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)
Publisher: Taylor and Francis Ltd
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.
Document Type: Research article
Publication date: 2003-07-01