Symmetry Breaking and Modal Localization in a System of Parametrically Excited Microbeam Resonators

Abstract

In this work, we study the nonlinear dynamics of parametrically excited bending vibrations of two weakly coupled beam microresonators under electrothermal excitation. A steady-state harmonic temperature distribution in the volume of the resonators in the frequency domain was obtained. A system of equations for mechanically coupled beam resonators is derived, considering the deposited particle on one of them. Using asymptotic methods of nonlinear dynamics, equations in slow variables were obtained, which were studied by methods of the theory of bifurcations. It is shown that in a perfectly symmetrical system in a certain frequency range, the effect of symmetry breaking is observed – the emergence of a mode with different amplitudes of oscillations of two beam resonators, which can be the basis for a new principle of high-precision measurements of weak disturbances of various physical natures, in particular – measurements of ultra-low masses of deposited particles.