Nonlinear Dynamics of Seat-Occupant Systems with Nonlinear Viscoelastic Models of Flexible Polyurethane Foam

Purdue University, West Lafayette IN

Investigators

Abstract

The static and dynamic (ride) comfort of seat occupants are of paramount importance. Most seat design is still done from experience, and trial and error prototyping. The experimentally measured responses for human subjects or mannequins are explained based on simplified vibratory motion models incorporating a series of linear springs, masses and dashpots. These models have no relationship to the actual physics of the system in terms of its geometry, rigid-body component properties, and the structural system of seat suspension and supportive flexible polyurethane foam. So, they cannot be used for understanding effects of design changes on occupant comfort or other measures used to distinguish between seats. Some recent efforts that have shown limited success have introduced two-dimensional models wherein the occupant is considered supported by a finite number of linear springs and dashpots. Such models, when developed sufficiently, have the potential to ultimately be useful for realistic simulations of the occupant's response to various road conditions. This capability will lead the way to significantly reduced dependence on trial-and-error prototyping and the associated costs in the development of future automotive seats. The key to this development is accurate models of flexible polyurethane foam (FPU). The overall system dynamics also depends on the interface between the seat foam and the occupant body, which is complex with possible slipping, as well as loss of contact and impacts at high vibration levels. Finally, the foam models will also be useful as this material has become the material of choice in cushioning and support applications, including automotive and airplane seats, wheelchairs and hospital bedding, and sports equipment like shoes and shin guards. The goal of this work is to develop comprehensive physics-based two-dimensional models of seat-mannequin systems and to investigate the performance of these dynamic models in predicting the response of mannequins to various dynamic inputs. The essential physical components of such a dynamic seat-mannequin system model include rigid-body model of the mannequin, a sufficiently realistic model of flexible polyurethane foam, and models for seat-occupant interfaces at the seatback and the seat bottom. 1. Flexible Polyurethane Foam (FPU) is a highly nonlinear and viscoelastic material whose behavior is also dependent on its microstructural properties. This work will construct 2D- and 3D-nonlinear visco-hyperelastic material models of polyurethane foam for accurate modeling of foam behavior and the complex shear interactions that arise at the seat-occupant interface. Finite element models of microstructure of foam utilizing interconnected nonlinear viscoelastic beams will be used to model the microstructural behavior. Experiments and system identification techniques will be utilized to extract parameters for macroscopic models to fit experimental results as well as predictions from microstructure-based models. 2. The nonlinear viscoelastic models of foam will be incorporated into multi-body seat-occupant models, with special attention paid to models of interactions at the interfaces. The resulting seat-mannequin models will be in the form of nonlinear integro-differential-algebraic equations. These models are expected to be capable of predicting system responses under realistic excitations including transients and steady vibrations to periodic inputs. Solution techniques for such mathematical models are not well developed other than direct numerical simulation. Semi-analytical techniques based on multi-frequency harmonic balance method will be developed to predict responses for periodic excitations. The frequency-amplitude response predictions will be compared to results of direct time-integration and experimentally measured responses at different levels of vertical excitations, thus verifying the model as well as the model development methodology. Thus, the research undertaken is expected to advance the modeling of nonlinear viscoelastic materials with microstructure as well as the ability to accurately simulate the dynamics of seat-occupant systems.