A Study on the Relationship of Frequency and Deformation for Viscoelastic Material

Viscoelastic materials are used in automobiles and other products. However, because of theoretical complexity, it has not been easy to put all the energy exhausted into the automotive viscoelastic materials. Since time is the most important factor in the study of viscoelastic material, creep and stress relaxation functions are very important. In this study, a bushing was selected for special viscoelastic material. A bushing is a device used in automotive suspension systems to cushion the force transmitted from the wheel to the frame of the vehicle. A bushing is essentially a hollow cylinder which is bonded to a solid metal shaft at its inner surface and a metal sleeve at its outer surface. The shaft is connected to the suspension and the sleeve is connected to the frame. The cylinder provides the cushion when it deforms due to relative motion between the shaft and sleeve. The relation between the force applied to the shaft or sleeve and their deformation is nonlinear and exhibits features of viscoelasticity. A force-displacement relation for a bushing is important for multi-body dynamics numerical simulations. Hence, an explicit force-displacement relation has been introduced. The relation is expressed in terms of a force relaxation function. With Pipkin-Rogers model, the direct relation of force and displacement that has been derived from experiment and numerical simulation, the sinusoidal displacement was chosen and the relation of frequency and deformation for the viscoelastic material was studied.