Diffraction impulse response of rectangular transducers

Abstract

A closed-form expression for the impulse velocity potential of rectangular pistonlike transducers, without any far field or paraxial approximation, is presented. The classical timedomain impulse response approach is used considering free-field, rigid baffle, and pressure release boundary conditions. Previous approaches to the rigid baffled rectangular piston require the use of superposition methods in order to find a general solution numerically. These must add or subtract, according to the field point location, the analytical expressions that were derived only for specific field points or geometrical regions. In this paper the complexity introduced by the geometrical discontinuities of rectangular apertures is analyzed. A new compacting methodology is proposed and applied to obtain a general solution for the impulse response. This new solution provides the value of the impulse response directly in the time domain, without requiting superposition methods. In addition, a closed-form solution for the pressure impulse response is also presented. This can be useful for physical insight and a qualitative analysis of transient and continuous wave pressure fields. Also included is a description of the temporal behavior of the impulse velocity potential and the pressure impulse response for field points in different regions. The proposed solution allows an efficient and accurate computation of pressure fields under realistic excitations. Several examples illustrate the use of this new solution in the computation of transient pressure waveforms, when wideband and relatively narrow-band excitation pulses are used. Three-dimensional plots of the peak amplitude of the transient pressure near field are presented, and certain characteristics are analyzed using the pressure impulse response. PACS numbers: 43.88.Ar, 43.20.Px, 43.20.Bi, 43.20.Fn INTRODUCTION The transient pressure field generated in a fluid medium by a planar transducer surrounded by an infinite rigid bafflehas been widely investigated. Harris, 1 in 1981, presented an excellent review of the theoretical approaches and mathematical methods. For a time-space separable excitation of the transducer, the acoustic field can be evaluated using fundamental concepts of linear system theory. The velocity potential at a field point P(•) generated by an impulse velocity motion •5(t) of the source defines a diffraction impulse response h(•,t). This function corresponds to the impulse velocity potential, and has also been called "impulse response, "2 "spatial impulse response, "1 and "aperture impulse response. "3 Two basic approaches, denoted by Fink and Cardoso 4 as "local observer" and "instantaneous approach," have been used. In the first case, the impulse response is regarded as a function of time for a fixed field point. This approach has been formalized mainly by Stepanishen. 2 The resulting pressure is obtained by the temporal convolution between the time derivative of the excitation signal and the diffraction impulse response. Following this method, analytical express...

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