对边简支同性圆柱壳薄板Hamilton算子本征函数系的完备性

Completeness of Eigenfunction System of Hamiltonian Operator Arising from Isotropic Cylindrical Shell Thin Plate

研究均布荷载下各向同性圆柱壳薄板在对边简支边界条件下的弯曲问题。首先将各向同性圆柱壳薄板方程组转化为Hamilton系统,通过计算得到对边简支条件所对应Hamilton算子的本征值及本征函数系。然后证明本征函数系的辛正交性及其在Cauchy主值意义下的完备性,并根据完备性定理推导出相应Hamilton系统的通解,从而得到了沿纵向、环向和法向三个方向的挠度解。

The bending problem of the isotropic thin cylindrical shell plate with simply supported at two opposite sides under uniform load is studied.First,the equations of the isotropic thin cylindrical shell plate are transformed into the Hamiltonian system,and the eigenvalues and eigenfunction system of the corresponding Hamiltonian operator are obtained by calculation.The symplectic orthogonality and completeness,in the sense of Cauchy’s principal value,of the eigenfunction system are proved.And then the general solution of the corresponding Hamiltonian system is derived.Furthermore,the deflection solutions along the longitudinal,circumferential and normal directions are obtained respectively.