2-D modeling of mechanical cross-coupling in linear arrays

The influence of the mechanical coupling between the elements (cross-coupling) on the final performances of a piezoelectric array transducer is a well-known matter. Different solutions have been proposed to reduce, as much as possible, its effects. The approaches studied are not very generalist, because normally they are related to a specific transducer design. The model we propose is based on a 2-D model of the array, which is able to describe the vibration of each element (piezoceramic and polymer) both in the radiation (thickness) and the lateral (width) direction and, therefore, to take the coupling between the elements into account. The model, which also accounts for the load and the backing, gives as output the transfer functions of each acoustic array element and the input electrical impedance of each piezoelement. With this approach it is possible to check both the delay of the cross-coupled signal when it arrives to each passive element, and the interference of direct and coupled signals at each piezoelectric element. In order to investigate the influence of the lateral coupling in the array emission, we simulate several air-backed, air-loaded arrays composed of only few elements; the same arrays has been manufactured, and several mechanical and electrical measurements were done on these samples. We measured the input electrical impedance exciting separately each piezoelectric element; in this way both the symmetric and antimetric modes are evidenced. The nature of each mode (symmetric or antimetric) and the deformation of the array have been investigated by measuring the transfer function, and corroborated by means of interferometric measurements. The comparison between computed and experimental results shows a sufficient agreement and confirms the usefulness of the model for linear array design. The approach easily permits to model array structures in which two or more different polymers are used and will be extended in order to take into account also the coupling via the matching layers and the backing.