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

座椅乘员的静态和动态（乘坐）舒适性至关重要。大多数座椅设计仍然是根据经验和试错原型来完成的。实验测量的人体或人体模型的响应是基于包含一系列线性弹簧、质量和阻尼器的简化振动运动模型来解释的。这些模型在几何形状、刚体部件性能以及座椅悬架和支撑柔性聚氨酯泡沫的结构系统方面与系统的实际物理特性没有关系。因此，它们不能用于理解设计变化对乘员舒适度的影响，也不能用于区分座椅的其他措施。最近的一些努力已经显示出有限的成功，他们引入了二维模型，其中乘员被认为是由有限数量的线性弹簧和减震器支撑的。当这些模型得到充分发展时，最终有可能用于模拟乘员对各种道路状况的反应。这种能力将大大减少对试错原型的依赖，并降低未来汽车座椅开发的相关成本。这一发展的关键是柔性聚氨酯泡沫（FPU）的精确模型。整体系统动力学还取决于座椅泡沫和乘员身体之间的界面，这是复杂的，可能会滑动，以及在高振动水平下失去接触和冲击。最后，泡沫模型也将是有用的，因为这种材料已经成为缓冲和支撑应用的首选材料，包括汽车和飞机座椅，轮椅和医院床上用品，以及运动鞋和护胫等运动设备。这项工作的目标是开发基于物理的座椅-人体模型的综合二维模型，并研究这些动态模型在预测人体对各种动态输入的响应方面的性能。这种动态座椅-人体系统模型的基本物理组成部分包括人体模型的刚体模型、柔性聚氨酯泡沫的足够逼真的模型以及座椅靠背和座椅底部的座椅-乘员界面模型。1. 柔性聚氨酯泡沫塑料（FPU）是一种高度非线性的粘弹性材料，其性能也取决于其微观结构特性。这项工作将构建聚氨酯泡沫的二维和三维非线性粘超弹性材料模型，以准确模拟泡沫行为和座位-乘员界面上出现的复杂剪切相互作用。泡沫材料微观结构的有限元模型采用相互连接的非线性粘弹性梁来模拟其微观结构行为。实验和系统识别技术将用于提取宏观模型的参数，以拟合实验结果以及基于微观结构的模型的预测。2. 非线性泡沫粘弹性模型将被纳入多体座员模型，并特别关注界面处的相互作用模型。所得到的座椅-人体模型将以非线性积分-微分-代数方程的形式出现。这些模型预计能够预测系统在实际激励下的响应，包括对周期性输入的瞬态和稳定振动。除了直接的数值模拟之外，这种数学模型的求解技术还没有得到很好的发展。将发展基于多频谐波平衡法的半解析技术来预测周期性激励的响应。频率-振幅响应预测将与直接时间积分结果和不同水平垂直激励下实验测量的响应进行比较，从而验证模型以及模型开发方法。因此，所进行的研究有望推进具有微观结构的非线性粘弹性材料的建模以及精确模拟座椅-乘员系统动力学的能力。

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.