Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

doi:10.1088/1674-1056/20/12/124601

Abstract The completeness theorem of the eigenfunction systems for the product of two 2×2 symmetric operator matrices is proved. The result is applied to 4×4 infinite-dimensional Hamiltonian operators. A modified method of separation of variables is proposed for a separable Hamiltonian system. As an application of the theorem, the general solutions for the plate bending equation and the free vibration of rectangular thin plates are obtained. Finally, a numerical test is analysed to show the correctness of the results.

Keywords: operator matrix Hamiltonian operator symplectic orthogonal eigenfunction system completeness

Received: 16 August 2011
Revised: 16 August 2011
Accepted manuscript online:

PACS:	46.25.-y	(Static elasticity)
	02.30.Jr	(Partial differential equations)
	02.30.Tb	(Operator theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10962004) and the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 20080404MS0104).

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Qi Gao-Wa(齐高娃), Hou Guo-Lin(侯国林), and Alatancang(阿拉坦仓) Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity 2011 Chin. Phys. B 20 124601

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Completeness of eigenfunction systems for the product of two symmetric operator matrices and its application in elasticity

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