Probability distribution function inspired structural optimization for frequency response problems

This study introduces an innovative topological optimization scheme for frequency response problems using the phase field design method. In the proposed approach, the frequency response function is mapped onto a probability distribution function where the mean value of the probability distribution function becomes the resonance frequency and the variance corresponds to its bandwidth. Using the mapping concept, the frequency characteristics such as the resonance frequency and bandwidth can be directly included in the formulation of the design objective function. Therefore, the mapping process enables to handle frequency characteristics in topological design for frequency response problems. As numerical examples, the resonance frequency maximization problem of a cantilever beam, bandwidth maximization of a clamped end beam and the bandwidth minimization problem of a plasmonic grating coupler are presented to demonstrate the validity of the proposed method.