基于薄板样条径向基函数的复合材料层合板自由振动分析  

Free vibration analysis of laminated composite plates based on thin plate spline radial basis functions

作　　者：宋薇薇[1,2,3] 项松 赵锐[1,2] 赵为平 郭晗 SONG Wei-wei;XIANG Song;ZHAO Rui;ZHAO Wei-ping;GUO Han(General Aviation Key Laboratory of Liaoning Province,Shenyang Aerospace University,Shenyang 110136,China;Liaoning General Aviation Academy,Shenyang 110136,China;Department of Civil Aviation,Shenyang Aerospace University,Shenyang 110136,China)

机构地区：[1]沈阳航空航天大学辽宁省通用航空重点实验室,沈阳110136 [2]辽宁通用航空研究院,沈阳110136 [3]沈阳航空航天大学民用航空学院,沈阳110136

出　　处：《计算力学学报》2024年第5期954-962,共9页Chinese Journal of Computational Mechanics

摘　　要：基于复合材料层合板的三角剪切变形理论,推导了对称复合材料层合板的控制微分方程。利用基于薄板样条径向基函数的无网格配置方法离散的控制微分方程,预测了对称复合材料层合板的自由振动行为。计算了不同材料参数和层合板几何参数的固有频率,并与文献结果进行了比较。还研究了节点排布、模量比和边厚比对固有频率的影响。结果表明,本文结果与文献结果具有较好的一致性,节点数量越大,无量纲频率对网格分布越不敏感,固有频率随着边厚比和模量比的增加而增加。通过数值实验,证明了用薄板样条径向基函数离散的三角剪切变形理论对对称复合材料层合板的自由振动分析具有较高的数值精度和良好的收敛性。Based on the trigonometric shear deformation theory of laminated composite plates,the governing differential equation of symmetric laminated composite plates is derived.The free vibration behavior of symmetric composite laminates is predicted using discrete governing differential equation derived from a meshless collocation method based on the spline radial basis functions for a thin plate.The natural frequencies of the laminated composite plates with different material parameters and geometric parameters were calculated and compared with some published results.The effects of the grid pattern modulus ratio,and the side-to-thickness ratio on natural frequencies are also studied.The results show that the calculation results of this article are in good agreement with the published results.The larger the number of nodes,the less sensitive the dimensionless frequency is to the grid distribution.The natural frequency increases with the increase of the edge thickness ratio and modulus ratio.Through numerical experiments,it is proved that the trigonometric shear deformation theory combined with the thin plate spline radial basis functions for a thin plate has high numerical accuracy and good convergence for the free vibration analysis of symmetric composite laminated plates.

关 键 词：三角剪切变形理论 复合材料层合板 自由振动 薄板样条径向基函数 固有频率 

分 类 号：O342[理学—固体力学]