Forced Vibration Behaviour of Elastically Constrained Graphene Origami-Enabled Auxetic Metamaterial Beams

• Published in: Mathematical and computational applications Vol. 30; no. 1; p. 5
• Main Authors: Karami, Behrouz, Ghayesh, Mergen H.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.02.2025
• Subjects: Behavior; Boundary conditions; Civil engineering; Constraints; Design; Equations of motion; Forced vibration; forced vibrations; Genetic algorithms; Graphene; graphene origami; Graphite; Mechanical properties; metamaterial beam; Metamaterials; Resonant frequencies; Shear layers; Trigonometric functions; Vibration; Vibration analysis; Vibration response; Winkler–Pasternak foundation
• ISSN: 2297-8747; 1300-686X; 2297-8747
• DOI: 10.3390/mca30010005

This paper explores the vibration behaviour of an elastically constrained graphene origami-enabled auxetic metamaterial beam subject to a harmonic external force. The effective mechanical properties of the metamaterial are approximated using a micromechanical model trained via a genetic algorithm provided in the literature. The three coupled equations of motion are solved numerically; a set of trigonometric functions is used to approximate the displacement components. The accuracy of the proposed model is confirmed by comparing it with the natural frequencies of a simplified non-metamaterial structure available in the literature. Following this validation, the investigation extends to investigate the forced vibration response of the metamaterial beam, examining the influence of the graphene origami distribution pattern and content, graphene folding degree, linear and shear layer stiffness, and geometrical parameters on the dynamic behaviour of the structure. The results generally highlight the considerable effect of the shear layer, modelled as a Pasternak foundation, on the vibration behaviour of the elastically constrained metamaterial beams.