Macromechanical parametric amplification with a base-excited doubly clamped beam

Parametric amplification is realized by adding parametric excitation to externally driven near-resonant oscillations. The effect of specific cubic nonlinearities on the parametrically amplified steady-state vibrations and gain is investigated theoretically. Here, gain is defined as the ratio of steady-state vibration amplitude of the directly and parametrically excited system, to vibration amplitude of the directly excited only system. The nonlinear effect of midplane stretching is compared to the effects of nonlinear inertia and curvature. An approximate analytical expression for the vibration amplitude is derived. For a given small level of transverse displacement for both the cantilever and doubly clamped beam, the effect of midplane stretching is dominant compared to those caused by nonlinear inertia and curvature. It was found that the beam slenderness ratio can be used as an effective design parameter for parametric amplifiers.