Harmonic and Superharmonic Components in Periodic Waves Propagating Through Mechanical Metamaterials with Inertial Amplification

In the nonlinear dynamics of periodic microstructured systems, the amplitude-dependent dispersion properties of mechanical metamaterials are attracting increasing interest. The present paper investigates the free propagation of harmonic and superharmonic waves through a non-dissipative one-dimensional metamaterial with pantographic mass amplification. The effects of the quadratic and cubic inertial nonlinearities on the dispersion curve are analyzed. A perturbation strategy based on the Fourier series decomposition is adopted to determine the superharmonic amplitudes of the propagating periodic waves.