| Abstract In this letter, we used plane wave expansion (PWE) method to compute the band structure of a two-dimensional phononic crystal of epoxy embedded in Magnetorheological elastomers (MRE). Phononic crystals (PCs), also named acoustic band gap (ABG) materials are composites made of periodic distributions of scatters embedded in matrix. The most interesting phenomena of these structures is the existence of complete phononic band gaps, which forbid the propagation of elastic or acoustic waves regardless of mode or wave vector. Potential applications of these structures include acoustic filters, sound and vibration isolators, and acoustic waveguide et al. Recently, magnetorheological (MR) materials have attracted much attention. As a class of new smart materials, its mechanical and rheological properties can be controlled continuously, rapidly and reversibly by the application of an external magnetic field. This is called magnetorheological effect. Magnetorheological elastomers are such composites where magnetic particles (like carbonyl iron particles) are suspended in a non-magnetic solid or gel-like matrix (like natural and synthetic rubbers). The shear-modulus of MRE varies with applied magnetic field. With the research on the MRE materials, it will be possible to tune the band structure of PCs intellectually. Statement of plane wave expansion method Because of the periodicity of the PCs system, those material parameters in the equation of propagation of elastic waves can be expanded in the 2D Fourier space. By applying Bloch theorem, we can obtain an algebra eigenvalue equation. Accordingly, the band structures for the transverse modes can be obtained by letting K scan the irreducible region of the first Brillouin zone. Results and Discussion 1. Calculated the band structure of the PC composites and obtained large sonic band gaps; 2. Discussed the dependence of the band gap on the filling fraction. |