Numerical Analysis of a Three Element Microbeam Array Subject to Electrodynamical Parametric Excitation

The dynamic response of parametrically excited microbeam arrays is governed by nonlinear effects which directly influence their performance. To date, documented theoretical models consist of lumped-mass models. While a lumped-mass approach is useful for a qualitative understanding of the system response it does not resolve the spatio-temporal interaction of the individual elements in the array. Thus, we employ a consistent nonlinear continuum model to investigate the nonlinear dynamic behavior of an array of N nonlinearly coupled microbeams. Investigations focus on the behavior of a small size array in its 1:1:1 internal, parametric, and 3:1 internal resonances, which correspond to low, medium and high DC-voltage input, respectively. The dynamic equations of motion are solved numerically. The dynamic behavior of the three beam systems reveals coexisting periodic and aperiodic solutions. Similarities in the comprehensive bifurcation structures of the three beam systems provide insight to the nearest neighbor response of multi-element microbeam arrays subject to electrodynamic parametric excitation.