Prediction and verification of the periodic response of a single-degree-of-freedom foam-mass system by using incremental harmonic balance

Abstract

Vehicle occupants are exposed to low-frequency vibration that can cause fatigue, lower back pain, spine injuries, etc. Understanding the behavior of a seat-occupant system is helpful for minimizing these harmful vibrations. The behavior of a seat-occupant system is strongly affected by the properties of seating foam which exhibits nonlinear viscoelastic properties. Therefore, understanding the foam behavior and the way it affects the occupant response is a prerequisite for any successful and realistic seat-occupant model. The simplest model representing a seat-occupant system is a single-degree-of-freedom foam-mass system, which is also the simplest model representing a seat-occupant system. Here the dynamic response of such a system is studied. The governing equations of the system are developed for three different nonlinear viscoelastic foam models with real system parameters estimated using data from slow cyclic compression tests on a foam sample cut from a car seat. Being highly nonlinear, the local stiffness and hence the dynamic response of the foam-mass system in vertical direction highly depends on the supported mass. The incremental harmonic balance method is used to determine the steady-state behavior of the system subjected to a harmonic base excitation at different excitation levels and frequencies. This method significantly reduces the time required to generate the steady-state response compared to the time required when using direct time integration. The effects of riding mass, base excitation levels, system parameters and damping coefficients on the response are investigated. The predicted system response is seen to depend on the foam model type although each model’s parameters are identified using the same compression test data. To study this dependence on foam constitutive model, experiments are conducted on a single-degree-of-freedom foam-mass system subjected to harmonic base excitation. The simulated response predictions using the three models are found to significantly deviate from the experimental results. One of the foam models is then modified to incorporate rate dependence of foam parameters resulting in response predictions that are in good agreement with experimental results.