Vibration of FG-GRC beam on elastic foundation

Abstract

Abstract: The vibration of a graphene platelets reinforced functionally graded composite (FG-GRC) beam placed on an elastic foundation is studied. Firstly, the dynamic governing differential equations of the problem are established by applying the variational principle based on the classical beam theory, in which the material properties of the composites are described according to the mechanical models of Halpin-Tsai and the rule of mixture. Then, the governing equations are solved analytically by the method of separated variables, yielding the dimensionless natural frequencies of the beam with three kinds of boundary constraints on the elastic foundation. Furthermore, the results are compared with the existing ones in the literatures by reduced to no foundation, which proves correctness of the theoretical derivations and numerical calculations. Finally, effects of foundation stiffness, graphene content and geometric parameters on the natural frequencies of the FG-GRC beam are discussed by analyzing of the numerical results. It is found that the influence of the elastic foundation on the fundamental frequencies is obvious, with the influence diminishing as the mode order increases. In addition, the variations of the geometric shapes of graphene platelets have great influences on the natural frequencies.

Key words: graphene reinforced, functionally graded beam, free vibration, elastic foundation

CLC Number:

TH113.1
O343

ZHANG Jing-hua, YAO Yu-qin. Vibration of FG-GRC beam on elastic foundation[J]. Journal of Lanzhou University of Technology, 2025, 51(2): 38-43.

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