Transverse, tilting and cross-coupling stiffness of cylindrical rubber isolators in the audible frequency range—The wave-guide solution

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.