Calculation method of complex band structure of phononic plates

Phononic crystals possess elastic wave band-gaps, which can be used to control the vibration and noise of structures. To obtain the band structures of the phononic crystals, the conventional procedures are as follows: given the wave vector k, whose value sweep the boundary of Brillouin zone, the eigenfrequency ω can be evaluated, resulting in the ω-k curve. However, this method can only yield the real band structure. In order to get the complex band structure, the frequency ω usually is given and then the eigenvalue of wave vector k is calculated, resulting in the k-ω curve. This work proposes a parameter transformation method, which can resolve the complicated non-linear eigenvalue problem and achieve the rapid solution of complex band structure. Finally, two examples, i.e., a Bragg phononic plate and a locally resonant phononic plate, are adopted to validate the proposed method. The variation of the attenuation constant along with the wave direction in the band gap and the influence of damping on the band gap are investigated in detail. © 2019, Nanjing Univ. of Aeronautics an Astronautics. All right reserved.