Review of inerters: from traditional inerters to smart material driven innovation and development

With the continuous advancement of vibration control technologies, inerters-devices capable of modulating inertial forceshave garnered significant attention across diverse engineering domains. While conventional mechanical inerters have demonstrated robust performance in applications such as vehicles, bridges, and buildings, their fixed inertial parameters limit adaptability to complex and dynamic operating conditions. Recent integration of smart materials offers promising pathways for dynamic adjustability and intelligent control of inertial systems. In particular, semi-active inerters driven by magnetorheological fluids (MRFs), shape memory alloys (SMAs), and piezoelectric materials have emerged as prominent research frontiers. This review provides a comprehensive overview of the historical evolution, classification schemes, and engineering applications of inerters, with a focused analysis of recent progress in smart-material-based semi-active designs. By comparing actuation mechanisms, dynamic response characteristics, and applicable scenarios of various smart materials, the key advantages of intelligent inerters-in terms of response speed, tunable inertial performance, and system integration-are elucidated. The review concludes by outlining current challenges and proposing future research directions, aiming to guide theoretical advances, technological innovation, and practical implementation of next-generation inertial devices toward greater intelligence, efficiency, and adaptability.