Optimization and Analysis of Plates with a Variable Stiffness Distribution in Terms of Dynamic Properties

Abstract

This study investigates the optimization of thickness distribution in simply supported and cantilever plates to maximize gaps between adjacent natural frequencies. The research employs a genetic algorithm (GA) as the primary optimization tool, with the finite element method (FEM) integrated for structural dynamics analysis. The optimization process focuses on tailoring the plate thickness (stiffness) while maintaining fixed overall dimensions. The study considers square and rectangular plates with two boundary conditions: simply supported and cantilever. The optimization targets gaps between the first three natural frequencies. The GA-based optimizer demonstrates effectiveness in increasing the relative separation between neighboring natural frequencies, as defined by the fitness function. Compared to the reference individuals, the optimized individuals achieve objective function values from 0.25 to 2.5 times higher. The GA optimization tool is also compared with an alternative optimization tool achieving up to 35% better results. This research contributes to the field of structural dynamics by demonstrating the potential of genetic algorithms in optimizing plate designs for enhanced vibrational characteristics. Such optimization is particularly relevant in civil engineering, where plate elements are widely used, and where controlling dynamic properties can improve serviceability and reduce the risk of resonance under operational or environmental loads. The findings have implications for various engineering applications where controlling dynamic properties of plate structures is crucial.