Weak formulation of Biot's equations in cylindrical coordinates with harmonic expansion in the circumferential direction

Abstract

Abstract A weak symmetric form of Biot's equation in cylindrical coordinates with a spatial Fourier expansion in the circumferential direction is presented. The solid phase displacement and the pore pressure are used as the dependent variables. The original three‐dimensional boundary value problem is here, due to the orthogonality of the harmonic functions and the rotationally symmetric geometry, decomposed into independent two‐dimensional problems, one for each harmonic function. This formulation provides a computationally efficient procedure for vibroacoustic finite element modelling of rotationally symmetric three‐dimensional multilayered structures including porous elastic materials. By numerical simulations, this method is compared with, and verified against, full three‐dimensional Cartesian coordinate system finite element models. Copyright © 2009 John Wiley & Sons, Ltd.