Abstract
In vibration optimization problems, eigen-frequencies are usually maximized in the optimization since resonance in a mechanical structure must be avoided. However, vibrating mechanical structures can provide additional useful dynamic functions if desired eigen-frequencies and eigen-modes in the structures can be implemented. In this paper, we shall discuss a method for obtaining optimal topologies for vibrating structures that have desired eigen-frequencies and eigen-modes, in order to successfully create mechanical resonator designs. First, we clarify the mechanical requirements and design specifications of the vibrating structure, and construct objective functions that satisfy these design specifications. A new type of multi-objective function is formulated in order to find an optimal configuration incorporating all objective functions. Next, the optimization algorithm is constructed, based on the ground structure and continuum mechanics approaches. Finally, we examine the characteristics of the optimization formulations and optimal solutions.
