Nonlinear vibration analysis of functionally graded GPL-RC conical panels resting on elastic medium

The detailed investigation on the nonlinear vibration analysis of functionally graded graphene platelets reinforced composites (FG GPL-RC) conical panels on the elastic medium is presented. The nonlinear governing equations of nanocomposite panels are derived following the first-order shear deformation shell theory (FSDST) and the von Karman nonlinear kinematic relations using Hamilton's principle, while the overall mechanical properties of the composite panel are estimated through the refined Halpin-Tsai approach. The numerical solution based on the 2-D differential quadrature method (DQM), arc-length continuation technique and the harmonic balance approach is presented to solve the problem numerically and find the frequency response. A diverse range of results is delivered to show the effect of essential parameters such as volume fraction and distribution pattern of GPLs, semi-vertex angle, elastic foundation and boundary supports on the nonlinear vibrational of nanocomposite conical panels.

Automated summary

This study presents a detailed investigation on the nonlinear vibration analysis of functionally graded graphene platelets reinforced composites conical panels on an elastic medium. The study derives the nonlinear governing equations of nanocomposite panels using first-order shear deformation shell theory and von Karman nonlinear kinematic relations, estimates the overall mechanical properties of the composite panel through the refined Halpin-Tsai approach, and presents a numerical solution based on the 2-D differential quadrature method, arc-length continuation technique, and harmonic balance approach to find the frequency response. The study delivers a diverse range of results to show the effect of essential parameters on the nonlinear vibrational of nanocomposite conical panels, such as volume fraction and distribution pattern of GPLs, semi-vertex angle, elastic foundation, and boundary supports.