Numerical and experimental investigation of a variable-curvature shell class I flextensional transducer

Class I flextensional transducers cannot form broadband characteristics because of the deep valley between their first- and second-order response curves. This valley arises from the sound pressure cancellation produced by the vibration in different areas of the shell. This paper examines the cause of the deep valley by analyzing the three-dimensional equivalent radiated sound field of the transducer. By solving the three-dimensional vibration equation of the shell of revolution and reducing its dimensionality, it can be concluded that its vibration state is related to the positive and negative curvatures in both main directions. Therefore, a variable-curvature shell class I flextensional transducer is proposed, and the second-order vibration of the transducer is changed by the variable-curvature structure composed of positive and negative Gaussian curvature surfaces. The proposed transducer avoids sound pressure cancellation and achieves broadband characteristics. After optimization, a transducer prototype is fabricated, and a pool test is conducted. The test results show that the transducer couples the first three vibration modes, attaining broadband characteristics with an in-band fluctuation of less than 8 dB and a bandwidth of more than 5.4 kHz in the axial and circumferential directions.