Band gaps for wave propagation in 2-D periodic three-phase composites with coated star-shaped inclusions and an orthotropic matrix

A new model for determining band gaps for wave propagation in two-dimensional (2-D) periodic three-phase composites containing coated star-shaped inclusions and an orthotropic matrix is developed using an extended version of the modified couple stress theory. An improved plane wave expansion method and the Bloch theorem for periodic media are employed to solve the 2-D elastic wave equations, which are converted to an eigenvalue problem. The shape functions for the newly proposed three-phase composites are analytically derived and utilized for the first time. The new model reduces to the classical elasticity-based counterpart when the microstructure effects are suppressed. To quantitatively illustrate the newly developed model, a parametric study is conducted. The numerical results reveal that the first band gap size predicted by the current non-classical model is larger than that given by the classical elasticity-based model, and the difference between the two sets of band gap values is significant when the unit cell size is very small. Also, it is seen that the inclusion geometry and coating thickness have significant effects on the band gap size. These indicate that large band gaps can be attained by tailoring microstructural parameters including the unit cell size and geometrical variables for the inclusion and coating.