A MATHEMATICAL MODEL FOR THE CLASS V FLEXTENSIONAL UNDERWATER ACOUSTIC TRANSDUCER
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR ACOUSTICAL STUDIES
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The purpose of this investigation is to develop a mathematical model for the Class V flextensional underwater acoustic transducer. The transducer is approximated through the consideration of three distinct problems. The problem of a thin piezoelectric disk with an arbitrary impedance on its edge is solved in terms of Bessel functions. The shell vibration problem is solved using a finite difference model to approximate the shell. The acoustic radiation problem is solved by obtaining the source density distribution for a system of quadrilaterals representing the transducer. With the source density of each quadrilateral, the near and far field pressures and velocities can be found. Utilizing these three components, a model is then constructed for the transducer. A comparison of the results from the mathematical model with those obtained from experiments is made in order to validate the model.
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