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Applied Mathematics and Mechanics

, Volume 39, Issue 9, pp 1219–1238 | Cite as

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

  • R. GholamiEmail author
  • R. Ansari
Article

Abstract

The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes (SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection, geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.

Key words

nonlinear dynamical characteristics imperfect functionally graded carbon nanotube-reinforced composite (FG-CNTRC) rectangular plate geometric imperfection sensitivity 

Chinese Library Classification

O32 O242.2 

2010 Mathematics Subject Classification

82D60 82D80 74K20 82B21 74H45 74G15 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Lahijan BranchIslamic Azad UniversityLahijanIran
  2. 2.Department of Mechanical EngineeringUniversity of GuilanRashtIran

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