A Power-Based Framework for Quantifying Parameter Uncertainties in Finite Vibroacoustic Metamaterial Plates

Abstract

Vibroacoustic metamaterials (VAMMs) are artificial materials that are specifically designed to control, direct, and manipulate sound waves by creating a frequency gap, known as the stop band, which blocks free wave propagation. In this paper, a new power-based approach that relies on the active structural intensity (STI) for predicting the stop band behavior of finite VAMM structures is presented. The proposed method quantifies the power loss in a locally resonant finite VAMM plate in terms of percentage, such as STI99% and STI90%, for stop band prediction. This allows for the quantitative analysis of the vibration attenuation capabilities of a VAMM structure. This study is presented in the context of a two-dimensional VAMM plate with 25 resonators mounted in the middle section of the plate. It has been demonstrated that this method can predict the stop band limits of a finite VAMM plate more accurately than using negative effective mass, unit cell dispersion analysis, or the frequency response function methods. The proposed approach is then implemented to establish a framework for investigating the influence of parameter uncertainties on the stop band behavior of the VAMM plate. Based on the STI99% method, which aims for significant vibration reduction, stricter tolerances in the mass fabrication process are required to ensure the robustness of VAMM. Conversely, the STI90% method suggests that larger fabrication tolerances can be leveraged to achieve a broader stop band range while still meeting the desired performance level, leading to cost savings in manufacturing.