Abstract: The application of porous materials is increasingly widespread, but due to the limitation of their own special pore structure, the strength of porous materials is not high. Laying carbon fiber cloth on the surface of porous media material can obtain the excellent comprehensive performance of porous medium material and the high strength of carbon fiber cloth simultaneously. The finite element method (FEM) is mostly used to analyze the mechanical properties of the porous laminated structure with carbon fiber cloth. Because of the particularity of porous structure, the calculation accuracy and efficiency of FEM are low. Based on the Biot theory and the lamination theory, combining the control equation of porous layer and carbon fiber cloth, the integrated first-order ordinary differential matrix governing equations of porous laminated beams with carbon fiber cloth under harmonic excitation are derived by considering the continuity condition between layers. Combined with the boundary conditions of the structure, the precise integration method with high precision is used to solve the integrated governing equations. The feasibility and correctness of the model are verified compared with the finite element model, and the dynamic characteristics of the porous laminate beam with carbon fiber cloth are also analyzed by the present method.

Key words: Porous medium laminated beam; Carbon fiber cloth; Precise integration method; Kinetic characteristics

摘要： 多孔材料的应用日益广泛，但受自身特殊孔隙结构的限制，多孔材料的强度不高。在 多孔介质材料表面敷设碳纤维布可以同时得到多孔介质材料优异的综合性能和碳纤维布的高 强度。敷设碳纤维布多孔介质叠层结构的力学性能研究多采用有限元法，由于多孔材料结构 的特殊性，该方法的计算精度和效率较低。文章基于 Biot 理论和层合理论，结合多孔介质层 和碳纤维布的控制方程，考虑层间的连续性条件，推导敷设碳纤维布多孔介质叠层梁在谐激 励作用下的整合一阶常微分矩阵控制方程。结合结构的边界条件，利用具有高精度的精细积 分法对整合控制方程进行求解。通过与有限元模型的对比，验证了所建模型的可行性和正确 性，并利用所提方法分析了敷设碳纤维布多孔介质叠层梁的动力学特性。

关键词: 多孔介质叠层梁；碳纤维布；精细积分法；动力学特性