Acoustical properties of solid-liquid composites and related computational problems

Abstract

The thesis provides a study of acoustical performance and characterisation of solid-liquid composites. We address both experimental and numerical aspects of fluid-solid interaction problems.

In the experimental part, we perform a comparative study of the sound damping properties of perforated plates with viscoelastic inclusions, such as polyurethane and soap emulsified with oil grease lubricant, as well as layered plates with isolated viscoelastic inclusions.

One of the computational problems closely related to the experimantal study, is an acoustic fluid-solid interaction problem for plates with a rough surface. We propose an iterative algorithm for the numerical solution of acoustic fluid-solid interaction problems based on a partitioning method.

Another fundamental task in acoustics is to model the sound pressure field under harmonic excitation. We apply a machine learning approach and present a feedforward dense neural network for computing the average sound pressure over a frequency range in polygonal cylinders.

The sound waves propagation in fluid media is described by a wave equation with corresponding boundary and initial conditions. Given the parameters of the medium, one can determine the acoustic pressure, which is called a direct task. In the last part of the thesis, we solve a coefficient inverse problem: Given the acoustic pressure in some domain, we determine the wave speed function in the time-harmonic acoustic wave equation. For this purpose, the Lagrangian approach for the optimization of the Tikhonov functional is used.