Strong nonlinearity and external high-frequency forcing for controlling effective mechanical stiffness: theory and experiment

High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quantities such as resonance frequencies, wave speeds, buckling loads, and equilibrium states. There are two ways to do this: by using parametric HFE (with or without nonlinearity) or by using external HFE along with strong nonlinearity. The first way, parametric stiffening, has been examined for many different systems, and analytical predictions exist that have been repeatedly confirmed against numerical simulation and laboratory experiments. The current work presents results using the other way, external stiffening: Combining the method of direct separation of motions with results of a modified multiple-scale approach, valid also for strong or even essential nonlinearity, quantitative measures of the stiffening effect are predicted for a generic 1-DOF system and tested with generally good agreement against numerical simulation and laboratory experiments.