Excitation of multiple spatial modes of a MEMS cantilever in the pulsed digital oscillator

The aim of this paper is to apply an approach that will allow us to consider different mechanical modes of a MEMS cantilever in the form of separate mass-spring-damper equations with the appropriate form of an external driving. In the paper, we focus on a specific MEMS cantilever and use a pulsed digital oscillator (PDO) to keep self-sustained oscillations of the mechanical structure. By applying the order-reduction procedure to a partial differential equation that describes the transversal deflections, we obtain a system of coupled ordinary differential equations that describes the excitation of multiple spatial modes. On the basis of these ordinary differential equations, we formulate a set of iterative maps to describe the evolution of the modes between two sampling events. The numerical simulations we present are focused on the most common case when the first two mechanical modes are taken into consideration.