The Matlab-based software OptMet provides a rational approach for the robust and optimal design of 3D printed metamaterial beams. Uncertainties derived from the additive manufacturing process are rigorously quantified. Variability about the performance function is also considered, thus conferring the optimal design with robustness. The optimal design looks for maximizing vibration attenuation considering different number for added resonators with different masses.
As an example of the output of OptMet, some files are contained in this repository assuming:
- The frequency range in which the attenuation is to be maximized is: [280, 380] Hz
- Discretization of the mass variable of the vibration attenuation: 0.05 : 0.05 : 1 (ratio of the sum of resonator massesto the mass of the beam)
- Number of samples from the material properties PDFs (Young's modulus E ~ N(1621.7, 49.9^2) and Density ~ N(948.9, 7.4^2) ): 100
- Trade-off variable between expectation and variance of the performance function (A): 0.5
- Maximum number of resonators: 15
- Cost function defined with
pchipMatlab function and the following interpolating points: (1,0), (8,0.3), (12,0.65) (15,0.9)
The software performs an exhaustive search in the discretrized mass variable for each number of resonators, up to the maximum number. Therefore, the optimal mass is obtained for each of these number of resonators. The output of each of these sub-steps are stored in the folder res. For example, for 4 resonators:
In this case, the optimal design using the robust objective function (solid line) provides a different optimal value of the mass percentage with respect to the expectation alone (dashed line), which highlights the relevance of the robust optimal design. This robust design avoids optimal designs which, in average, the performance function is optimized but are highly prone to uncertainties.
Finally, once the algorithm searches over the provided set of possible number of resnoators, the final optimal design, considering cost-related aspects, uncertainties, and performance is provided as follows:
Here, the optimal design would be having 5 resonators with a mass percentage of 95% of the mass of the beam.
The OptMet Matlab-based software is based on the following references:
H. Meng, D. Chronopoulos, A. T. Fabro, W. Elmadih, I. Maskery, Rainbow metamaterials for broadband multi-frequency vibration attenua-350tion: Numerical analysis and experimental validation, Journal of Sound and Vibration 465 (2020) 115005.
H. Meng, D. Chronopoulos, A. T. Fabro, I. Maskery, Y. Chen, Optimal design of rainbow elastic metamaterials, International Journal of Mechanical Sciences (2019) 105185.
H. Meng, D. Chronopoulos, A. T. Fabro, Numerical simulation data for the dynamic properties of rainbow metamaterials, Data in Brief (2019) 104772.
The authors would like to acknowledge the support acquired by the H2020 DiaMoND project (Grant Agreement ID:785859), FAPESP Thematic Grant ENVIBRO (Grant Agreement ID: 2018/15894-0), the Brazilian National Council of Research CNPq (Grant Agreement ID: 420304/2018-5), the Science and Technology Development Fund, Macau SAR (File no. SKL-IOTSC-2018-2020) and the Start-up Research Grant of University of Macau (File No. SRG2019-00194-IOTSC).