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 - <p style="text-align: justify;">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.</p>