Free and forced vibrations of graphene platelets reinforced composite laminated arches subjected to moving load

• Published in: Meccanica (Milan) Vol. 57; no. 5; pp. 1105 - 1124
• Main Authors: Moghaddasi, Mehdi, Kiani, Yaser
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2022; Springer Nature B.V
• Subjects: Arches; Automotive Engineering; Civil Engineering; Classical Mechanics; Curved beams; Eigenvalues; Elastic deformation; Engineering; Equations of motion; Forced vibration; Free vibration; Graphene; Hamilton's principle; Laminar composites; Mechanical Engineering; Moving loads; Platelets (materials); Polar coordinates; Shear deformation; Strain; Time marching; Vibration; Vibration analysis; Vibration response; Curved beam; Graphene reinforced composite; Navier method; Moving load; Halpin-Tsai rule
• ISSN: 0025-6455; 1572-9648
• DOI: 10.1007/s11012-022-01476-x

In the present investigation, free vibration and also forced vibration response of a graphene platelet reinforced composite (GPLRC) laminated curved beam is investigated. It is assumed that each layer of the laminated composite curved beam is reinforced with different amount of graphene platelets which results in a piecewise functionally graded media. Using the first order shear deformation theory, linear strain-displacement relations in polar coordinates, linear elastic constitutive law and the Hamilton principle, the basic governing equations of the curved beam subjected to a moving load are obtained. For the case of a beam with both ends simply supported and applying the Galerkin technique, the governing equations of motion are established. In free vibration analysis, an eigenvalue problem is established while for the case of forced vibration, the Newmark time marching scheme is applied to obtain the temporal evolution of displacement field. The obtained results are well-validated with the available data in the open literature. After that, novel numerical results are provided to explore the influences of different parameters. It is shown that geometrical characteristics of the curved beam and also the weight fraction and distribution patterns of GPLs have significant effects on the free and forced vibration responses of the curved beam. In general, as the weight fraction of GPLs enhances, the frequencies of the curved beam increase and also the induced deflections due to moving load decrease.