Nonlinear Axisymmetric Forced Vibrations of CNT-Reinforced FGM Plate with Elastic Boundary Conditions Using Multiple Scales Method

Document Type : Original Research Paper

Authors

1 Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran.

2 Composite Research Centre, Malek-Ashtar University of Technology, Tehran, Iran.

10.22084/jrstan.2025.29427.1257

Abstract

 Nonlinear axisymmetric forced vibrations of annular circular plates reinforced by functionally graded carbon nanotubes (FG-CNTs) under elastic boundary conditions and harmonic pressure are studied in this paper. The material properties of the plate are assumed to be graded according to the different types of distribution patterns along the plate thickness. Using Hamilton’s principle and Von Karman’s nonlinear strain-displacement relations, partial differential equations of motion are derived. In the first step, the linear equations of the system are using the generalized differential quadratic
method (GDQM), and the linear natural frequencies and mode shapes of the plate are obtained. In the second step, after applying the Galerkin method, the nonlinear partial differential equations of the plate are converted into nonlinear ordinary differential equations. Afterward, in order to acquire the nonlinear frequencies of the plate, the nonlinear equations of the plate are solved analytically using the multiple time-scales method. Finally, the effects of some system parameters, such as the volume fraction and distribution pattern of the CNTs, the aspect ratios of the plate, the boundary conditions and the elastic foundation on the nonlinear frequency response and time history of the plate are studied. In order to validate the outcomes, the presented results are compared with those obtained by the previously published papers as well as ABAQUS software.

Keywords

References

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Journal of Stress Analysis
Volume 9, Issue 1
2025
Pages 9-25

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