Sound Back-Reflection On 1-Dimensional Periodic Interfaces

It is well-known that there exist forbidden bands in periodic structures due to the Bragg resonance. If locally resonant units are embedded in these structures, then there will introduce spatially local modes in addition to the spatially extended Bragg modes. Here in this paper we study the new acoustical phenomena associated with the doubly resonant structures, specifically, the one-dimenal interfaces that are periodically embedded with locally resonant units.As the dimension of the locally resonant element is small compared with the wave length considered, a locally resonant element can be modeled as a lumped parameter element with a simple acoustical impedance. When a plane wave is incident on a surface periodically embedded with locally resonant units, the scattering is somewhat different from the usual, and there will appear scattered waves in several different directions determined by the Bragg modes. We find that if there only the (0)-th and the (-1)-th modes are propagating, and if both the Bragg resonance and the local resonance are fulfilled, the reflected wave disappears in the usual direction, but all appears in the direction opposite to the incidence. We call this phenomenon as full back-reflection. Since the reflection angle is just negative to the usual one, we also call it as negative reflection in the context. Theoretical analysis is made to formulate this phenomenon, and inspect its dependences on incident angle and frequency, and the geometrical parameters of the periodical structure and local units.We understand the back-reflection as being due to the existence of higher-order propagating modes induced by the periodicity and the balance between the reactance induced by the evanescent waves on the periodic interface and the capacitance inherent in the locally resonant units.To further understand the phenomenon, simulation is made with the help of the finite element method, with the use of a Gaussian bean as the incidence. The numerical results are in good agreement with what are predicted by our theoretical analysis.Finally, we discuss the possibility of implementing the back-reflection phenomenon in experiment, including the design of various parameters and the effective range of frequency.Sound back-reflection, as a completely new type of reflection, not only enriches our understanding of the basic laws of acoustics, but also may be used for designing special-purpose materials that may find applications in acoustical engineering.