Dynamics Modeling and Optimization of Locally Resonant Metastructures for Vibration Suppression and Energy Harvesting

Abstract

This dissertation presents advanced analytical, numerical, and experimental frameworks for the dynamic modeling, optimization, and practical validation of locally resonant metastructures, specifically aimed at vibration suppression and efficient energy harvesting. By combining lumped and distributed parameter modeling, the thesis develops comprehensive and closed-form analytical solutions that allow precise predictions and facilitate real-time adaptive control.

Novel contributions of this work include the in-depth exploration of nonlinear dynamics within resonators, enabling the design of metastructures that robustly suppress vibrations across broader frequency bands. A generalized nonlinear formulation for piezoelectric energy harvesting systems has been developed, significantly enhancing both harvested energy and vibration suppression performance. Additionally, this thesis introduces internally coupled mechanical and electromechanical resonators, deriving closed-form transfer functions suitable for control engineering applications, substantially improving vibration isolation capabilities, and facilitating the generation of multiple bandgaps.

To address practical challenges, advanced techniques were proposed, such as piezoelectric actuation integrated with tailored notch-filtered controllers for structural damping compensation, which substantially deepened and widened the effective bandgaps. Furthermore, the incorporation of AI-driven hybrid optimization algorithms (Genetic Algorithm-Particle Swarm Optimization) provided robust parameter tuning and improved the performance of vibration suppression and energy harvesting.

The theoretical predictions and methodologies have been rigorously validated through comprehensive numerical simulations, employing Finite Element Methods (FEM), and systematically verified with experimental setups, ensuring their effectiveness in realistic engineering contexts. This thesis ultimately provides a versatile and validated framework for systematically designing and optimizing metastructures with significant implications for structural engineering, energy harvesting, and vibration mitigation technologies.

Related publications

• H. Alimohammadi, K. Vassiljeva, H. HosseinNia, P. Ellervee, and E. Petlenkov, “Damping Optimization in Locally Resonant Metastructures via Hybrid GA-PSO Algorithms and Modal Analysis,” in ASME 2024 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2024. [DOI] [Bib]
• H. Alimohammadi, K. Vassiljeva, H. HosseinNia, P. Ellervee, and E. Petlenkov, “Exploring the Real-World Challenges and Efficacy of Internal Coupling in Metastructures: An Experimental Perspective,” in 2024 International Conference on Electrical, Computer and Energy Technologies (ICECET. IEEE, 2024, pp. 1–6. [DOI] [Bib]
• H. Alimohammadi, K. Vassiljeva, S. HosseinNia, and E. Petlenkov, “Enhancing Bandgap Depth in Locally Resonant Metastructures via Notch-Filtered Piezoelectric Actuation,” in 2024 IEEE International Conference on Industrial Technology (ICIT). IEEE, 2024, pp. 1–5. [DOI] [Bib]
• H. Alimohammadi, K. Vassiljeva, H. HosseinNia, and E. Petlenkov, “Nonlinear dynamics in PEH for enhanced power output and vibration suppression in metastructures,” Nonlinear Dynamics, 2024. [DOI] [Bib]
• H. Alimohammadi, K. Vassiljeva, H. HosseinNia, and E. Petlenkov, “Exploring internally coupled resonator’s dynamics and spatial variability in metamaterials for vibration suppression,” in Active and Passive Smart Structures and Integrated Systems XVIII. SPIE, 2024. [DOI] [Bib]