Analytical solutions for free vibration of functionally graded graphene reinforced beam

Abstract

Abstract: Based on Euler-Bernoulli beam theory, free vibration characteristics of functionally graded beams reinforced by graphene platelets are examined. In the study, it is considered that the graphene platelets are randomly and uniformly distributed in each layer of matrix, and its content varies in three different patterns along the thickness. Firstly, equivalent material properties are obtained according to Halpin-Tsai mechanical model and rule of mixture. And then, dynamic governing differential equations of the graphene platelets reinforced functionally graded beam are derived by Hamiltonian principle. Finally, the analytical expressions of natural frequency and mode are obtained through solving free vibration equations accurately and analytically. Meanwhile, analytic expression between the natural frequencies of this composite beam and that of a uniform beam with the same boundary conditions is given. The influence of the mass fraction, geometry and distribution of the graphene platelets on the natural frequency of the free vibration of the beam is analyzed through parametric research.

Key words: free vibration, functionally graded structure, graphene reinforced, beam

CLC Number:

TH113.1
O343

ZHANG Jing-hua, SI Cheng-long, MA Hao. Analytical solutions for free vibration of functionally graded graphene reinforced beam[J]. Journal of Lanzhou University of Technology, 2023, 49(2): 49-55.

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