Nonlinear mode saturation in a U-shaped micro-resonator

Abstract

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.

Design, simulation, and testing of a tunable MEMS multi-threshold inertial switch

“…The microcantilever beam in Fig. 1a is modeled as a continuum system through Hamilton’s principle 37 , 38 , yielding the equations of motion below where the boundary conditions and coefficients are expressed in Eqs. (S 16 ) and (S 17a–c) in the Supplementary Materials along with the equation derivation.…”

One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity

“…Most of these studies have demonstrated the M-shaped resonance curve with strong quadratic coupling compared to the Duffing nonlinearity. For instance, U-shaped resonators [31,32], disk resonators [14], arch beam resonators [33], and clamped-clamped beam resonators [20,21,28,34] have experimentally shown Mshaped resonances induced by 1:2 or 2:1 InRes. While these studies have contributed to understanding 1:2 and 2:1 InRes, the ZD point was not demonstrated due to the relatively small hardening effect.…”