A semi-analytical method for the dispersion analysis of orthotropic composite plates with periodically attached acoustic black hole resonators

A semi-analytical method is developed to calculate the wave propagation properties of thin orthotropic composite plate structures periodically attached to acoustic black hole (ABH) resonators. First, the free and forced vibration of the host orthotropic plate is described in terms of the analytical wave shapes obtained by the symplectic method. Second, a wave-based description is provided for the ABH resonators using the higher-order WKB method. Third, the equivalent dynamic stiffness of the resonator is obtained by considering the deformation-force relationship at the connections. Finally, an eigenvalue problem is established for the dispersion of the periodic plate based on wave propagation analysis, where the dynamic coupling between the host plate and resonator is innovatively described in terms of directly excited waves. Because the wave-based derivations in the proposed method are analytical, the calculations highly efficient and accurate, and were validated through several numerical examples.