Analytical Investigation of Electromechanical Hierarchical Metamaterials for Vibration Attenuation and Energy Harvesting
Abstract
:1. Introduction
2. Mathematical Modeling
3. Band Structure of Hierarchical Metamaterials
3.1. Effect of Electromechanical Coupling Coefficients and Shunt Circuit Resistances
3.2. Effect of Resonator Mass Ratios
4. Transmissibility
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. The Determinant of The First-Order Outward and Inward Configurations
Appendix B. Mechanically Damped Resonators Equation of Motion
Appendix C. Transfer Functions T1 and T2, Calculation
References
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Properties | , | ||
---|---|---|---|
Value | kg | rad/s | F |
Parameter | Effect on Vibration Attenuation | Effect on Energy Harvesting | Remarks |
---|---|---|---|
Strong Electromechanical Coupling | |||
and | Increase in band gap width, mode merging, and reduction in resonance peaks. | Power output increases with and . | This is critical for optimizing dual functionality. |
and | For lower frequency attenuation, smaller and values are preferred, for higher frequency and stronger attenuation, higher and values. | Between and ohms results in power output with minimal drop. | Higher frequency passbands are predominantly impacted. |
Smaller or higher creates broad band gap, which is desirable for vibration attenuation. | Power output in the third passband decreases as deviates farther from . | It affects performance based on configuration type. | |
Weak Electromechanical Coupling | |||
and | Minimal effect. | Increasing and raises the local power output peaks. | Less effective for attenuating vibrations. |
and | Minimal effect. | Increases the local peaks of the power output. | Resistance mainly influences energy harvesting. |
As moves farther from 0.5, the vibration attenuation spectrum increases. The inward configuration suppresses lower frequency vibrations. | Power can be harvested across a broad frequency range by varying . | It offers tunability for specific applications depending on configuration type. |
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Mebrat, A.A.; LeGrande, J.; Barry, O. Analytical Investigation of Electromechanical Hierarchical Metamaterials for Vibration Attenuation and Energy Harvesting. Appl. Sci. 2025, 15, 3464. https://doi.org/10.3390/app15073464
Mebrat AA, LeGrande J, Barry O. Analytical Investigation of Electromechanical Hierarchical Metamaterials for Vibration Attenuation and Energy Harvesting. Applied Sciences. 2025; 15(7):3464. https://doi.org/10.3390/app15073464
Chicago/Turabian StyleMebrat, Ashenafi Abebe, Joshua LeGrande, and Oumar Barry. 2025. "Analytical Investigation of Electromechanical Hierarchical Metamaterials for Vibration Attenuation and Energy Harvesting" Applied Sciences 15, no. 7: 3464. https://doi.org/10.3390/app15073464
APA StyleMebrat, A. A., LeGrande, J., & Barry, O. (2025). Analytical Investigation of Electromechanical Hierarchical Metamaterials for Vibration Attenuation and Energy Harvesting. Applied Sciences, 15(7), 3464. https://doi.org/10.3390/app15073464