相邻两边固支其余边自由正交各向异性矩形薄板屈曲的辛叠加解  

Symplectic superposition solution for the buckling problem of orthotropic rectangular thin plates with two adjacent edges clamped and the others free

作　　者：王菁龙 额布日力吐[1] WANG Jinglong;Eburilitu(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《振动与冲击》2025年第2期112-119,共8页Journal of Vibration and Shock

基　　金：国家自然科学基金(12362001,11862019);内蒙古自然科学基金(2023MS01008)。

摘　　要：运用辛叠加方法求出相邻两边固支其他两边自由(two adjacent edges clamped and the other edges free, CCFF)正交各向异性矩形薄板屈曲问题的级数展开解。首先,将原屈曲问题的控制方程转化为哈密顿系统,通过分析边界条件,将原屈曲问题分解为两个子屈曲问题,再利用辛本征函数展开法分别求得两个子屈曲问题的通解;然后,利用叠加方法得到原屈曲问题的辛叠加解;最后,应用所得辛叠加解分别计算了单/双向载荷作用下的CCFF各向同性和正交各向异性矩形薄板的屈曲问题。计算结果表明,所得辛叠加解是正确的并且其收敛速度较快。The series expansion solution for the buckling problem of orthotropic rectangular thin plates with two adjacent edges clamped and the other edges free(CCFF)was derived by using the symplectic superposition method.At first,the governing equation for the initial buckling problem was converted into the Hamiltonian system.Through the analysis of the boundary conditions,the initial buckling problem was decomposed into two sub-buckling problems,whose general solutions were obtained through the use of the symplectic eigenfunction expansion method.Afterwards the symplectic superposition solution for the initial buckling problem was obtained through the superposition method.Eventually,the buckling problems of CCFF isotropic and orthotropic rectangular thin plates under uniaxial/biaxial loading were computed through the obtained symplectic superposition solution respectively.The calculations show that the obtained symplectic superposition solution is correct and its convergence speed is very fast.

关 键 词：辛叠加方法 正交各向异性矩形薄板 哈密顿系统 屈曲 辛叠加解 

分 类 号：O302[理学—力学]