Scale Effect on Tension-Induced Intermodal Coupling in Nanomechanical Resonators

Abstract

Scale effect on the tension-induced intermodal coupling between the flexural modes in nanomechanical resonators is investigated. Based on the nonlocal theory of elasticity, a theoretical model is developed to depict the scale effect on the intermodal coupling in nanomechanical resonators. The experimental and theoretical validations suggest that the results of the present work are in agreement with the experimental data. The tuning effects of mode coupling on the pull-in voltage and resonant frequency of the doubly clamped beam with the scale effect are analyzed in detail. The results show that the coupling between in-plane and out-of-plane modes increases as the scale reduces since the scale effect could make the energy between mechanical modes transfer more easily. The mode coupling with scale effect can increase the tuning range of the pull-in voltages and positions. The contributions of each term included by the scale effect to the coupling strength, pull-in voltages and frequencies of nanoresonators are discussed. Furthermore, approximate critical formulae are obtained to predict the scale effect on the resonant frequency of nanoresonators. The work demonstrates that the scale effect should be taken into account for the further understanding of the coupling mechanism of nanoresonators.