Axial stiffness of carbon black filled rubber bushings -: Frequency and amplitude dependence

A simple engineering model for the axial dynamic stiffness of carbon black filled rubber bushings in the frequency domain including amplitude dependence is presented. The axial stiffness is calculated by applying a newly developed rubber model to an equivalent strain of the strain state inside the bushing, thus yielding an equivalent shear modulus which is inserted into an analytical formula for the stiffness. Therefore, this procedure includes the Fletcher-Gent effect inside the bushing due to non-homogeneous strain states. An experimental verification is carried out on a commercially available bushing. Firstly, the model parameters are obtained from two different experiments: elastic and friction parameters are achieved from one quasistatic test performed at 0.1 Hz and 1 mm amplitude, while frequency dependence parameters are obtained from one dynamic test at 0.1 mm of amplitude over a frequency range from 1 to 100 Hz. Secondly, new dynamic tests at five amplitudes are performed on the same bushing and the results are compared to those of the model showing good agreements.