Mathematical modelling and virtual design of metamaterials for reducing noise and vibration in built-up structures

Noise and vibration pose significant challenges in built-up structures, affecting structural integrity and occupant comfort. Traditional materials often fail to address these issues effectively across all relevant frequencies, particularly in urban and industrial environments. This paper presents a mathematical modeling approach and virtual design framework for developing metamaterials specifically tailored to mitigate noise and vibration in built-up structures. By leveraging finite element analysis, dynamic energy analysis, and optimization algorithms, the study demonstrates how metamaterials can create frequency-specific barriers. Comparative analyses with previous studies, performance metrics, and sensitivity evaluations reveal the robustness and unique contributions of this approach. Validation through simulations and benchmarking confirms the model’s effectiveness, enhancing structural resilience and human comfort in complex environments. Additionally, this study surveys natural metamaterials and the urban environment. The major findings highlight the effectiveness of natural metamaterials (NMs) in ground vibration attenuation, offering diverse applications and proposing a roadmap for developing natural materials for clean and quiet environments