Construction and application of wave function of sound field of rectangular element
In the wave superposition method,the sound field outside the structure is obtained by integrating and superimposing the Green function on the discrete boundary,but the computational efficiency of numerical integration is low.Although the equivalent source method improves the calculation efficiency,there is a large integral approximation error in the process of simplifying the area source to the point source.In view of the defects of the above two methods,a wave function is constructed to replace the sound field of the discrete element integration about Green function.First of all,using the solution of Helmholtz equation in spherical coordinates,the general wave function which replaces the rectangular element integral and the more efficient internal wave function are derived.Secondly,when the discrete element is square,it is approximated to a circu-lar domain,which further simplifies the expression of the extrapolated wave function.Finally,the constructed wave function is applied to sound field calculation.The numerical results show that the constructed wave func-tion not only guarantees the calculation accuracy,but also greatly improves the calculation efficiency compared with direct integration when calculating the external radiation sound field of a single rectangular element.Among them,the wave function calculation efficiency of the general form and the extrapolation form in the rectangular domain is 5-6 times higher than that of the direct integration,and the wave function calculation efficiency in the circular domain is 12-13 times higher than that of the direct integration.In the numerical examples of simply supported plate sound source and cubic box radiation sound source,the accuracy of the wave extrapolation function in the circular domain is higher than that of the equivalent source method in the whole calculation frequency band.
Equivalent source methodWave superposition methodWave functionRadiated sound field
NETL
NSTL
万方数据
维普
