Computer simulation of a transiently excited underwater sound projector

A computer simulation model of a transiently excited plane piston underwater sound projector is developed, which yields solutions of the acoustic performance of the transducer system to three figure accuracy, at a cost of about $30.00 per case. The methodology outlined, is capable of dealing with the non linearities of an electrodynamic source of the "boomer" type, and in addition, is particularly suitable for mechanically "stiff" systems, where the time constants of the electrical equation of motion are some three orders of magnitude shorter than the time constants of the mechanical equation of motion. It is shown that the convolution integral representing the transient radiation loading of the medium on the piston appearing in the mechanical equation of motion, may be dealt with by decomposing the electro-mechanical system equations, into two coupled sub systems, the first of which is solved by the method of state variables, and the second, which is solved by direct integration using Simpson\´s method. A comparison of experimental data and data predicted by the model, agree within the experimental error, in this case about 10%. The model is completely general, and may be adapted to yield both the transient and steady state solutions for any type of transducer, including sonar type projectors.