Analysis of multiply coupled, multimode sonar transducer arrays

Abstract

Sonar transducer element and array performance predictions using linear analysis methods have been usefully performed for over two decades. These analyses were first performed for single degree of freedom (DOF) piston transducers including only the acoustical coupling through the radiating medium. More recently, single DOF transducers including both acoustical and mechanical coupling through their common mounting surface have been analyzed [D. T. Porter, J. Acoust. Soc. Am. Suppl. 1 78, S73 (1985)]. However, many of the transducer types currently under consideration for use in sonar arrays are multiple DOF systems having two or more resonant modes of significance within their operating frequency band. Flextensional and flexural mode transducers, as well as several types of multimode or multiply resonant piston transducer structures, are examples of multiple DOF elements. A general method for the analysis of multiply coupled, multiple DOF transducer arrays will be presented. The equations describing the general case have the same form as those used previously. As a consequence, many of the lessons learned from experience on arrays of single DOF elements can be extended in a straightforward manner. As an example, the concept of velocity control will be explored in different examples of multimode arrays. It will be shown that velocity control can be achieved in only a special class of multimode transducer elements—those having as many control ports (i.e., electrical) as there are structural modes.