Diagnosis of local uncertain modifications in the boundary conditions of a rectangular plate via convex modeling

Abstract

In this study the diagnosis of the boundary conditions is treated as the identification of the adversely affected region on the boundary and estimation of limits on the magnitude of possible change in the stiffness. Convex models are utilized to represent the degree of uncertainty in the boundary condition modification. This means that the diagnosis is actually the identification of the convex model to which the actual boundary stiffness profile belongs. As a result, the diagnosis is formulated as a discrete multi-hypothesis decision problem with attendant formulation of the adaptive termination of this algorithm. The generalized Bolotin's dynamic edge effect method is employed to determine the approximate natural frequencies and normal modes of elastically supported isotropic, uniform rectangular plates employed in the analysis. The entire procedure of diagnosis of local modifications is implemented and results of such an identification are reported.