Spectral integral formulae for the response of acoustic transducersin cylindrically curved configurations

摘要

High-frequency spectral integral formulae are derived for thenfrequency-domain voltage of reciprocal electro-acoustic ultrasonicntransducers interacting with a fluid-immersed cylindrically-layerednelastic configuration. The transducers may insonify the cylindricalnconfiguration from either the interior or the exterior and may benoperated in either pulse-echo or pitch-catch mode. The formulae arenarrived at through the use of a traveling wave spectral representationnof all pertinent wave fields along the azimuthal and axial directionsnand use of Plancherel's theorem to convert the conventional surfacenintegral for the transducer voltage into a spectral one. Within thisnrepresentation, the transducers are expressed in terms of theirnradiation and reception spectral amplitudes on a cylindrical surface andnthe interaction of their fields with the cylindrically layerednenvironment is expressed in terms of a composite spectral reflectionncoefficient. The integral formulae allow for computation of thentransducer voltage and transducer beam interaction with the cylindricalnenvironment in one step. The derivation is carried out fornthree-dimensional beams and specialized to two-dimensional (sheet) beamsnthat extend to infinity along the axial direction. Furthermore, thenformulae are applied to the case where complex transducer points arenused to simulate transducers with quasi-Gaussian distribution profiles