Connectivity constraints for eigenvalue reduction in level-set topology optimization

Eigenvalue problems play a fundamental role in structural dynamics and engineering design, with topology optimization offering powerful tools for achieving superior performance. While most research has focused on eigenvalue maximization, only a few studies have explored eigenvalue assignment or reduction. This work investigates the challenges associated with eigenfrequency minimization in level-set topology optimization, highlighting the risk of infeasible or fragmented designs. To overcome these issues, we propose a formulation that integrates connectivity constraints to preserve structural integrity, thereby addressing an inherent limitation of eigenfrequency reduction. A comparative analysis of eigenfrequency minimization and maximization is presented, emphasizing the role of the ersatz material interpolation scheme and the impact of constraint enforcement. The proposed methodology is demonstrated through numerical examples, illustrating its effectiveness in achieving feasible layouts and highlighting its potential applications across a wide class of structural dynamics problems.