The current paper offers a novel paradigm to parametric mechanical amplifiers (PA) by introducing multi-frequency parametric excitation and by exploiting nonlinear effects. The realization of the proposed method comprises combination of 3 frequencies, dual parametric excitation and external excitation to improve the signal to noise ratio of measured response. The system is parametrically excited at its principal parametric resonance (PR - ratio of 2:1) while the external excitation frequency is being mixed with one of the structural natural frequencies. Any mechanical structure exhibits some cubic nonlinearity easily observed when the PA is tuned to create PR conditions due to large deformations. It appears that nonlinearity creates two main principal differences from the linear model. First, the amplitude is bounded and the gain is finite. Second, there may be several possible solutions or states for a system under a given set of parameters, due to bifurcations or jump phenomena. Nonlinear single degree of freedom (DOF) model was built and solved analytically using the method of multiple scales. The analytic solutions were in agreement with the numeric solutions and showed good gain and sensitivity for small input signals. Furthermore, nonlinear 2 DOF model was built and solved in the same manner as the former. Similarly to the case of single DOF, good gain and sensitivity were achieved for small input signals. However in the latter case we had the option to operate at each of the two natural frequencies, and thus calculate the projection of the input signal on the corresponding mode.
