Dynamic topology optimization for structures exhibiting frequency-dependent material properties with prescribed frequency forbidden band

In dynamic vibration reduction design, the frequency-dependent material properties are crucial for the optimal configuration, especially in the problem of prescribed frequency forbidden band. In this paper, a new dynamic topology optimization method for structures with frequencydependent material properties is proposed to achieve the vibration reduction design in the prescribed frequency forbidden band. First, a dynamic topology optimization model is established for the problem studied in this paper. This model integrates the solution method for frequencydependent problem, dynamic isolated structures elimination method and the formulation of prescribed frequency forbidden band constraints, which are based on the research results previously developed by the authors. Additionally, different interpolation schemes are used for different number of material designs. The above optimization model is intended to consider nonlinear terms and design several frequency-dependent structures with prescribed frequency forbidden bands that are more in line with practical engineering problems, so that they can accurately avoid the operating frequency range, thus improving the service life of engineering equipment. Finally, to address common numerical problems, the "bound formulation" and "robust formulation" are employed, enhancing the applicability and robustness of the method for the application in topology optimization. The effectiveness of the developed method is supported by two types optimization problems, including single-material and bi-material examples. The crosscheck results reveal that when considering frequency-dependent terms, the design results are better and closer to the practical engineering problem compared to linear structures.