On the Threshold of Stress Invariant Second Mode Excitation in Buckled MEMS Resonators

In post-buckled vibration of fixed-fixed beam resonators, behavior of the even modes are very interesting, as their frequencies remain invariant with change in axial load due to their anti-symmetric shape. This phenomenon opens up avenues for potential applications requiring stable resonant frequencies. Theoretically, it is known that when the buckled beams are subjected to a uniform base excitation, the even modes are not excited directly. Stability of the even mode is related to various system parameters, such as degree of buckling, amplitude and frequency of excitation. Reliable and repeatable actuation of even modes is essential for developing practical applications around them. This necessitates sound determination of the conditions essential for triggering their excitation. In this work, we have fabricated and measured the forced vibration response of micromechanical fixed-fixed buckled beam resonators of varying length and our study is focused on the excitation of the second mode. Presence of compressive residual stress and varying length results in a range of effective axial load in these resonators and hence, varying degree of nonlinearity. From the experiment, we have confirmed the existence of a threshold limit in the level of buckling for excitation of the second mode. Further, we have matched this finding with predictions from a theoretical model.