Tailoring the resonances of nonlinear mechanical systems

The objective of this paper is the realization of a desired frequency–amplitude dependence of a specific vibration mode of a nonlinear system. To this end, we introduce an additional nonlinearity with an a priori arbitrary mathematical form in the considered system and synthesize its restoring force through optimization. To greatly facilitate the optimization process, the restoring force is optimized piece by piece from low to large motion amplitudes. The suppression of a modal interaction and the enforcement of isochronicity are considered to demonstrate the proposed procedure.