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Volume 1, Issue 1
The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations

Jianbo Zhu & Xianlong Fu

DOI: 10.12150/jnma.2019.93

J. Nonl. Mod. Anal., 1 (2019), pp. 93-105.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

In this paper, we first establish the separable $Hamiltonian$ system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional $Hamiltonian$ operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported.

  • Keywords

Rectangular cantilever thin plate, Hamiltonian operator, biorthogonal expansion theorem, general solutions, completeness.

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COPYRIGHT: © Global Science Press

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@Article{JNMA-1-93, author = {Zhu , Jianbo and Fu , Xianlong}, title = {The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {1}, pages = {93--105}, abstract = {

In this paper, we first establish the separable $Hamiltonian$ system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional $Hamiltonian$ operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.93}, url = {http://global-sci.org/intro/article_detail/jnma/18870.html} }
TY - JOUR T1 - The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations AU - Zhu , Jianbo AU - Fu , Xianlong JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 93 EP - 105 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.93 UR - https://global-sci.org/intro/article_detail/jnma/18870.html KW - Rectangular cantilever thin plate, Hamiltonian operator, biorthogonal expansion theorem, general solutions, completeness. AB -

In this paper, we first establish the separable $Hamiltonian$ system of rectangular cantilever thin plate bending problems by choosing proper dual vectors. Then using the characteristics of off-diagonal infinite-dimensional $Hamiltonian$ operator matrix, we derive the biorthogonal relationships of the eigenfunction systems and based on it we further obtain the complete biorthogonal expansion theorem. Finally, applying this theorem we obtain the general solutions of rectangular cantilever thin plate bending problems with two opposite edges slidingly supported.

Jianbo Zhu & Xianlong Fu. (1970). The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations. Journal of Nonlinear Modeling and Analysis. 1 (1). 93-105. doi:10.12150/jnma.2019.93
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