Assembling of metamaterials beams with uncertain scattering properties

Abstract

Metamaterials, or locally resonant metamaterials, are a class of structures that
have been used to control and to manipulate acoustic and elastic waves with applications in vibration attenuation. A great amount of research has been done on acoustic and structural metamaterials but very few attention has been given to the effects of coupling conditions on structural assemblies, even though this is typical case on mechanical engineering applications. In this work, the wave attenuation in a metamaterial beam assembly is investigated considering uncertain connections. A beam, with attached resonators, undergoing longitu dinal and flexural vibration is connected to homogeneous beams at each end. It is assumed a large enough number of identical resonators such that effective longitudinal and flexural wavenumbers are derived. Wave modes are assumed unchanged by the attachments and analytical expressions can be derived. A point connection is considered with an assembly angle such that wave mode conversion, between flexural and longitudinal waves, can happen. The reflection and transmission properties of the assemble are then calculated and it is shown that the angle of the assembly has a significant effect on the band gap performance. The uncertainty analysis focus on the variability of the connection angles and ensemble statistics are investigated.