On the waveguide modelling of dynamic stiffness of cylindrical vibration isolators. Part I: The model, solution and experimental comparison

A waveguide model of the axial dynamic stiffness for cylindrical vibration isolators in the audible frequency range is presented. The problems of sati sfying the cylinder boundary conditions simultaneously are removed, by adop ting the mode-matching technique, using the dispersion relation for an infi nite cylinder and approximately satisfying the boundary conditions at the l ateral surfaces by a circle-wise fulfilment or a subregion method. The rubb er material is assumed to be nearly incompressible with deviatoric viscoela sticity based on a fractional order derivative model. The main advantage of the viscoelastic model is the minimum parameter number required to model t he material properties successfully over a broad structure-borne sound freq uency domain. The work is verified by experiments on a rubber cylinder, equ ipped with bonded circular steel plates, in the frequency range 100-5000 Hz . The model and the measurements are shown to agree strikingly well within the whole frequency range. Comparisons with alternative material models, kn own as the Kelvin-Voigt and frequency-independent or 'hysteric' material mo dels, are made. The results are shown to diverge substantially from the pre sented material model; in particular, the Kelvin-Voigt model overestimates the material damping in the high-frequency region, while the frequency-inde pendent model underestimates it. In addition, the resonance and anti-resona nce frequencies are incorrectly predicted. In a companion paper the dispers ion relation solution, convergence analysis and comparison with simple mode ls are addressed. (C) 2001 Academic Press.