Abstract
In this study, the first-order shear deformation theory (FSDT) is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite (FG-GPLRC). The vibration analyses of the FG-GPLRC truncated conical shell are presented. Considering the graphene platelets (GPLs) of the FG-GPLRC truncated conical shell with three different distribution patterns, the modified Halpin-Tsai model is used to calculate the effective Young’s modulus. Hamilton’s principle, the FSDT, and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell. The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell. Then, the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method. The effects of the weight fraction and distribution pattern of the GPLs, the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed. This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.
Highlights
The outstanding material properties of graphene composites, e.g., excellent thermal, mechanical, physicochemical, and electronic properties, have attracted the attention of many researchers
This study focuses on the analyses of the nonlinear vibrations of the FG-GPLRC truncated conical shell
Hamilton’s principle, the first-order shear deformation theory (FSDT), and the von-Karman type nonlinear geometric relationship are used to derive a system of partial differential equations for the FG-GPLRC truncated conical shell
Summary
The outstanding material properties of graphene composites, e.g., excellent thermal, mechanical, physicochemical, and electronic properties, have attracted the attention of many researchers. Researchers have increasingly paid attention to graphene-reinforced composite structures because of their exceptional mechanical properties Yang and his group conducted numerous studies to assess the bending, vibration, and buckling of beam and plate structures of the functionally graded graphene platelet-reinforced composite (FG-GPLRC)[7,8,9,10,11]. With the classical shell theory, Chan et al.[35,36] analyzed the nonlinear buckling of the truncated stiffened FG conical shell and a conical shell reinforced by FG carbon nanotubes under an axial compressive load. Few scholars have paid attention to graphene-reinforced composite truncated conical shell structures This motivates our study, which involves nonlinear vibrational analyses of the FG-GPLRC truncated conical shell. This study leads to the discovery of the chaotic and periodic motions of the FG-GPLRC truncated conical shell
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