Summary
The free undamped propagation of nonlinear multi-harmonic waves in mechanical 2D metamaterials with inertial amplification is investigated. A Lagrangian model is formulated to describe the weakly nonlinear dynamics of a periodic array of elastically coupled oscillators, pantographically connected with inertia-amplifying auxiliary point masses. The space-time periodic solutions of the differential difference equations of motion, characterized by inertial and elastic nonlinearities, are described asymptotically by means of a perturbation approach. The linear dispersion relations for harmonic waves are determined at the first order. The higher order solutions provide the amplitudes of superharmonic components generated by quadratic and cubic nonlinearities, as explicit functions of the linear harmonic amplitudes. An interesting dynamic phenomenon of superharmonic depolarization is disclosed.
