Steel and Composite Structures

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Frequency analysis of deep curved nonlocal FG nanobeam via DTM

  • S. A. H. Hosseini (Department of Industrial, Mechanical and Aerospace Engineering, Buein Zahra Technical University) ;
  • O. Rahmani (Smart Structures and New Advanced Materials Laboratory, Department of Mechanical Engineering, University of Zanjan)
  • Received : 2022.04.07
  • Accepted : 2023.04.03
  • Published : 2023.12.25
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Abstract

In this paper, frequency analysis of curved functionally graded (FG) nanobeam by consideration of deepness effect has been studied. Differential transform method (DTM) has been used to obtain frequency responses. The nonlocal theory of Eringen has been applied to consider nanoscales. Material properties are supposed to vary in radial direction according to power-law distribution. Differential equations and related boundary conditions have been derived using Hamilton's principle. Finally, by consideration of nonlocal theory, the governing equations have been derived. Natural frequencies have been obtained using semi analytical method (DTM) for different boundary conditions. In order to study the effect of deepness, the deepness term is considered in strain field. The effects of the gradient index, radius of curvature, the aspect ratio, the nonlocal parameter and interaction of aforementioned parameters on frequency value for different boundary conditions such as clamped-clamped (C-C), clamped-hinged (C-H), and clamped-free (C-F) have been investigated. In addition, the obtained results are compared with the results in previous literature in order to validate present study, a good agreement was observed in the present results.

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