Topology Optimization of Mechanical Structures Targeting Vibration Characteristics

Abstract

This paper proposes a structural topology optimization method for obtaining mechanical structures incorporating desired vibration characteristics for the design of mechanical resonators and vibromotors. First, a new type of homogenization design method is introduced, in which the continuous material distributions are assumed using a continuous interpolation function at each node, in order to overcome numerical instabilities such as checkerboard patterns. Next, three design requirements to implement specific vibration characteristics in the mechanical structures are clarified, namely eigen-frequency matching, eigen-mode control, and stiffness, and the corresponding objective functions are formulated. A new type of multi-objective function incorporating the three objective functions is proposed. The optimization problem is formulated using this multi-objective function, and an optimization algorithm is developed using Sequential Linear Programming (SLP). Finally, several examples are provided in order to confirm the usefulness of the generated optimal designs for vibrating mechanical structures.