Theoretical modeling and modal analysis of multi-element coupled transducers

Low-frequency transducers are considerably smaller than the wavelength. When multiple low-frequency transducers are closely packed, they couple with the surrounding water and form a transducer-water-transducer coupling structure called multi-element coupled transducers (MCT). This study presents a theoretical model of the MCT based on radiation and mutual radiation theory and analyzes it under multiple resonance frequencies and vibration modes. The MCT comprising N single-degree-of-freedom elements possesses N resonance frequencies and corresponding vibration modes, and the resonance frequency varies with the spacing between elements. Additionally, the elements have different vibration amplitudes, with the phases of vibration among the elements manifesting as different combinations of in-phase and anti-phase in different vibration modes. Validation is performed through finite element analysis (FEA) and measurements of binary and ternary coupled transducer prototypes. The prototypes comprise bender transducers closely packed in a vertical configuration. The theoretical predictions agree with the FEA and measurement results. Thus, the theoretical model contributes to enhancing the understanding of acoustic transducer behavior in coupled configurations and optimizing the design of low-frequency acoustic arrays.