The present work introduces a tunable parametric amplifier (PA) with a hardening, Duffing-type nonlinearity. By introducing a multi-frequency parametric excitation, one is able to achieve both: (i) High amplification of the weak, low-frequency external excitation (ii) Projection of the low frequency on any natural frequency of the system, thus transforming the low frequency excitation to a frequency band where signal levels are considerably higher. Having developed multiple-scales based expressions for the response of such systems, it is demonstrated that (a) The analytical analysis agrees well with numerically obtained simulations. (b) Both the phase, magnitude and spatial projection of this force on any system’s eigenvector can be retrieved by appropriate selection of parameters, with superior signal to noise levels.
Closed form analytic expressions for the sensitivity and gain are derived and analyzed. Additionally, some practical applications envisaged for the proposed method will be outlined.