This paper introduces a novel family of single-track vehicle models that incorporate a distributed representation of transient tyre dynamics, whilst simultaneously accounting for nonlinear effects induced by friction. The core of the proposed framework is represented by the distributed Friction with Bristle Dynamics (FrBD) model, which unifies and extends classical formulations such as Dahl and LuGre by describing the rolling contact process as a spatially distributed system governed by semilinear partial differential equations (PDEs). This model is systematically integrated into a single-track vehicle framework, where the resulting semilinear ODE-PDE interconnection captures the interaction between lateral vehicle motion and tyre deformation. Two main variants are considered: one with rigid tyre carcass and another with flexible carcass, each admitting a compact state-space representation. Local and global well-posedness properties for the coupled system are established rigorously, highlighting the dissipative and physically consistent properties of the distributed FrBD model. A linearisation procedure is also presented, enabling spectral analysis and transfer function derivation, and potentially facilitating the synthesis of controllers and observers. Numerical simulations demonstrate the model's capability to capture micro-shimmy oscillations and transient lateral responses to advanced steering manoeuvres. The proposed formulation advances the state-of-the-art in vehicle dynamics modelling by providing a physically grounded, mathematically rigorous, and computationally tractable approach to incorporating transient tyre behaviour in lateral vehicle dynamics, when accounting for the effect of limited friction.

翻译：本文提出了一类新颖的单轨车辆模型，该模型结合了瞬态轮胎动力学的分布式表示，同时考虑了摩擦引起的非线性效应。所提出框架的核心是分布式摩擦与刷毛动力学模型，该模型通过将滚动接触过程描述为由半线性偏微分方程控制的空间分布式系统，统一并扩展了如Dahl和LuGre等经典公式。该模型被系统地集成到单轨车辆框架中，由此产生的半线性ODE-PDE互联结构捕捉了车辆横向运动与轮胎变形之间的相互作用。研究考虑了两种主要变体：一种具有刚性轮胎胎体，另一种具有柔性胎体，每种变体都允许紧凑的状态空间表示。严格建立了耦合系统的局部和全局适定性，突出了分布式FrBD模型的耗散性和物理一致性特性。本文还提出了一种线性化方法，支持谱分析和传递函数推导，并可能促进控制器和观测器的综合设计。数值模拟证明了该模型能够捕捉微幅摆振振荡以及对高级转向操作的瞬态横向响应。所提出的公式通过提供一种物理基础坚实、数学严谨且计算上易于处理的途径，在考虑有限摩擦效应的情况下将瞬态轮胎行为纳入车辆横向动力学，从而推动了车辆动力学建模领域的技术发展。