Topology Optimization of Undamped Plates for the Extremization of Natural Frequencies

Resumo

In the design of mechanical components subjected to vibrations, it is important to understand how the natural frequencies of a structure are distributed and whether any of them coincides with the operating range of the equipment. When this occurs, the phenomenon of resonance can significantly amplify vibrations, compromising the structural integrity and potentially leading to failures and/or accidents.In this context, a topology optimization methodology is proposed to extremize the ranges of natural frequencies in plate-type structures. In the optimization problem, is employed a Solid Isotropic Microstructure with Penalization (SIMP) with volume constraints. A functional is used to penalize regions with intermediate densities, and the main contribution of this work lies in the application of a functional based on the penalization of the density field gradient to mitigate the occurrence of the checkerboard phenomenon, a technique not previously applied in topology optimization with the objective of extremizing the natural frequencies of plates. The optimization problem is solved using the Augmented Lagrangian Method (ALM), aiming for efficient and stable solutions.With this approach, new geometric configurations for plates used in various applications can be obtained, significantly increasing or shifting natural frequency values. As a result, the structure becomes less prone to resonance, reducing excessive vibration propagation and improving the performance and durability of mechanical components.