Three‐dimensional finite element analysis of waves in an acoustic medium with inclusion

Abstract

By using the pressure field as the basic unknown variable, two three‐dimensional acoustic finite element algorithms computer codes, viz., ACOU3.A and ACOU3.B, have been implemented. Code ACOU3.A is designed for the uniform‐grid space discretization such that the storage of the global pseudostiffness matrix is reduced to a single column vector of “27” elements, applicable to any inhomogeneous media. Likewise code ACOU3.B is designed for the irregular‐grid space descretization and possesses the same feature of a reduced global pseudostiffness matrix of ACOU3.A. By using ACOU3.A, three 30 × 30 × 30 elements models were investigated. including (i) a half‐space, (ii) a half‐space with a 10 × 7 × 5 elements inclusion. and (iii) a half‐space with a 10 × 2 × 5 elements inclusion, where the inclusion has the physical property different from the halfspace. In order to demonstrate the third dimension effects on wave propagation. the above posed three‐dimensional problem to the equivalent axial‐symmetric and two‐dimensional approximation models was reduced. By using a full three‐dimensional algorithm, the amplitude of the reflected waves carries the information of the third dimension thickness of the inclusion, which cannot be obtained by either the axial‐symmetric, or the two‐dimensional approximations.