Summary
In this study, we develop an optimization procedure for the initial curvature of a mechanical beam that maximizes the inherent amplification of the forced transverse vibrations of the beam due to a nonlinear interaction with driven longitudinal vibrations. We focus on two possible cases, (i) direct amplification which is obtained when the driving frequency of the longitudinal vibrations is close to the eigenfrequency of the transverse mode, and, (ii) parametric amplification, which is obtained when the driving frequency of the longitudinal vibrations is close to twice the eigenfrequency of the transverse mode. By using a simple genetic algorithm scheme we find that the optimal curved beam enhances the amplification by a factor of 125 for direct amplification, and by a factor of 60 for parametric amplification.
