Analysis and Applications of Extended Kantorovich–Krylov Method

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 tooi for the boundary value problems of partial differential equations in the structural vibrations.

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