Analysis of 3D Sound Fields by Use of Analytic Solutions

(Simulation and Experimental Studies of Free and Forced Vibrations)

Abstract

This paper deals with an approximate numerical simulation method of the three dimensional acoustic problems. Cores of this method consist in analytic solutions expressed in the 3D polar coordinates and the collocation method. Boundary conditions are satisfied approximately only at points placed on boundaries of domains. As numerical examples, free vibrations in a domain of frustum of pyramid are calculated. The domain is bordered with rigid walls. Calculated natural frequencies and calculated natural modes expressed by sound pressure distribution on a cross section agree well with experimental results. Furthermore, forced vibrations in a domain bordered with a sound absorbing wall and rigid walls are examined. Measured values of specific acoustic impedance of normal incident of sound absorbing material is used. Calculated results of sound pressure distribution on a cross section also agree with measured ones. It can be concluded that the proposed simulation method is reliable.