The separable Hamiltonian system and complete biorthogonal expansion method of Mindlin plate bending problems  

作　　者：HOU GuoLin QI GaoWa XU YaNan CHEN Alatancang 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University

出　　处：《Science China(Physics,Mechanics & Astronomy)》2013年第5期974-980,共7页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No. 10962004);the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2012MS0105)

摘　　要：A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differen form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presen! Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems x~ two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to ve~ the accuracy and validity of the expansion method.A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differential form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presented. Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems with two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections and bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to verify the accuracy and validity of the expansion method.

关 键 词：separable Hamiltonian system mindlin plate bending biorthogonal expansion off-diagonal Hamiltonian operator 

分 类 号：O175[理学—数学]