A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates
Abstract
:1. Introduction
- (1)
- The first one is the innovation of the research method, namely the FE-SEHM, developed for the structural modeling and band-gap characteristics analysis of metamaterial plates.
- (2)
- The second one is that an elastic metamaterial sandwich plate with the axially deformed Timoshenko beam cores, considering both the out-of-plane and in-plane deformations of the face plates, is designed and investigated.
- (3)
- The third one is that the metamaterial plate has flexural vibration band-gaps appearing near the flexural vibration natural frequencies of the beams, which uncouple with the axial vibration band-gaps.
2. Derivation of the Dynamic Stiffness Matrix
2.1. Spectral Element Formulation of the Beam with Axial Deformation
2.2. Finite Element Formulation of Thin Plates
2.3. Dynamic Stiffness Matrix of the Metamaterial Sandwich Plate
3. Numerical Results and Discussions
3.1. Validations
3.2. Band-Gap Characteristics Analysis
4. Conclusions
- (1)
- The FE-SEHM is developed to obtain the dynamic stiffness matrix of the metamaterial sandwich plate with axially deformed beam cores, and the vibration band-gap characteristics can be efficiently characterized by calculating the FRFs of the structure.
- (2)
- Compared with the metamaterial plate with rod cores, the positions and widths of the axial vibration band-gaps of the beams for the metamaterial plate with axially deformed beam cores are the same, but the vibration reduction effect is declined, which should be noticed in the practical applications.
- (3)
- The flexural vibration band-gaps of the beams for the metamaterial sandwich plate along the x and y axes appear near the flexural vibration natural frequencies of the axially deformed beams, and the lower order band-gaps are wider than the higher order ones.
- (4)
- The flexural vibration band-gaps of the metamaterial sandwich plate can be found uncoupling with the axial vibration band-gaps. The two kinds of band-gaps reduce the vibrations of the plate along the z axis and the x and y axes independently.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
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E, L.; Wu, Z.; Li, F.; Zou, G. A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates. Materials 2023, 16, 1098. https://doi.org/10.3390/ma16031098
E L, Wu Z, Li F, Zou G. A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates. Materials. 2023; 16(3):1098. https://doi.org/10.3390/ma16031098
Chicago/Turabian StyleE, Linzhongyang, Zhijing Wu, Fengming Li, and Guangping Zou. 2023. "A Finite/Spectral Element Hybrid Method for Modeling and Band-Gap Characterization of Metamaterial Sandwich Plates" Materials 16, no. 3: 1098. https://doi.org/10.3390/ma16031098