Rationally Derived Three-Parameter Models for Elastomeric Suspension Bushings: Theory and Experiment

Abstract

Abstract Linear, causal, and time-invariant viscoelastic material response models are of practical interest in many areas, including our interest in automotive suspension bushings. Empirical fits to experimental data may involve several fitted parameters which, if chosen arbitrarily, violate theoretical restrictions derived from causality, linearity, and time invariance. Here, we retain a correction term in an asymptotic expansion for Bode’s representation of the famous Kramers-Kronig relations. We then derive two new mathematical forms that both satisfy theoretical restrictions and fit experimental data well. Both forms proposed in this article have three free parameters each. The first form has logarithms and power law terms and is valid if the index in the power law is small. The second form has only logarithmic terms and satisfies restrictions exactly. Both forms successfully fit the test data for four different automotive suspension bushings in a frequency range of 1–30 Hz. The first form, with the power law, is more complicated but fits the data slightly better. Because the frequency response involves both a real and imaginary part, simultaneously fitting both parts well with merely three parameters validates the approximations proposed in this article.