Study on the Equivalent Stiffness of a Local Resonance Metamaterial Concrete Unit Cell

Abstract

This paper addresses the pressing scientific problem of accurately predicting the equivalent stiffness of local resonance metamaterial concrete unit cells. Existing theoretical models often fail to capture the nuanced dynamics of these complex systems, resulting in suboptimal predictions and hindering advancements in engineering applications. To address this deficit, this paper proposes a novel two-dimensional theoretical vibration model that incorporates shear stiffness, a crucial yet often overlooked parameter in previous formulations. Motivated by the need for improved predictive accuracy, this paper rigorously validates a new theoretical model through numerical simulations, considering variations in material parameters and geometric dimensions. The analysis reveals several key findings: firstly, the equivalent stiffness increases with elastic modulus while the error rate decreases, holding geometric parameters and Poisson’s ratio constant. Secondly, under fixed geometric parameters and coating elastic modulus, the equivalent stiffness rises with an increasing Poisson’s ratio, accompanied by a decrease in error rate. Importantly, this paper demonstrates that the proposed model exhibits the lowest error rate across all parameter conditions, facilitating superior prediction of equivalent stiffness. This advancement holds significant implications for the design and optimization of metamaterial structures in various engineering applications for vibration isolation, with promising enhancements of performance and efficiency.