Investigations on the Complex Band Diagram of Flexural Wave through the Fluid-Loaded Phononic Plate

This paper investigates the complex band diagram of flexural waves in the phononic plate with semi-infinite heavy fluid loading. The system under examination is a square plate lattice with two-dimensional periodicity immersed in a fluid domain with infinite height. The numerical models based on the wave field transformation and the Galerkin method combined with the finite element discretization technique are developed to investigate the real and imaginary parts of the dispersion relation of flexural waves propagating through the phononic plate incorporating the fluid-loading effects. A perfect agreement is found between the location and width of stop bands from the real band diagram and the attenuation diagram, which supports the validity of the numerical models. Moreover, the complex band diagram is verified by the transverse vibration transmittance of the finite phononic plate. The results demonstrate that the external fluid loading is able to adjust the location, bandwidth, and decaying level as well as affect the degree of attenuation anisotropy of the complete and directional band gaps.