Acoustic radiation efficiency of a periodically corrugated rigid piston

Abstract

The radiation of sound by a periodically corrugated rigid piston is explored using theoretical and numerical approaches and compared with the radiation of flat rigid piston. The depth and the period of the corrugation are considered to be comparable with the wavelength in the surrounding fluid. Radiation enhancement is predicted due to cavity resonances and coherent diffraction. In addition, broad regions of low radiation efficiency are observed. Both effects could have an impact in acoustic transducers technology, either to increase the piston radiated power or to create a source of evanescent acoustic waves. The possibilities offered by this strategy in the nonlinear acoustic regime are also briefly discussed. V C 2012 American Institute of Physics.[http://dx.doi.org/10.1063/1.4748868]The radiation of acoustic waves is used in a wide range of different applications ranging from biomedical ones to non-destructive testing. In any of these systems, the transducer is a crucial element. The performance of such a system is often limited by the transducer acoustic radiation properties. In addition, the behavior of an acoustic transducer is influenced by many factors, being its mechanical construction the most direct one. 1 Nowadays, the piston radiator is maybe the most important radiation source in ultrasonics and its radiation properties constitute a classical-physics problem. However, besides the great advancement in transducer arrays and beam steering, 2,3 piezo-composite materials, 4 capacitive micromachined transducers, 5 and matching layers, 6 very little has been done concerning the radiating surface of the transducer.On the other hand, recent advances in the study of periodically corrugated surfaces and perforated plates, mainly motivated from interesting results from optics, have shown exotic properties that could be used for modifying the propagation of elasto-acoustic waves. Most of these studies concentrate on the transmission and reflection properties of perforated/corrugated plates, as a direct translation of systems being studied in optics. 7 Resonant corrugated panels have been also considered for sound insulation purposes. 8 However, no study has been done considering how a corrugated surface will affect the radiation of acoustic waves in a transducer, despite its technological relevance.In this letter, we present a theoretical and numerical study on the effect of a rigid periodically corrugated surface in the radiation of acoustic waves compared with the classical rigid piston. The depth and the period of the corrugation have the same order of magnitude than the wavelength in the fluid. Coherent diffraction and cavity resonances give rise to both radiation enhancement and radiation inhibition depending on the geometrical properties of the corrugation.Given a fluid of density q and sound speed c, we consider a perfectly rigid surface vibrating at a frequency x with velocity v 0 as depicted in Figs. 1(a) and 1(b). Solving the two-dimensional problem by means of the finite element method (Comsol Multi...