Aplicação do problema inverso em tubos de impedância para determinação de propriedades acústica de materiais via modelagem para frentes não planas

Abstract

Acoustic characterization of materials using impedance tubes represents a highly relevant area in engineering, playing a fundamental role in applications such as noise control, medical tomography, and structural flaw detection. Traditionally, measurement methods in impedance tubes rely on the assumption of plane wave propagation, an approximation that becomes limiting under certain experimental conditions and specific frequency ranges. This work presents a modeling approach for the expansion of the sound field in acoustic impedance tubes, specifically considering non-planar wavefronts, aiming to overcome the limitations of conventional methods and significantly enhance the accuracy of acoustic measurements in various experimental setups. The theoretical framework includes wave acoustics concepts, such as reflection, transmission, and standing waves in confined environments. The knowledge base includes mathematical models for acoustic impedance, deconvolution techniques, sound pressure, wave number spectrum, and mathematical representation of sound fields. The impedance tube construction followed the criteria established by ISO 10534 standards. The ITA-Toolbox is employed as a tool for acquiring experimental sound pressures, in conjunction with the swips technique, windowing, and signal deconvolution, enabling sound field characterization and expanding it to account for situations where planar and non-planar wavefronts coexist, especially at high frequencies or in specific geometric configurations of the impedance tubes. The developed methodology incorporates Tikhonov regularization for the inverse problem of plane wave decomposition, using L-Curve and Fixed-Point methods to determine regularization parameters. The results revealed significant limitations in acoustic characterization at high frequencies, associated with the ill-conditioning of the inverse problem. The estimates showed strong dependence on regularization strategies and temporal processing, influencing the stability of the obtained absorption coefficients.