Topology optimization of damping material for reducing resonance response based on complex dynamic compliance

Akihiro Takezawa*, Masafumi Daifuku, Youhei Nakano, Kohya Nakagawa, Takashi Yamamoto, Mitsuru Kitamura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


In this research, we propose a new objective function for optimizing damping materials to reduce the resonance peak response in the frequency response problem, which cannot be achieved using existing criteria. The dynamic compliance in the frequency response problem is formulated as the scalar product of the conjugate transpose of the amplitude vector and the force vector of the loading nodes. The proposed objective function methodology is implemented using the common solid isotropic material with penalization (SIMP) method for topology optimization. The optimization problem is formulated as maximizing the complex part of the proposed complex dynamic compliance under a volume constraint. 2D and 3D numerical examples of optimizing the distribution of the damping material on the host structure are provided to illustrate the validity and utility of the proposed methodology. In these numerical studies, the proposed objective function worked well for reducing the response peak in both lower and upper excitation frequencies around the resonance. By adjusting the excitation frequency, multi-resonance peak reduction may be achieved with a single frequency excitation optimization.

Original languageEnglish
Pages (from-to)230-243
Number of pages14
JournalJournal of Sound and Vibration
Publication statusPublished - 2016 Mar 17
Externally publishedYes


  • Damping material
  • Finite element method
  • Optimal design
  • Sensitivity analysis
  • Topology optimization

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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