Axial dynamic stiffness of cylindrical vibration isolators - The 'exact' linear solution

A linear model of the axial dynamic stiffness for cylindrical vibration isolators in the audible frequency range is presented, where influences of material damping, higher order modes and structure borne sound dispersion are investigated. The problems of simultaneously satisfying the boundary conditions at the lateral and radial surfaces of the cylinder are removed, by adopting the mode matching technique, using the dispersion relation for an infinite cylinder and approximately satisfying the boundary conditions at the lateral surfaces by a circle-wise fulfillment or a subregion method. The rubber material is assumed to be nearly incompressible with deviatoric viscoelasticity based on an extended fractional order derivative model, its main advantage being the small number of material parameters. The results are verified by experiments on a rubber cylinder, equipped with bonded circular steel plates, in the frequency range 50 - 5 000 Hz. The model and the measurements are shown to agree strikingly well within the whole frequency range.