Wave propagation in phononic materials based on the reduced micromorphic model by one-sided Fourier transform

A one-dimensional problem of wave propagation in phononic materials is solved under the reduced micromorphic model introduced recently. An efficient technique is used for the solution, based on one-sided Fourier transform. This allows obtaining an exact solution in closed form, which can be utilized to check approximate solutions obtained by other methods. The results are confirmed numerically by the method of finite differences. They illustrate the existence of frequency band gaps.