Fractional viscoelastic models for the estimation of the frequency response of rubber bushings based on relaxation tests

Abstract

Estimation of the viscoelastic properties of rubber bushings at very high frequencies (up to 2 kHz) is a challenge for many damping component manufacturers in the design stage of a quality monitoring procedure. This investigation is focused on the capability of lower strain rate testing procedures, such as relaxation tests, to estimate and extrapolate the dynamic behavior of rubber bushings from low to moderate frequencies. Fractional Zener models are employed to approach bushing behavior in experimental relaxation tests, thus leading to a linear viscoelastic model which is employed to estimate the dynamic behavior of rubber bushing under harmonics loads up to 150 Hz. The validation of this extrapolation procedure is performed by comparing these analytical results with experimental dynamic harmonic tests applied to the same rubber bushings. The deviation between both curves demonstrates that it is difficult to compare the behavior from very small deformation rates (relaxation tests) to higher deformation rates (harmonic dynamic tests) due to the nonlinear behavior of the rubber and its amplitude dependence. However, this investigation demonstrates that the relaxation tests contain enough data to define the frequency behavior of linear viscoelastic materials up to moderate frequencies.

Keywords

• Viscoelasticity
• Rubber bushing
• Loss factor
• Dynamic stiffness
• Fractional derivative