Modeling of Coupled Dome-Shaped Microoscillators

Synchronized micromechanical oscillators have potential for applications in signal processing, neural computing, sensing, and other fields. This paper explores the conditions under which coupled nonlinear limit cycle microoscillators can synchronize. As an example of the modeling approach and to be able to obtain results for a system that has been experimentally realized, thermally excited dome oscillators, which are fabricated by buckling of a thin circular film of polysilicon, are modeled. Starting with the von Karman plate equations and an assumed mode shape, a Galerkin projection is performed to obtain an ordinary differential equation for the postbuckled dynamics of the mode. Because the structure is thermally excited, a thermal model is built by solving the heat equation on a disk with appropriate boundary conditions. Bifurcation analysis of the single oscillator model is performed to look for basic underlying phenomena. Conditions under which two slightly detuned coupled limit cycle dome oscillators will synchronize are explored.