Formulation and validation of the shift cell technique for acoustic applications of poro-elastic materials described by the Biot theory

The inclusion of vibroacoustic treatments at early stage of product development through the use of poro-elastic media with periodic inclusions, which exhibit proper dynamic filtering effects, is a powerful strategy for the achievement of lightweight sound packages and represents a convenient solution for manufacturing aspects. This can have different applications in transportation (aerospace, automotive, railway), energy and civil engineering fields, where weight, space and vibroacoustic comfort are still critical challenges. This paper develops the shift cell operator approach as a numerical tool to investigate the dispersion characteristics of periodic poro-elastic media. It belongs to the class of the k(ω) (wave number as a function of the angular frequency) methods and leads to a quadratic eigenvalue problem, even when considering frequency-dependent materials, contrarily to the ω(k) approach that would lead to a non-linear eigenvalue problem for frequency-dependent materials. The full formulation is detailed and the approach is successfully validate for a homogeneous poro-elastic material and a more complex periodic system containing periodic perfectly rigid circular inclusions.