The Complete Biorthogonal Expansion Theorem and Its Application to a Class of Rectangular Plate Equations
Year: 2019
Author: Jianbo Zhu, Xianlong Fu
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.93
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 93–105
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Rectangular cantilever thin plate Hamiltonian operator biorthogonal expansion theorem general solutions completeness.