Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory

Alaa A. Abdelrahman, Ismail Esen, Cevat Özarpa, Ramy Shaltout, Mohamed A. Eltaher, Amr E. Assie

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


The goal of this manuscript is to develop a nonclassical size dependent model to study and analyze the dynamic behaviour of the perforated Reddy nanobeam under moving load including the length scale and microstructure effects, that not considered before. The kinematic assumption of the third order shear deformation beam theory in conjunction with modified continuum constitutive equation of nonlocal strain gradient (NLSG) elasticity are proposed to derive the equation of motion of nanobeam included size scale (nonlocal) and microstructure (strain gradient) effects. Mathematical expressions for the equivalent geometrical parameters due to the perforation process of regular squared pattern are developed. Based on the virtual work principle, the governing equations of motion of perforated Reddy nanobeams are derived. Based on Navier’s approach, an analytical solution procedure is developed to obtain free and forced vibration response under moving load. The developed methodology is verified and checked with previous works. Impacts of perforation, moving load velocity, microstructure parameter and nonlocal size scale effects on the dynamic and vibration responses of perforated Reddy nanobeam structures have been investigated in a wide context. The obtained results are supportive for the design of MEMS/NEMS structures such as frequency filters, resonators, relay switches, accelerometers, and mass flow sensors, with perforation.

Original languageEnglish
Pages (from-to)515-533
Number of pages19
JournalSmart Structures and Systems
Issue number4
Publication statusPublished - Oct 2021
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright © 2021 Techno-Press, Ltd.


  • Analytical solution
  • Dynamic analysis of moving load
  • Higher order shear deformation
  • Nonlocal strain gradient theory
  • Perforated nanobeam

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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