Engineering the Structural Nonlinearity Using Multimodal-Shaped Springs in MEMS

The purpose of this paper is to introduce a novel technique to engineer in a precise way the structural nonlinearity in MEMS springs. To perform the adjustment of structural nonlinearity, the idea of using a sine-shaped beam following the combination of the natural bending modes of a straight one is explored to create a multimodal-shaped spring. The basic analytical model of multimodal beam bending is introduced and validated with finite element modeling. Proposed multimodal springs are fabricated by deep reactive ion etching on silicon on insulator wafer and their force-displacement characteristics are extracted using a force probe, with the resulting curves being close to the ones predicted by the theoretical calculations. The presented spring allows the engineering of structural nonlinearity by varying the amplitudes of the different modes used as initial shape. Thus, a straightforward method to create any type of structural nonlinearity starting from fully bistable up to the linear case, without the need to combine springs of several types, reducing the complexity of the targeted systems and their footprint. The proposed methodology was used to successfully design a suspension spring that exhibits flat force-displacement region with the aim to increase the bandwidth of vibrational energy harvesters.