Analysis and Applications of Extended Kantorovich-Krylov Method

Authors: Chang D-C.; Wang G.; Wereley N.M.

Source: Applicable Analysis, Volume 82, Number 7, July 2003 , pp. 713-740(28)

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Abstract:

In our prior work, the two-dimensional bending and in-plane mode shape functions of isotropic rectangular plates were solved based on the extended Kantorovich-Krylov method. These plate modes were then applied to sandwich plate analysis using the assumed modes method. Numerical results has shown these two-dimensional plate modes improved our sandwich plate analysis. However, the rigorous mathematical convergence proof of the extended Kantorovich-Krylov method is lacking. In this article, we provide a rigorous mathematical convergence proof of the extended Kantorovich-Krylov method using the example of rectangular plate bending vibration, in which the governing equation is a biharmonic equation. The predictions of natural frequency and mode shape functions based on the extended Kantorovich-Krylov method were calculated and the results were numerically validated by other analyses. A similar convergence proof can be applied to other types of partial differential equations (PDEs) that govern vibration problems in engineering applications. Based on these results, the extended Kantorovich-Krylov method was proven to be a powerful tool for the boundary value problems of partial differential equations in the structural vibrations.

Keywords: Kantorovich-Krylov method; Biharmonic equation; PDEs; Plate; Bending vibration; Mathematics Classifications Subject (2002): 35J25; 35E05

Document Type: Research article

DOI: http://dx.doi.org/10.1080/0003681031000148573

Publication date: 2003-07-01

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