Low-frequency gaps in a phononic crystal constituted of cylindrical dots deposited on a thin homogeneous plate

We investigate theoretically the band structure of a phononic crystal of finite thickness constituted of a periodical array of cylindrical dots deposited on a thin plate of a homogeneous material. We show that this structure can display a low-frequency gap, as compared to the acoustic wavelengths in the constituent materials, similarly to the case of locally resonant structures. The opening of this gap requires an appropriate choice of the geometrical parameters, and in particular the thickness of the homogeneous plate and the height of the dots. However, the gap persists for various combinations of the materials constituting the plate and the dots. Besides, the band structure can exhibit one or more higher gaps whose number increases with the height of the cylinders. We discuss the condition to realize waveguiding through a linear defect inside the phononic crystal dots. The numerical simulations are performed by using the finite difference time domain and the finite element methods.