Resonant frequency and instability of multi-layered micro-resonators with initial imperfection subject to piezoelectric loads

Abstract

The possibility to control the mistuned resonant frequency of multi-layered micro-resonators by piezoelectric actuations is numerically investigated. In many cases, there are mismatches of resonant frequency and initial imperfections of the multi-layered micro-resonators because of fabrication errors due to the difficulty of resolution control and mismatches of material properties. In this study, the multi-layered micro-resonators with initial imperfections were modeled by using refined layerwise theory and initial thermal loading. The nonlinear deformation and its attendant vibration characteristics of un-symmetrically deposited camped-camped micro-beams under piezoelectric and thermal actuations are extensively investigated. To derive the governing nonlinear finite element equations of the micro-beams, the incremental total Lagrangian description based on the multi-field layerwise theory is applied, considering geometric nonlinear strains and material inhomogeneity of multi-layered micro-resonators. Present results show that piezoelectric actuations can effectively tune the resonant frequencies of the imperfect multi-layered micro-resonators by controlling the in-plane and out-of-plane displacements. (c) 2007 Elsevier B.V. All rights reserved.