关键词: 复合材料地铁车顶板, 固有频率, 概率分析, 随机有限元法, 不确定性

Abstract: The material properties and physical parameters of composite structures have a quite important variability, which can influence the reliability of structure. In this paper, a stochastic finite element method, the Modal Stability Procedure (MSP), is applied for probabilistic free vibration analysis of carbon fiber reinforced composite metro roof panels. Material properties (elastic properties, densities…) and physical properties (layer thicknesses) are considered as uncertain parameters. The variability of natural frequencies is studied. The MSP is based on an assumption that the mode shapes of the structure are independent of input uncertainty. An explicit expression of natural frequencies, which contains all uncertain parameters, is proposed. Based on the assumption, perturbed modal strains and mode shapes in this expression are replaced by nominal ones. These nominal results are obtained by one nominal finite element analysis with a standard software (Abaqus in this paper). The statistical quantities (mean value, standard deviation, coefficient of variation and distribution) associated to the natural frequencies are evaluated by a Monte Carlo Simulation (MCS) using this expression. For calculating the variability of natural frequencies, the MSP can significantly reduce the computational time, requiring only one nominal finite element analysis and a fast MCS. Using the MSP and Sobol′ method, the influence of uncertain parameters on the first four natural frequencies is studied for sandwich metro roof panels, which are composed of foam cores and carbon fiber reinforced polymer (CFRP) faces. In this paper, the direct MCS is used as a reference. The results obtained by the MSP and the direct MSC are compared. The comparison shows that the MPS can provide accurate results with high computational efficiency. Under the same uncertainty level, the densities and thicknesses, especially the thickness of foam core, have a more important influence on the variability of natural frequencies. By comparison, the variability is not sensitive to uncertain shear moduli of CFRP faces and elastic modulus of foam cores.

Key words: composite metro roof panel, natural frequency, probabilistic analysis, stochastic finite element method, uncertainty