Piezoelectric Compensation of Structural Damping in Metamaterial Beams: Stability and Performance Analysis

This paper examines the stability implications of integrating piezoelectric actuators into metamaterial beams, focusing on the compensation of structural damping and its effect on the system's dynamic performance. Metamaterials, characterized by their unique bandgap properties, offer potential in various engineering applications, including vibration control and energy harvesting. However, structural damping inherent in such systems can degrade these properties, prompting the use of piezoelectric actuators as a compensatory mechanism. Through a distributed parameter model and modal analysis, this study explores the temporal and spatial dynamics of the metamaterial beam and investigates how piezoelectric actuation influences the natural frequencies and mode shapes, with a particular emphasis on stability thresholds. Employing root locus analysis, the paper visualizes the transition of system stability across different levels of actuation voltage, highlighting the delicate balance between enhanced performance and stability. The findings delineate a clear operational voltage range, within which piezoelectric actuation improves bandgap properties without compromising system stability.