An analytical stochastic dynamic stiffness formulation is developed for the dynamic analysis of damped membrane structures with parametric uncertainties. First, the exact general solution of a biaxially taut membrane in the frequency domain is derived, which is used as the frequency-dependent shape function. Both the material properties and the tension fields of the membrane are modelled as 2D random fields with an exponential autocorrelation function in both x and y directions. Then, the random fields are decomposed by Karhunen-Loève (KL) expansion. After a formulation procedure like the finite element method, the stochastic stiffness, and mass elemental matrices are derived based on the frequency-dependent shape function and the KL expansion, subsequently forming the stochastic dynamic stiffness matrix. The developed stochastic dynamic stiffness elements can be assembled to model membrane assemblies with general boundary conditions considering uncertainties. The proposed method can be utilized as a feasible technique for the efficient and accurate stochastic dynamic analysis in the whole frequency domain. The current research paves the way for stochastic dynamic stiffness formulation for other two-dimensional structures like plates and shells.

针对具有参数不确定性的阻尼膜结构的动力学分析，开发了一种分析随机动态刚度公式。首先，推导了双轴拉紧膜在频域中的精确一般解，并将其用作与频率相关的形状函数。膜的材料特性和张力场都被建模为二维随机场，在x和y方向上都具有指数自相关函数指示。然后，通过Karhunen-Loève（KL）扩展分解随机场。经过类似于有限元方法的公式化过程后，基于频率相关的形状函数和KL展开，得出了随机刚度和质量元素矩阵，随后形成了随机动态刚度矩阵。可以将已开发的随机动态刚度元件组装成具有不确定性的一般边界条件来模拟膜组件。该方法可作为一种可行的技术，用于在整个频域中进行高效，准确的随机动态分析。当前的研究为其他二维结构（如板和壳）的随机动态刚度公式化铺平了道路。