Acoustic modelling of surface sources. Part II. Piston model, asymmetrical function of vibration velocity, discretizing error, axisymmetrical problem

In the paper, by applying irregular discretization of the axisymmetrical plane source, an optimal piston model was obtained. An asymmetrical function of the vibration velocity, with regard to its zeros was assumed on vibrating surface. The vibration velocity of the single piston was calculated as an integral mean value of the vibration velocity of the vibrating surface. Then the model of the source consists of an array of driving pistons. In order to select the optimal position of the boundary between the pistons, the measure of the divergence/convergence between directivity function of the model and exact was analysed. The least squares distance and uniform distance were taken as a measure of deviation of the directivity function of the model from the exact one. Numerical calculations showed that the irregular discretization gives particularly good results for asymmetrical function of vibration velocity. It was also proved that the least squares distance is a better measure of directivity functions of the model and exact one the uniform distance. Its variation, as a function of vibration velocity or position of the vibrating surface in the baffle or nondimensional wave number, is more regular than the variation of uniform distance.