Parametric mode mixing in asymmetric doubly clamped beam resonators

A model for the microscopic mechanism of parametric mixing between different modes in a single doubly clamped beam resonator is presented. Sinusoidal tension modulation along the beam axis at the frequency difference between two oscillation modes mixes the modes. Although the mixing occurs only when both the modes have the same parity in a uniform beam structure, we show that the modulation can also mix modes with different parities by introducing the beam-shape and mass-load asymmetry. The dominant contribution comes from the mass-load nonuniformity, and the calculation results show good agreement with experiments.