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Maximization of natural frequencies and frequency gaps of continuum structures by an evolutionary topology optimization method

Grant number: 19/05393-7
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): May 01, 2019
Effective date (End): April 30, 2021
Field of knowledge:Engineering - Mechanical Engineering - Mechanics of Solids
Principal Investigator:Renato Pavanello
Grantee:Heitor Nigro Lopes
Home Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:13/08293-7 - CCES - Center for Computational Engineering and Sciences, AP.CEPID


To avoid resonance problems in vibrating mechanical structures it is desired to modify their natural frequencies, usually distancing them from an operating frequency range. In such manner, optimization methods can be used to identify geometries that maximize one or more frequencies or maximize the difference gap between consecutive natural frequencies. In this project, a topology optimization method was used to maximize a given eigenvalue or a given eigenvalue separation considering two and three-dimensional linear elastic structure. Also, a periodic analysis on elastic wave propagation will be performed to detect if phononic band gaps are present in the final topology. The BESO (Bidirectional Evolutionary Structural Optimization) is chosen for accomplish these tasks. The BESO is a sensitivity based method that uses discrete design variables. Numerical strategies will be studied to control the mode shift problem and the repeated modes problems. Furthermore, a method based on multi-objective optimization and penalty methods will be studied, implemented and tested to control the mode shift problem for a high-frequency range. The proposed multi-objective strategy is based on the weighted sum method, where additional frequencies are added on the objective function. In most cases, periodic geometries are obtained, therefore, a method using periodic constraints or an asymptotic homogenization technique combined with the mode shift control technique for high-frequency range will be developed. In this context, a concurrent topology optimization problem, in micro and macro scale will be studied. Ultimately, this study will be extended to the acoustic-structure interaction problem, expanding this analysis in regards to frequency gap maximization in high-frequency range. These problems will be solved considering two solid materials phases: either void and solid or two distinct materials. The obtained structures will be manufactured using 3D printing systems. A special experimental modal analysis for small parts and low density materials will be carried out in collaboration with INSA de Lyon Laboratories to check the validity of the implemented numerical methods. (AU)