Intermodal Targeted Energy Transfer in Two Dimensions - Part II: Forced Response

This paper is the second of a series devoted to the study of the two-dimensional intermodal targeted energy transfer (2D-IMTET). The 2D-IMTET mechanism for fully passive mitigation is explored in a harmonically excited three degrees-of-freedom planar oscillator driven close to one of its fundamental resonant frequencies. The oscillator is composed of a slab-like rigid body with a tilted elliptical-shape cavity, and it has two translation modes (horizontal and transversal) and one rotation mode. The natural frequencies of all modes are widely-spaced and far from any significant resonances. An intentional introduction of a rigid internal core, that is located inside the cavity, induces strong nonlinearity, giving rise to local vibro-impacts between the oscillator and the internal core. These vibro-impacts, combined with the geometry of the elliptical cavity, couple the linearly uncoupled normal modes. This coupling leads to strong non-resonant modal interactions, facilitating the transfer of energy among modes. Specifically, it results in a rapid scattering of energy from the fundamental structural mode, excited by the external forcing, to higher-frequency structural modes. It was observed that such nonlinear interactions and the directed energy transfer among modes ensure substantial increase of the effective stiffness, thus utilizing the inherent dissipative capacity of the system and shifting the structural response out of the resonance. The IMTET efficiency is explored using numerical simulations for three distinct structural configurations: linear unprotected system, nonlinear system with purely elastic frictionless impacts and nonlinear system with frictional and inelastic impacts.