An analytical solution for vibration response of CNT/GPL/fibre/polymer hybrid composite micro/nanoplates
Artikel i vetenskaplig tidskrift, 2022

In the present article, a closed-form solution is carried out for the vibration response of CNT/GPL/fiber/polymer hybrid composite macro/micro/nanoplates resting on elastic support. Multi-layered fiber/polymer hybrid plates with either functionally graded carbon nanotube reinforced composite (FG-CNTRC) material or functionally graded graphene platelets reinforced composite (FG-GPLRC) material are two different types of plate considered here. The distribution of reinforcing nanocomposites can be uniform or functionally graded through the plate layers. The governing vibration equations are developed in the framework of the nonlocal elasticity theory of Eringen and using the first-order shear deformation plate theory. In the analytical solution procedure, the partial differential equations of motion are simplified to a series of homogeneous ordinary differential equations using a displacement field for Levy-type of the boundary conditions. The general solution of the obtained equations is expressed in terms of exponential functions. Using that the displacements should satisfy the remaining boundary conditions, the vibrational frequencies are derived. Finally, the influences of different parameters including geometry and material properties such as nonlocal parameter, number and angle of layers, volume fraction, and type of distribution of reinforcing nanocomposites are investigated and discussed. Natural frequencies for various boundary conditions are illustrated. The numerical results illustrate that the effects of the nonlocal parameter on the frequency decrease when one of the boundaries is free, and these effects increase when one of the boundaries is clamped for both FG-CNTRC and FG-GPLRC plates.




Free vibration


nonlocal elasticity

polymer hybrid composite


closed-form solution


Levy-type boundary conditions


Hamzeh Salehipour

Ilam University of Medical Sciences

Mohammad Amin Shahmohammadi

Isfahan University of Technology

Peter Folkow

Chalmers, Mekanik och maritima vetenskaper, Dynamik

Omer Civalek

China Medical University

Akdeniz Universitesi

Mechanics of Advanced Materials and Structures

1537-6494 (ISSN) 1537-6532 (eISSN)

Vol. In Press


Teknisk mekanik

Kompositmaterial och -teknik

Matematisk analys



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