摘要
从实际力学问题出发抽象出一类矩形中厚板模型,并用辛体系方法进行求解。首先,通过适当的变换将该模型转化为Hamilton系统,得到了Hamilton算子的本征值和本征函数系,并证明了本征函数系的完备性,进而给出对边简支情形的一般解,最后对6种不同边界条件下的Mindlin板和Pasternak型双参数弹性地基的矩形中厚板的振动及屈曲问题进行了数值模拟。数据对比显示了本文模型的正确性和辛方法的有效性。
A class of rectangular moderately thick plate models was abstracted from the practical mechanics problems and solved by the symplectic system method.Firstly,the model was transformed into a Hamiltonian system through appropriate transformations.Then,the eigenvalues and eigenfunction systems of the Hamiltonian operator were obtained.The completeness of the eigenfunction systems was verified to give a general solution for the two opposite edges simply supported.Finally,the vibration and buckling problems of Mindlin plates and rectangular moderately thick plates on Pasternak-type two-parameter elastic foundations were considered under six different boundary conditions,and the data comparisons showed the correctness of the proposed model and the effectiveness of the symplectic method.
作者
吴美慧
侯国林
WU Meihui;HOU Guolin(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)
出处
《内蒙古大学学报（自然科学版）》
CAS
2024年第5期483-495,共13页
Journal of Inner Mongolia University：Natural Science Edition
基金
国家自然科学基金项目(12261064,11861048)
内蒙古自然科学基金项目(2021MS01004)。
关键词
矩形中厚板
辛方法
HAMILTON算子
自由振动
屈曲载荷
rectangular moderately thick plate
symplectic method
Hamiltonian operator
free vibration
buckling load
