Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low, medium and large DC-voltages

摘要: The dynamic response of parametrically excited microbeam arrays is governed by nonlinear effects which directly influence their performance. To date, most widely used theoretical approaches, although opposite extremes with respect to complexity, are lumped-mass and finite-element models. While a approach useful for qualitative understanding the system it does not resolve spatio-temporal interaction individual elements in array. Finite-element simulations, on other hand, adequate static analysis, but inadequate simulations. A third that reduced-order modeling has gained significant attention single-element micro-electromechanical systems (MEMS), yet leaves an open amount fundamental questions when applied MEMS arrays. In this work, we employ continuum-based model investigate behavior array N nonlinearly coupled microbeams. Investigations focus array’s regions its internal one-to-one, parametric, several three-to-one combination resonances, correspond low, medium large DC-voltage inputs, respectively. equations motion two-element solved using asymptotic multiple-scales method weakly afore mentioned resonance regions, Analytically obtained results verified numerically complemented numerical analysis three-beam two- reveal in- out-of-phase co-existing periodic aperiodic solutions. Stability such solutions enables construction detailed bifurcation structure. This study small-size serves design purposes nearest-neighbor interactions medium- large-size Furthermore, present work motivate future experimental can serve as guideline feasibility new applications.