, decoupling it into two scalar Hill equations and thereby reducing the linear stability criterion to a computationally efficient single-value test that enables rapid construction of parametric stability diagrams and identification of parametric-resonance regions. Second, in the unforced conservative system, we construct a static equilibrium skeleton by introducing an odd core function <i>H</i>(<i>x</i>) and level-set pairings, which together yield a complete, parameter-explicit catalogue of all symmetric, antisymmetric, and asymmetric equilibria, along with their existence and stability conditions and associated homoclinic and heteroclinic orbits. Furthermore, for the weakly forced system, we characterise quasi-periodic and chaotic responses and their transition. Numerical simulations show that the coupling strength primarily controls the geometry of the response set and the associated resonance tongues, while the drive frequency controls the onset of chaos. When small linear damping is included, broad conservative chaotic layers condense into persistent strange attractors confined to narrow frequency bands. By applying Melnikov theory, we derive an explicit approximate threshold that quantitatively describes this condensation. These results provide a practical, design-oriented viewpoint for analysing and designing nonlinear MEMS pairs and arrays.</p>

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Complexity of dynamics for symmetric coupled MEMS resonators

  • Zhen Wang,
  • Yicheng Liu,
  • Yu Guo,
  • Xiao Wang

摘要

Micro-electro-mechanical system (MEMS) is a key component in modern sensing and RF front-ends, playing a central role in numerous engineering applications. In this paper, we analyse the dynamic complexity of a symmetrically coupled pair of comb-drive MEMS resonators, and focus on the linear stability, static bifurcation structure, and weakly forced quasi-periodic and chaotic dynamics. First, we perform a modal decomposition of the linearized system, decoupling it into two scalar Hill equations and thereby reducing the linear stability criterion to a computationally efficient single-value test that enables rapid construction of parametric stability diagrams and identification of parametric-resonance regions. Second, in the unforced conservative system, we construct a static equilibrium skeleton by introducing an odd core function H(x) and level-set pairings, which together yield a complete, parameter-explicit catalogue of all symmetric, antisymmetric, and asymmetric equilibria, along with their existence and stability conditions and associated homoclinic and heteroclinic orbits. Furthermore, for the weakly forced system, we characterise quasi-periodic and chaotic responses and their transition. Numerical simulations show that the coupling strength primarily controls the geometry of the response set and the associated resonance tongues, while the drive frequency controls the onset of chaos. When small linear damping is included, broad conservative chaotic layers condense into persistent strange attractors confined to narrow frequency bands. By applying Melnikov theory, we derive an explicit approximate threshold that quantitatively describes this condensation. These results provide a practical, design-oriented viewpoint for analysing and designing nonlinear MEMS pairs and arrays.