Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium

Chih-Ping Wu, Yen Jung Chen

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Based on the Eringen nonlocal elasticity theory and multiple time scale method, an asymptotic nonlocal elasticity theory is developed for cylindrical bending vibration analysis of simply-supported, Nl-layered, and uniformly or nonuniformly-spaced, graphene sheet (GS) systems embedded in an elastic medium. Both the interactions between the top and bottom GSs and their surrounding medium and the interactions between each pair of adjacent GSs are modeled as one-parameter Winkler models with different stiffness coefficients. In the formulation, the small length scale effect is introduced to the nonlocal constitutive equations by using a nonlocal parameter. The nondimensionalization, asymptotic expansion, and successive integration mathematical processes are performed for a typical GS. After assembling the motion equations for each individual GS to form those of the multiple GS system, recurrent sets of motion equations can be obtained for various order problems. Nonlocal multiple classical plate theory (CPT) is derived as a first-order approximation of the current nonlocal plane strain problem, and the motion equations for higher-order problems retain the same differential operators as those of nonlocal multiple CPT, although with different nonhomogeneous terms. Some nonlocal plane strain solutions for the natural frequency parameters of the multiple GS system with and without being embedded in the elastic medium and their corresponding mode shapes are presented to demonstrate the performance of the asymptotic nonlocal elasticity theory.

Original languageEnglish
Article number1950035
JournalInternational Journal of Structural Stability and Dynamics
Volume19
Issue number4
DOIs
Publication statusPublished - 2019 Apr 1

Fingerprint

Graphene
Embedded systems
Embedded Systems
Nonlocal Elasticity
Vibration
Elasticity Theory
Equations of motion
Elasticity
Plate Theory
Plane Strain
Scale Effect
Multiple Time Scales
Nonlocal Equations
Mode Shape
Motion
Vibration Analysis
Vibration analysis
Constitutive Equation
Constitutive equations
Natural Frequency

All Science Journal Classification (ASJC) codes

  • Civil and Structural Engineering
  • Building and Construction
  • Aerospace Engineering
  • Ocean Engineering
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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Cylindrical Bending Vibration of Multiple Graphene Sheet Systems Embedded in an Elastic Medium. / Wu, Chih-Ping; Chen, Yen Jung.

In: International Journal of Structural Stability and Dynamics, Vol. 19, No. 4, 1950035, 01.04.2019.

Research output: Contribution to journalArticle

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