Please wait a minute...
Chin. Phys. B, 2011, Vol. 20(12): 124601    DOI: 10.1088/1674-1056/20/12/124601
CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next  

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

Qi Gao-Wa(齐高娃), Hou Guo-Lin(侯国林), and Alatancang(阿拉坦仓)
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
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).

Cite this article: 

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

[1] Zhong W X 1991 Chin. J. Comput. Mech. 8 229 (in Chinese)
[2] Zhong W X 1994 Appl. Math. Mech. (English Edn.) 15 1113 %% 引用期刊的格式
[3] Zhong W X 1995 A New Systematic Methodology for Theory of Elasticity (Dalian: Dalian University of Technology Press) (in Chinese)
[4] Zhong W X and Yao W A 1999 Acta Mech. Sin. 31 173 (in Chinese)
[5] Yao W A and Sun Z 2008 Chin. J. Theor. Appl. Mech. 40 557 (in Chinese)
[6] Yao W A, Cai Z Y and Hu X F 2011 J. Dyn. Control 9 12 (in Chinese)
[7] Lim C W, Li C F, Xiang Y and Yao W A 2009 Int. J. Engrg. Sci. 47 131
[8] Xu X S, Zhong W X, Li X and Wang G P 2006 Int. J. Engrg. Sci. 44 897
[9] Zhong Y, Li R, Liu Y M and Tian B 2009 Int. J. Solids Structures 46 2506
[10] Chen W Q and Zhao L 2009 Chin. J. Theor. Appl. Mech. 41 588 (in Chinese)
[11] Hou G L and Alatancang 2008 Chin. Phys. B 17 2753
[12] Alatancang and Wu D Y 2008 Sci. Chin. Ser. A 38 904
[13] Hou G L and Alatancang 2010 Commun. Theor. Phys. (Beijing) 53 237
[14] Huang J J, Alatancang and Wang H 2009 Chin. Phys. B 18 3616
[15] Huang J J, Alatancang and Wang H 2010 Chin. Phys. B 19 120101
[16] Wang H, Alatancang and Huang J J 2011 Chin. Phys. B 20 010209
[17] Luo J H, Li Q S and Liu G D 2009 Sci. Chin. Ser. G 52 270
[18] Tang L M 1991 Chin. J. Comput. Mech. 8 343 (in Chinese)
[19] Wu C X, Zhou Z Y and Ding P Z 1997 Chin. J. Comput. Phys. 14 702 (in Chinese)
[1] Erratum to “ Accurate GW0 band gaps and their phonon-induced renormalization in solids”
Tong Shen(申彤), Xiao-Wei Zhang(张小伟), Min-Ye Zhang(张旻烨), Hong Jiang(蒋鸿), and Xin-Zheng Li(李新征). Chin. Phys. B, 2022, 31(5): 059901.
[2] Furi-Martelli-Vignoli spectrum and Feng spectrum of nonlinear block operator matrices
Xiao-Mei Dong(董小梅), De-Yu Wu(吴德玉), and Alatancang Chen(陈阿拉坦仓). Chin. Phys. B, 2021, 30(4): 040201.
[3] Accurate GW0 band gaps and their phonon-induced renormalization in solids
Tong Shen(申彤), Xiao-Wei Zhang(张小伟), Min-Ye Zhang(张旻烨), Hong Jiang(蒋鸿), and Xin-Zheng Li(李新征). Chin. Phys. B, 2021, 30(11): 117101.
[4] On the ascent of infinite dimensional Hamiltonian operators
Wu De-Yu (吴德玉), Chen Alatancang (陈阿拉坦仓). Chin. Phys. B, 2015, 24(8): 084601.
[5] On the completeness of eigen and root vector systems for fourth-order operator matrices and their applications
Wang Hua(王华), Alatancang (阿拉坦仓), and Huang Jun-Jie(黄俊杰) . Chin. Phys. B, 2011, 20(10): 100202.
[6] Symplectic eigenvector expansion theorem of a class of operator matrices arising from elasticity theory
Wang Hua(王华), Alatancang(阿拉坦仓), and Huang Jun-Jie(黄俊杰) . Chin. Phys. B, 2011, 20(1): 010209.
[7] Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory
Huang Jun-Jie(黄俊杰),Alatancang(阿拉坦仓), and Wang Hua(王华). Chin. Phys. B, 2010, 19(12): 120201.
[8] The symplectic eigenfunction expansion theorem and its application to the plate bending equation
Huang Jun-Jie(黄俊杰), Alatancang(阿拉坦仓), and Wang Hua(王华). Chin. Phys. B, 2009, 18(9): 3616-3623.
[9] The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique
Meng Xiang-Guo(孟祥国), Wang Ji-Suo(王继锁), and Li Hong-Qi(李洪奇). Chin. Phys. B, 2008, 17(8): 2973-2978.
[10] On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids
Hou Guo-Lin(侯国林) and Alatancang(阿拉坦仓). Chin. Phys. B, 2008, 17(8): 2753-2758.
[11] q-NONLINEAR CAVITY FIELD STATES GENERATED BY THE EXCITATIONS ON A q-COHERENT STATE
Xi Ding-ping (韦联福), Wei Lian-fu (奚定平). Chin. Phys. B, 2000, 9(8): 586-589.
No Suggested Reading articles found!