Analytical analysis of nonlinear internal resonance bandgap of pendulum-type metamaterial

In this paper, a pendulum-type metamaterial (PTM) is designed with pendulum bob hinged at the primary mass. Considering effect of geometric nonlinearity, nonlinear dynamic equations PTM unit cell are presented aid Bloch theorem. The analytical formula dispersion equation deduced to discuss internal resonance bandgap using harmonic balance method. obtained in good agreement numerical simulation result. influence on bandwidth significant. bandgaps under different resonances substantially from each other due effects. upper boundaries frequency 1:1/2 and 1:1/3 rise nonlinearly higher than those linear 1:1 conditions. It shows that impact could be more obvious as strong nonlinearity taken into consideration.