Modal Shapes Selection Criterion for Modal Reconstruction Aimed at Structural Health Monitoring

This paper aims to demonstrate the applicability of a modal selection criterion based on strain energy potential for describing static deformations in a commonly used engineering geometry, specifically a circular plate. The analytical model relies on the definition of internal strain potential energy, enabling the calculation of the energy contribution of each mode derived from a modal analysis to the actual static deformation of the structure. The modal selection is designed to reconstruct the displacement and strain fields under linear elastic conditions, assuming small displacements and strains. This represents the initial phase of a research effort concerning structural health monitoring, where evaluating the displacement, strain, and stress fields is critical for assessing the integrity of mechanical systems. The study examines two loading conditions: axisymmetric and non-axisymmetric bending, which are prevalent in mechanical applications involving circular plates. Modal selection is performed using results from all nodes in the finite element model, as well as from a subset of nodes, demonstrating the feasibility of applying the selection method while reducing the number of equations in the problem. The results indicate a robust comparison between the finite element solution and the modal reconstruction, showcasing the flexibility of the proposed method for the given geometry.