Original Article

Vibration attenuation using a 3D cubic re-entrant metamaterial structure with tunable bandgaps induced by variations in the re-entrant angle

¹ School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang, Liaoning, 110168, PR China
² Joint International Research Laboratory of Modern Construction Engineering Equipment and Technology, Shenyang, Liaoning, 110168, PR China
³ National Space Research and Development Agency, Abuja, 900107, Nigeria
⁴ School of Mechanical Engineering and Automation, Northeastern University, Shenyang, PR China
⁵ School of Mechanical Engineering, Shenyang University of Technology, Shenyang, PR China
⁶ College of Mechanical and Automative Engineering, Ningbo University of Technology, Ningbo, PR China

^* e-mail: musaabubakar2000@yahoo.com

Received: 9 June 2025
Accepted: 23 October 2025
Published online: 17 December 2025

Abstract

This study explores the vibration attenuation capabilities of three-dimensional metamaterial periodic structures, leveraging the properties of auxetic structures and phononic crystals in forming bandgaps. While most conventional periodic structures exhibit vibration attenuation within limited, fixed frequency ranges, achieving tunable bandgaps remains a significant challenge. In this work, a novel three-dimensional auxetic re-entrant cubic periodic structure is proposed. The bandgap characteristics of this structure were analysed with and without internal resonators. Furthermore, the bandgap was examined with respect to the re-entrant angle (θ), revealing that both the position and width of the phononic bandgap can be adjusted by modifying the re-entrant angle. Our findings show that as the re-entrant angle is increased, the frequency at which the stopbands start decreases. To achieve real-time bandgap tunability, external compression deformation was applied, causing the unit cell to compress in both directions. This compression alters the angle of the re-entrant structure, which in turn changes the frequencies and modes of the bandgap, demonstrating a viable pathway to programmable control over elastic wave behaviour. The 3D auxetic structure can be utilised as a programmable vibration isolation device for a number of purposes, including wave filtering, waveguiding, and micro-vibration attenuation in precision engineering and aerospace systems.