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 satisfying the cylinder boundary conditions simultaneously 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 fulfilment or a subregion method. The rubber material is assumed to be nearly incompressible with deviatoric viscoelasticity based on a fractional order derivative model. The main advantage of the viscoelastic model is the minimum parameter number required to model the material properties successfully over a broad structure-borne sound frequency domain. The work is verified by experiments on a rubber cylinder, equipped 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, known as the Kelvin–Voigt and frequency-independent or ‘hysteric’ material models, are made. The results are shown to diverge substantially from the presented material model; in particular, the Kelvin–Voigt model overestimates the material damping in the high-frequency region, while the frequency-independent model underestimates it. In addition, the resonance and anti-resonance frequencies are incorrectly predicted. In a companion paper the dispersion relation solution, convergence analysis and comparison with simple models are addressed.