Eigen-vector expansion theorem of a class of operator matrices appearing in elasticity and applications
Zhang Guo-ting, Huang Jun-Jie, Alatancang · Acta Physica Sinica · 2012
For a class of operator matrices appearing in elasticity, the eigen-vector expansion theorem is considered. It is shown that the eigen-vectors possess the symplectic orthogonality. And a necessary and sufficient condition for the completeness of the eigen-vector system is further given. As concrete applications, the obtained results are tested for the plate bending equation and the buckling deflection problem of rectangular thin plates.