Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial
Abstract
:1. Introduction
2. Locally Resonant Double-Cone PMs
2.1. The Formation Mechanism of Bandgap
2.2. The Regulation Method of Bandgap
3. Modeling Description
3.1. Geometrical Configuration
3.2. Finite Element Model
4. The Bandgap Properties of PMs with Various Unit Cell Arrangements
4.1. The Indicators of Bandgap Properties
4.2. The Bandgap Properties of PMHs
4.3. The Bandgap Properties of PMS and PMT
4.4. Comparison of the Bandgap Properties of PMs with Distinct Unit Cell Arrangements
5. The Bandgap Properties of PM with Different Material and Geometry Parameters
5.1. The Bandgap Properties of PMH with Various Material Parameters
5.1.1. The Bandgap Properties of PMH with Different Density
5.1.2. The Bandgap Properties of PMH with Different Poisson’s Ratio
5.1.3. The Bandgap Properties of PMH with Different Young’s Modulus
5.2. The Bandgap Properties of PMH with Different Geometry Parameters
5.2.1. The Bandgap Properties of PMH with Different Double-Cone Width
5.2.2. The Bandgap Properties of PMH with Different Node Radius
6. Discussion
6.1. The Effects of Unit Cell Arrangements on Bandgap Properties
6.2. The Effects of Component Material on Bandgap Properties
6.3. The Effects of Geometry Parameter on Bandgap Properties
7. Optimization Methodology
7.1. Definition of Optimization Problem
7.2. The overall Process of Optimization
7.3. The Construction of Kriging Model
7.4. Optimization Results
8. Conclusions
- The unit cell arrangement has a significant effect on bandgap properties. Increasing the double-cone array number from three to four to six gradually moves the PBG of PM to the high-frequency region. Meanwhile, its bandwidth rises by about 3.8 and 1.7 times, respectively. Another interesting finding is that the PMS loses SPBG characteristics when its double-cone array number increases from three to four.
- The density of double-cone region as well as Poisson’s ratio and Young’s modulus of node regions have an important influence on bandgap properties. The relationship between the PBG and SPBG of PMT and the double-cone region density is that the former shifts to the low-frequency region as the latter increases. However, the reverse is the relationship between the PBG and SPBG of PMT and Young’s modulus of node region. The bandwidth of PBG descends with the increase of Poisson’s ratio in node region.
- The double-cone width has a momentous effect on bandgap properties, while the influence of node radius on bandgap properties is slight. With the increase of double-cone width, the PBG moves to the low-frequency region, and its bandwidth is reduced. At the same time, the SPBG shifts to the high-frequency region.
- The bandgap properties of optimized PMT are improved compared to the initial PMT; in other words, the bandwidths of PBG and total bandgap are increased by nearly 2.2 and 0.27 times, respectively. However, the SPBG is narrowed by about 0.51 times. The research provides a systematic understanding for developing PM with excellent bandgap properties.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Response | θ1(D) | θ2(r) | R2 | MAX |
---|---|---|---|---|
Abw1 | 1.2374 | 0.0040 | 0.99422 | 0.03993 |
Abw2 | 1.0004 | 0.0065 | 0.99234 | 0.04548 |
Variables | Initial Values | Optimized Values | Verification Values |
---|---|---|---|
D(mm) | 3 | 0.8 | 0.8 |
r(mm) | 0.3 | 0.1 | 0.1 |
Abw1 (Hz) | 34.55 | 111.41 | 111.26 |
Abw2 (Hz) | 87.32 | 43.20 | 43.19 |
Atotal (Hz) | 121.87 | 154.61 | 154.45 |
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Zou, Z.; Xu, F.; Pan, Y.; Niu, X.; Fang, T.; Zeng, C. Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial. Sustainability 2023, 15, 3421. https://doi.org/10.3390/su15043421
Zou Z, Xu F, Pan Y, Niu X, Fang T, Zeng C. Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial. Sustainability. 2023; 15(4):3421. https://doi.org/10.3390/su15043421
Chicago/Turabian StyleZou, Zhen, Fengxiang Xu, Yuxiong Pan, Xiaoqiang Niu, Tengyuan Fang, and Chao Zeng. 2023. "Parametric Analysis and Multi-Objective Optimization of Pentamode Metamaterial" Sustainability 15, no. 4: 3421. https://doi.org/10.3390/su15043421