中文摘要：

基于宏—细观力学分析,考虑编织纱线连续性对材料性能的影响,建立了三维编织复合材料板的单胞模型。采用Reddy高阶剪切板理论,给出四边简支编织材料矩形板在不同几何参数、纤维体积含量和弹性地基参数情况下的von Kármán-Donnell型振动方程的解,并讨论了弹性基础刚度、面内载荷、边厚比和编织角等对编织复合材料板的振动频率的影响。理论分析结果与文献结果吻合较好。

英文摘要：

A nonlinear vibration analysis is presented for a 3D braided rectangular plate resting on a two-parameter （Pasternak-type） elastic foundation. Based on a micro-macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross-section of the plate.The governing equations are based on Reddy＇s higher order shear deformation plate theory with a yon K6rm6n-Donnell-type of kinematic nonlinearity. All four edges of the plates are assumed to be simply supported with no in-plane displacements.The numerical examples concern the free vibration of braided composite plates with different values of geometric parameter, fiber volume fraction,and braiding angle which resting on Pasternak-type elastic foundations with the Winkler elastic foundations being a limiting case. Effects of foundation stiffness, in-plane loads, plate side-to-thickness ratio are also studied. A detailed study on the free vibration of simply supported rectangular thick plates was performed.