Nonlinear mode saturation in a U-shaped micro-resonator

Saturation is an intriguing phenomenon that has captured the attention of scientists since the time of Froude when he reported it for ship motion in the mid of the nineteenth century. This work presents the demonstration and a comprehensive study of the nonlinear saturation phenomenon on a compound micromachined structure of U-shape (micro portal frame). The frame is designed and fabricated as a multi-input and multi-output device for actuating the 1st (sway) and 2nd (symmetric) in-plane vibration modes. Geometric nonlinearities along with the softening effect of the electrostatic force present the necessary conditions for the activation of a 2:1 internal (auto-parametric) resonance between the 1st and 2nd modes. Experimental data complemented with analytical simulations are obtained showing the internal resonance and the saturation phenomenon. These results are promising for further exploration of such compound structures and for further in-depth studies of the saturation phenomenon on a variety of other systems and applications.