Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates

作者：Wang Hua; Alatancang; Huang Jun Jie^*

来源：Communications in Theoretical Physics, 2009, 52(6): 1087-1092.

• free vibration of rectangular thin plate
• double symplectic eigenfunction expansion method
• upper triangular matrix differential system
• general solution

The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectic eigenfunction expansion method.

• 出版日期2009-12
• 单位内蒙古大学; 内蒙古工业大学