Audio-frequency wave-guide models for antisymmetric dynamic stiffness of arbitrary long elastomer cylinders are presented. The locally non-mixed boundary conditions at the lateral and radial surfaces are simultaneously satisfied by using the modes corresponding to the dispersion relation for axial waves in cylinders satisfying the stress free boundary conditions at the curved radial boundaries, while the displacement conditions on the flat cylinder ends are satisfied by mode matching. The elastomer is modelled as nearly incompressible with deviatoric visco-elasticity based on a fractional derivative, standard linear solid embodying a Mittag-Leffler relaxation kernel, the main advantage being the minimum parameter number required to successfully model the material properties over a broad frequency band. The stiffness is found to depend strongly on frequency: displaying resonances and anti-resonances. The method is compared with and verified against finite element models. In addition, comparison to thin beam theories, i.e. Euler and Timoschenko theory and a simple shear model, is presented, illustrating the limitations of these models.

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.

A weak form of the anisotropic Biot's equation represented in a cylindrical coordinate system using a spatial Fourier expansion in the circumferential direction is presented. The original three dimensional Cartesian anisotropic weak formulation is rewritten in an arbitrary orthogonal curvilinear basis. Introducing a cylindrical coordinate system and expanding the circumferential wave propagation in terms of orthogonal harmonic functions, the original, geometrically rotationally symmetric three dimensional boundary value problem, is decomposed into independent two-dimensional problems, one for each harmonic function. Using a minimum number of dependent variables, pore pressure and frame displacement, a computationally efficient procedure for vibro-acoustic finite element modelling of rotationally symmetric three-dimensional multilayered structures including anisotropic porous elastic materials is thus obtained. By numerical simulations, this method is compared with, and the correctness is verified against, a full three-dimensional Cartesian coordinate system finite element model.