Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book concerns the mathematical analysis - modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. - involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or o

Mathematical analysis --- Nonlinear acoustics --- Mechanics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The research concerns the modelling of wave propagation in macroscopically inhomogeneous porous materials and the resolution of the direct and inverse scattering problems. The first part is bibliographical, in order to extend the generalized Biot’s theory. Hence, the case is reduced to rigid frame porous materials, in which the solid part is considered not moving when an oscillating pressure gradient is applied to the light fluid saturating the pore volume. The second part aims to solve the direct scattering problem, which means to model the wave propagation through porous samples. A unidimensional model of plane wave propagation is chosen. A first method is the Wave Splitting and Transmission Green’s functions approach (WS-TGF). After the decomposition of the total pressure wavefield into up- and down-going components, the transmission Green’s functions yield the internal pressure field and the reflection/transmission coefficients. A second method is based on a domain integral formulation. A specific Green’s function is defined to take into account the inhomogeneities of the fluid-like porous material. The scattered pressure field is obtained iteratively using the Born approximation. The third part comprises the resolution of the inverse scattering problem, which is the retrieval of the inhomogeneous properties along the sample thickness from the reflected and/or transmitted pressure fields. In the time domain, semi-analyticalmethods based onwave splitting and Green’s functions techniques exist, but only for unbounded or non-viscous fluid-like media. In the frequency domain, an optimization method based on the minimization of an objective function related to the least square difference betweenmeasurements and calculations carried out from the wave splitting and invariant imbedding method. Perspectives are discussed.