摘要
矩形板的自由振动和本征屈曲等本征值问题一直受到学者们的关注和研究。本文总结了已有的矩形板本征值问题的封闭解法,包括Navier方法、Levy方法、分离变量(SOV)方法和Kantorovich-Krylov方法。对于每一种方法,首先介绍了它的基本思想、发展历程以及应用范围,之后以矩形一阶剪切板的自由振动问题为例,详述了各种方法的求解过程。本文重点介绍近20年来发展的各类SOV方法,包括直接、变分、迭代、改进和扩展SOV方法。最后,借助数值结果,对各种封闭解法进行了总结与比较。对于对边简支矩形板,各种方法皆可以得到精确解;对于具有其他齐次边界的矩形板,SOV方法和Kantorovich-Krylov方法都可以获得高精度解。
The eigenvalue problems of rectangular plates, including the free vibration and eigenbuckling problems, have been attracting considerable interest of researchers. This paper reviews the available closed-form solution methods for the eigenvalue problems of rectangular plates, which are the Navier, Levy, Separation-of-Variable(SOV) and Kantorovich-Krylov methods. For each method, the basic idea, development history and application scopes are introduced first, and the free vibration problem of a rectangular first-order shear deformation plate is taken as the example to illustrate the solution procedures of each method. Especially, this paper focuses on various SOV methods developed in recent 20 years, including the direct, variational, iterative, improved and extended SOV methods. Finally, all the reviewed methods are summarized and compared from various perspectives with the help of numerical result. For Levy-type of plates, all methods can provide the exact solutions. For plates with other homogeneous boundary conditions, both Kantorovich-Krylov method and SOV methods can produce highly-accurate solutions.
作者
邢誉峰
李根
袁冶
XING Yufeng;LI Gen;YUAN Ye(School of Aeronautic Science and Engineering,Beihang University,Beijing 100083,China)
出处
《航空学报》
EI
CAS
CSCD
北大核心
2022年第10期183-207,共25页
Acta Aeronautica et Astronautica Sinica
基金
国家自然科学基金(12172023,11872090)。
