A multi-line source sound field model, for high-efficiency phased array ultrasonic detection of damage on the inner surface of curved artillery shell casing

It is significant to study the focused sound field distribution of curved transducers to guide its optimized design and fabrication. Aiming at the problems of the complex beam model and low computational efficiency of the linear curved phased array transducer, this paper optimizes the Non-paraxial approximation multi-gaussian beam model (NMG) and proposes a two-dimensional Multi-linear source field model (MLS). The high-frequency analytical expression of the Rayleigh integral is derived using the Hankel equation, yielding semi-analytical solutions. Taking the simulation results of the high-frequency focused sound field by the Finite element method (FEM) as the reference standard: the NMG model demonstrated axial and off-axis errors below 8.57 % and 6.93 % respectively, while requiring only 9.15 % of the computational time compared to FEM models. The developed MLS model exhibited superior performance with maximum errors of 3.44 % (axial) and 1.87 % (off-axis), achieving a minimum computation time reduction to 1.06 % of FEM models while maintaining higher computational efficiency than NMG models under refined resolution conditions. Parametric analysis revealed the influence of transducer radius, element width, and center frequency on focusing performance, demonstrating the capability of the MLS beam model in transducer parameter configuration and optimization design. Guided by beam field simulations for optimal transmitter aperture configuration, the ultrasonic B-scan technology is used to solve the problem of accurate imaging detection of various damages on the inner side surface of the artillery shell casing. This research establishes a reliable technical framework for rapid experimental configuration and high-precision imaging applications of linear curved phased array transducers.