Free vibration analysis of embedded single-layered nanoplates and graphene sheets by using the multiple time scale method

Chih Ping Wu, Wei Chen Li

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

An asymptotic approach using the Eringen nonlocal elasticity theory and multiple time scale method is developed for the three-dimensional (3D) free vibration analysis of simply-supported, single-layered nanoplates and graphene sheets (GSs) embedded in an elastic medium. In the formulation, the small length scale effect is first introduced to the nonlocal constitutive equations by using a nonlocal parameter, then the mathematical processes of nondimensionalization, asymptotic expansion and successive integration are performed, and finally recurrent sets of motion equations for various order problems are obtained. The interactions between the nanoplates (or GSs) and their surrounding medium are modeled as a two-parameter Pasternak foundation. Nonlocal classical plate theory (CPT) is derived as a first-order approximation of the 3D nonlocal elasticity theory, and the motion equations for higher-order problems retain the same differential operators as those of nonlocal CPT, although with different nonhomogeneous terms. Some 3D nonlocal elasticity solutions of the natural frequency parameters of nanoplates (or GSs) with and without being embedded in the elastic medium and their corresponding through-thickness distributions of modal field variables are given to demonstrate the performance of the 3D asymptotic nonlocal elasticity theory.

Original languageEnglish
Pages (from-to)838-854
Number of pages17
JournalComputers and Mathematics with Applications
Volume73
Issue number5
DOIs
Publication statusPublished - 2017 Mar 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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