Stochastic Modelling of Wave Scattering in Metastructures for Vibration Attenuation

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 little 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 longitudinal 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 full assembly are then calculated and it is shown that the connection angle has significant effects on the band gap performance, which cannot be captured by a purely deterministic model of the straight assembly. Furthermore, the effects of some stochastic models, derived based on the Maximum Entropy principle, on the overall metastructure vibration attenuation performance are investigated. It is shown that the connection angle can considerably widen the metastructure band gap and that the joint uncertainties can play a major role on the vibration attenuation.