Application of plane wave expansion and stiffness matrix methods to study transmission properties and guided mode of phononic plates

• Generalization of the stiffness matrix method for bidirectional phononic plates.
• Agreement was found between the band structure and the transmission spectrum.
• Guided modes appear in stop band when a homogeneous layer replaces phononic layer.

Numerical procedure based on plane wave expansion and stiffness matrix method is developed to calculate the transmission factor of a micro two-dimensional phononic plate. Calculations of the dispersion curve have been achieved by introducing particular functions which transform motion equations into an eigenvalue problem. The state vector has been generalized to a phononic material, it leads to a comparatively convenient matrix formulation. The influence of the layer number on the transmission factor is studied. In addition, our interest is focused on the observed gap and how it behaves when phononic structure undergoes a slight change. The result shows that if the central phononic layer is replaced by one or two homogeneous layers, guided modes originate inside the frequency band gaps.