Emergence of Lamb Wave Pass and Gap Bands in Waveguides with Periodic Elastic Inclusions
摘要
Propagation and diffraction of Lamb waves in a free elastic layer with a finite set of uniformly distributed inclusions is considered. The frequency dependencies of the modal transmission coefficients are analyzed using a hybrid local-global FEM-analytic computer model. The development of the pass and stop ranges with increasing the number of obstacles M and the role of resonance scattering effects in this process are investigated. Previously, similar studies have been carried out for one-dimensional waveguides with point obstacles and two-dimensional waveguides with a set of infinitely thin cracks or rigid inclusions. It is shown that, like in the previous cases, resonance transmission occurs at the resonance scattering frequencies associated with nearly real complex spectral points of the corresponding wave diffraction problem. The number of the latter is proportional to M, and they fill certain intervals as M increases. As a consequence, the resonance transmission peaks merge into pass bands alternating with stop ranges. Thus, a material with such a set of periodic inclusions becomes a metamaterial with selective transmission or blocking of traveling Lamb waves.