MFS analysis of the vibration filtering effect of periodic structures in elastic media

Abstract

Phononic crystals have been extensively studied, and their capacity to attenuate the propagation of sound waves at specific frequency bands is well known and documented in the literature. However, few studies exist concerning the behaviour of such structures in the context of elastic media, with the purpose of attenuating the transmission of vibrations. Applying this concept can be quite interesting, and may allow new vibration control devices to be developed, tailored at specific applications. As an example, buried periodic structures may be used to control elastic wave propagation in the ground, and thus to help reducing the vibrations that can reach sensible structures. In this work, the authors make use of a 2.5D numerical model based on the Method of Fundamental Solutions (MFS) to analyse this complex problem, considering the case of arrays of elastic inclusions buried in a homogeneous medium, fully considering the complete elastodynamic interaction between the inclusions and the host medium. Due to the geometric periodicity of the analysed problem, the numerical formulation can be simplified, particularly in what concerns the calculation of the system matrix, and significant computational gains can be obtained. The results of a numerical study concerning the behaviour of a sequence of embedded inclusions within an elastic material, when subject to the incidence of waves with different frequencies, is here presented, and the interpretation of the involved phenomena is described in order to clarify the main wave propagation features in the presence of multiple elastic inclusions. The computed results are promising, clearly revealing the existence of band gaps where large attenuation occurs, although limitations related to the existence of guided waves traveling along the inclusions are also identified.