### Abstract

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.

Original language | English |
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Pages (from-to) | 783-802 |

Number of pages | 20 |

Journal | Computer Methods in Applied Mechanics and Engineering |

Volume | 318 |

DOIs | |

Publication status | Published - 2017 May 1 |

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### All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science Applications

### Cite this

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**Probability distribution function inspired structural optimization for frequency response problems.** / Seong, Hong Kyoung; Yoo, Jeonghoon.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Probability distribution function inspired structural optimization for frequency response problems

AU - Seong, Hong Kyoung

AU - Yoo, Jeonghoon

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85014465876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85014465876&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2017.02.012

DO - 10.1016/j.cma.2017.02.012

M3 - Article

AN - SCOPUS:85014465876

VL - 318

SP - 783

EP - 802

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0374-2830

ER -