Dynamic instability induced by infinite-dimensional homoclinic bifurcations of FG-MFCPs under 1:2 parametric resonance

This paper investigates the persistence of homoclinic structures resulting in the dynamic pull-in instability for MFCPs under 1:2 parametric resonance. The multi-scale technique is conducted to convert the governing equation describing the motions of the MFCPs to an equivalent equation. The IDGDT is applied to demonstrate the homoclinic bifurcations for the equivalent system under perturbations, and a more precise threshold condition for homoclinic bifurcation is derived according to higher-order Taylor expansion. Numerical simulations validate the theoretical predictions and analyze the impact of different boundary conditions and parametric excitation on the dynamic behaviors. The results demonstrate that reinforced boundary constraints effectively suppress nonlinear responses. The numerical analysis demonstrates that under the four boundary conditions, the excitation amplitude required to induce homoclinic bifurcation is markedly greater for the CC boundary than for the others, whereas the CF boundary necessitates the lowest amplitude. This research holds significant theoretical and practical value for micro/nanofluidic systems, sensor technology, and the optimization of microstructural dynamics.