Nonlinear Vibration of Functionally Graded Graphene Nanoplatelets Polymer Nanocomposite Sandwich Beams

We provide an analytical investigation of the nonlinear vibration behavior of thick sandwich nanocomposite beams reinforced by functionally graded (FG) graphene nanoplatelet (GPL) sheets, with a power-law-based distribution throughout the thickness. We assume the total amount of the reinforcement ph...

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Bibliographic Details
Published in:Applied sciences 2020-08, Vol.10 (16), p.5669
Main Authors: Nematollahi, Mohammad Sadegh, Mohammadi, Hossein, Dimitri, Rossana, Tornabene, Francesco
Format: Article
Language:English
Subjects:
Composite beams
Differential equations
Environmental changes
Environmental conditions
Free vibration
functional reinforcement
Functionally gradient materials
Graphene
graphene nanoplatelets
higher-order shear deformable laminated beams
Laminar composites
Mechanical properties
Nanocomposites
Nonlinear differential equations
Nonlinear equations
nonlinear free vibration
Ordinary differential equations
Partial differential equations
Polymers
Power law
sandwich beams
Sandwich structures
Sheets
Stiffness
Theory
Thickness
Vibration
Vibration mode
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Summary:We provide an analytical investigation of the nonlinear vibration behavior of thick sandwich nanocomposite beams reinforced by functionally graded (FG) graphene nanoplatelet (GPL) sheets, with a power-law-based distribution throughout the thickness. We assume the total amount of the reinforcement phase to remain constant in the beam, while defining a relationship between the GPL maximum weight fraction, the power-law parameter, and the thickness of the face sheets. The shear and rotation effects are here considered using a higher-order laminated beam model. The nonlinear partial differential equations (PDEs) of motion are derived from the Von Kármán strain-displacement relationships, here solved by applying an expansion of free vibration modes. The numerical results demonstrate the key role of the amplitudes on the vibration response of GPL-reinforced sandwich beams, whose nonlinear oscillation behavior is very important in the physical science, mechanical structures and other mathematical analyses. The sensitivity of the response to the total amount of GPLs is explored herein, along with the possible effects related to the power-law parameter, the structural geometry, and the environmental conditions. The results indicate that changing the nanofiller distribution patterns with the proposed model can remarkably increase or decrease the effective stiffness of laminated composite beams.
ISSN:2076-3417
2076-3417
DOI:10.3390/app10165669