Fractional variable exponents Sobolev trace spaces and Dirichlet problem for the regional fractional p(.) -Laplacian

This paper presents an improvement to the modal strain energy (MSE) method for identifying structural damages in plate-type structures. A two-step MSE-based damage localization procedure, including a global step and a local step, is newly proposed to enhance the accuracy of detecting the location of structural damage. Firstly, the global step uses the mode shape data on the whole plate to locate the potentially damaged areas. Then, MSE is applied with a more dense mesh size on these local areas to detect damage in more detail. The proposed procedure’s feasibility is verified by analyzing an aluminum plate with various damaged scenarios. This study uses finite element analysis to acquire the plate's natural frequencies and mode shapes in intact and damaged states. A set of two damage detection capacity indicators are also newly presented to evaluate the precision of the proposed procedure. The diagnostic results demonstrate that the proposed approach uses less modal data than the original MSE method and accurately identifies the damage's locations in the plates with various edge conditions. Moreover, the combination of three first mode shapes and a damage threshold of 40% of the maximum normalized damage index gives the best results of damage localization.

Structural Damage Localization in Plates Using Global and Local Modal Strain Energy Method

A Two-Stage Approach to Solve Structural Damage Detection Problem in Plate Structures

Abstract In this paper, we study a class of fractional p(x)-Laplacian Dirichlet problems in a bounded domain with Lipschitz boundary. Using variational methods, we prove in different situations the existence and multiplicity of solutions.

Kamel Belhadj

Papers

A Two-Stage Approach to Solve Structural Damage Detection Problem in Plate Structures

Existence and multiplicity results for fractional p(x)-Laplacian Dirichlet problem

Optimization of Diffuser Angle to Reduce the Drag of a Light Car