Contributions in the acoustic study of fluid-structure interaction problems with porous materials and thin structures

Abstract

his thesis addresses a vibroacoustic problem in a coupled system consisting of a fluid domain, a poroelastic domain, and a thin elastic solid, such as a flexible plate, through a numerical and experimental method. The understanding of acoustic wave propagation in this coupled problem and the search for mathematical models to simulate and predict the attenuation introduced by porous materials in industrial case studies were proposed within the mechanical engineering research group at the technological centre IKERLAN. To achieve this, a literature review is first conducted on poroelastic materials to understand the parameters they depend on, how they are measured and experimentally characterized, and the study of the different existing mathematical models to simulate wave propagation through these materials. Subsequently, the coupled problem is modeled by developing a finite element numerical code applied to the specific case study of a hexahedral cavity with rigid walls except for the upper wall, which is formed by a thin flexible aluminium plate screwed to the cavity and covered with a layer of poroelastic material. Different models for poroelastic material modeling are compared, ranging from empirical models and phenomenological models of equivalent fluid to models that take into account both the fluid and solid phases of the material. The pressure in the fluid domain is discretized with continuous Q1-Lagrange elements, the plate is discretized by combining standard Q1-Lagrange elements for membrane displacements with MITC4 elements for bending displacements. The poroelastic domain is modeled in each case through its characteristic impedance (considering rigid or movil wall impedance) in empirical models, discretized as the fluid but with density and compressibility modulus with dissipative parts in the equivalent fluid models, and discretized through displacement-displacement degrees of freedom using (Q1)3-Lagrange elements when both solid and fluid phases are modeled. Experimental work is carried out, both for the characterisation of material properties (porous materials and plate) and the sound source excitation, and an experimental validation of the problem is performed by comparing the different models.