Mechanically coupling microscale or nanoscale resonators in more than one dimension requires a departure from classic beam resonator designs. A square paddle resonator is a simple geometry that allows easy coupling into two-dimensional arrays. These resonators can have high quality factors in the fundamental vibration mode if operated in vacuum. In this paper we summarize the behavior of such a resonator and describe several design considerations. We develop an expression for the inter-resonator coupling in terms of coupling beam geometry, estimate energy dissipation due to a variety of physical mechanisms, and empirically determine the vibration amplitude at which geometric nonlinearity becomes significant. Future experimental studies can exploit the expressions presented here, which facilitate design of two-dimensional arrays of square-paddle resonators that will be useful for a variety of potential applications.

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