Material and geometrical parameters of tires involve some degree of uncertainty mainly related to production processes. Accordingly, the associated structural responses are affected by these uncertainties. In this study, a novel theoretical ring model is presented to describe the in-plane and out-of-plane vibrations as well as the steady-state response of tires, and then to evaluate the influence of the uncertainties in structural parameters on the natural frequencies and the sound radiation characteristics under uncertain excitations. The Hamilton principle is applied here to derive the governing equations. The modal superposition method is used to calculate the steady-state response of the tire. In the sound radiation analysis, the in-plane and out-of-plane bending and torsional vibrations under a set of harmonic unit forces and moments are treated as the source of noise generation. On this basis, the generalized polynomial chaos expansion method is then adopted to evaluate the influence of the uncertainty on the natural frequencies and the sound power. To obtain the unknown coefficients of the expansions, the nonintrusive probabilistic collocation method is employed. Moreover, considering the concept of linear independence of vectors, the number of collocation points is reduced. It is applied to investigate the impacts of the elastic and structural uncertainties on the natural frequencies of the tire. This yields an efficient simulation in terms of computational costs. Finally, the distributions of the sound power due to the forced vibration under the random concentrated line forces are given.

中文翻译：

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轮胎固有频率和声辐射特性不确定性量化的三维环形模型

轮胎的材料和几何参数涉及一定程度的不确定性，主要与生产过程有关。因此，相关的结构响应受到这些不确定性的影响。在这项研究中，提出了一种新的理论环模型来描述平面内和平面外振动以及轮胎的稳态响应，然后评估结构参数的不确定性对自然振动的影响。不确定激励下的频率和声辐射特性。此处应用汉密尔顿原理来推导控制方程。模态叠加法用于计算轮胎的稳态响应。在声辐射分析中，在一组谐波单位力和力矩下的平面内和平面外弯曲和扭转振动被视为噪声产生的来源。在此基础上，采用广义多项式混沌展开法评估不确定性对固有频率和声功率的影响。为了获得展开的未知系数，采用了非侵入式概率搭配方法。此外，考虑到向量线性独立的概念，减少了搭配点的数量。它用于研究弹性和结构不确定性对轮胎固有频率的影响。这在计算成本方面产生了有效的模拟。最后，