Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(12): 120201    DOI: 10.1088/1674-1056/19/12/120201
GENERAL   Next  

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

Huang Jun-Jie(黄俊杰)a),Alatancang(阿拉坦仓)a), and Wang Hua(王华)a)b)
a School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; b Department of Mathematics, College of Science, Inner Mongolia University of Technology, Hohhot 010051, China
Abstract  This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.
Keywords:  off-diagonal operator matrix      completeness      double eigenfunction expansion method      elasticity theory  
Received:  27 January 2010      Revised:  15 March 2010      Accepted manuscript online: 
PACS:  0200  
  0340D  
  0420J  
  4630C  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10962004 and 11061019), the Doctoral Foundation of Inner Mongolia (Grant Nos. 2009BS0101 and 2010MS0110), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20070126002), and the Chunhui Program of the Ministry of Education of China (Grant No. Z2009-1-01010).

Cite this article: 

Huang Jun-Jie(黄俊杰),Alatancang(阿拉坦仓), and Wang Hua(王华) Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory 2010 Chin. Phys. B 19 120201

[1] Hardt V and Mennicken R 2001 Operator Theory: Advances and Applications (Birkhddotauser Verlag) 124 243
[2] Hardt V, Konstantinov A and Mennicken R 2000 Math. Nachr. 215 91
[3] Schhatmboxoichi,hatmboxOta and Schmddotmboxudgen K 2003 Integr. Equ. Oper. Theory 45 475
[4] Hou G L and Alatancang 2009 Commun. Theor. Phys. 51 200
[5] Huang J J and Alatancang 2006 Mongolian Mathematical Journal 10 1
[6] Alatancang, Huang J J and Fan X Y 2008 Sci. Chin. Ser. A: Mathematics 51 915
[7] Zhong W X 2004 Duality System in Applied Mechanics and Optimal Control (Dordrecht: Kluwer Academic Publishers)
[8] Xu X, Chu H and Lim C 2008 International Journal of Structural Stability and Dynamics 8 487
[9] Zhang W 2009 Arch. Appl. Mech. 79 793
[10] Huang J J, Alatancang and Chen A 2008 Acta Mathematicae Applicatae Sinica Chinese Series 31 457
[11] Alatancang and Wu D Y 2009 Sci. Chin. Ser. A: Mathematics 52 173
[12] Huang J J, Alatancang and Wang H 2009 Chin. Phys. B 18 3616
[13] Wang H, Alatancang and Huang J J 2009 Commun. Theor. Phys. 52 1087
[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] 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.
[3] Enhanced effect of dimension of receptor-ligand complex and depletion effect on receptor-mediated endocytosis of nanoparticles
Ye Liu(刘野), Qingqing Gao(高庆庆), Yijun Liu(刘益军), Chuang Zhao(赵闯), Zongliang Mao(毛宗良), Lin Hu(胡林), Yanhui Liu(刘艳辉). Chin. Phys. B, 2017, 26(12): 128704.
[4] Vibration and buckling analyses of nanobeams embedded in an elastic medium
S Chakraverty, Laxmi Behera. Chin. Phys. B, 2015, 24(9): 097305.
[5] 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.
[6] The effect of fractional thermoelasticity on a two-dimensional problem of a mode I crack in a rotating fiber-reinforced thermoelastic medium
Ahmed E. Abouelregal, Ashraf M. Zenkour. Chin. Phys. B, 2013, 22(10): 108102.
[7] 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) . Chin. Phys. B, 2011, 20(12): 124601.
[8] 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.
[9] 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.
[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] 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.
[12] 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!