Optimizing Truss Dynamics: A Multi-Objective Approach to Modify Natural Frequencies and Mode Shapes with Geometric Constraints

This article presents a comprehensive optimization approach to dynamically enhance a truss structure. The optimization problem addresses the systematic modification of the truss dynamics, focusing on achieving a specific set of natural frequencies without compromising the geometrical integrity. The truss structure is redesigned through the exploration of diverse cost functions, considering both minimization and maximization strategies for targeted subsets of natural frequencies and mode shape elements but also preserving essential geometric properties including dimensional intervals, symmetry conditions, and adherence to topological constraints. A dual-objective optimization paradigm is adopted; concurrently pursuing the minimization and maximization objectives together with various constraints are introduced to enforce geometric limits on each truss member, providing a holistic solution for effectively tailoring the dynamic characteristics of the truss structure. This study represents a nuanced understanding of dynamic optimization in truss design. The article's main contribution is improving balance between optimizing the dynamic requirements of the truss structure and considering the essential geometry constraints that ensures its practical utility. By doing so, the research not only advances the understanding of truss dynamics but also provides a framework for approaching similar optimization challenges in mechanical engineering.