用广义协调元分析复合式多层无孔和开孔矩形薄板的振动

复合式多层无孔和开孔矩形薄板是桥梁结构和建筑等结构中的最重要的组成部分。当研究它们的振动问题时，用解析法求解自振频率十分困难，而采用通用的有限元法求解自由度数目多，收敛也比较慢。本文利用三角形薄板广义协调元分析了复合式多层四边简支、四边固定无孔和开孔矩形薄板的自由振动，求出了前几阶频率系数，其结果与用ANSYS软件算出的结果基本接近，当为单层无孔和开孔板时，与文献[8]的结果完全相同，且与文献[10]的解析解吻合较好，证明了本文理论推导及程序编制的正确性，表明广义协调元与有限元相比具有自由度少、精度高、程序简便以及收敛快等优点。

Vibration analysis of complex layered rectangular thin plate with or without holes by generalized conforming element

Complex layered rectangular thin plate with or without holes is an important component of structures such as bridge and architecture. When we study their vibration, it is rather difficult to acquire free vibration frequency using analytical methods. Although the finite element method is capable of coping with the problem, a large number of degrees of freedom is often needed and the convergence speed is slow. In this paper, a generalized conforming triangular plate element is employed to analyze the free vibration of complex layered rectangular simply-supported and clamped thin plate with or without holes, then the frequency coefficients are obtained. The results are approaching to those of software ANSYS and reference and reference . It is shown that the present theory and computer code are correct, and that the generalized conforming element has many advantages such as less degrees of freedom, higher precision, easy to be programmed and rapid convergence.