Chebyshev coefficients in modeling the wave process by the method of normal modes - Залевська, О. В.; Пуха, Г. С.; Варава, І. А.; Коваль, О. В.; Пироговська, Т. В.; Мусієнко, А. П. (Інститут проблем реєстрації інформації НАН України, 2024)
A method of taking into account the time parameter in the three-dimensional method of normal modes, which is used in the development of software for modeling the propagation of the hydro-acoustic field, is considered. A transition from classical time accounting to discrete and vice versa is proposed. The introduction of the time coordinate expands the possibilities of research and modeling of wave equations. In a dynamic emitter-receiver system, the weight of influence on the system of each mode is different. The influence of a normal wave on the system during a certain period of time is provided by Chebyshov's polynomial coefficients. During the statistical analysis of the obtained data, data interpolation was considered using linear, exponential, quadratic and logarithmic functions. It was established that quadratic and exponential functions have the same values of model adequacy parameters and approximation accuracy. In the future, it is proposed to approximate the resulting series with a quadratic function, which reduces calculations and the load on computing equipment. The hydro-acoustic field simulation software complex was used for modeling. The software complex consists of 5 packages: HydroAcModComp, HydroAcModCompViewModels, ModCompGeoFunction, SQLData, NormalModes. The implementation of simulation calculations by the method of normal modes is carried out in the NormalModes package. A computer simulation was carried out using hydro-acoustic field simulation software, the results of which obtained dependencies allow entering a time parameter into the solution of the wave equation by the method of normal waves. This provides the possibility of predicting the development of the sound wave over time and does not require additional studies of the time variable. Tabl.: 1. Fig.: 5. Refs: 12 titles.