Thermal vibration analysis of cracked nanobeams submerged in elastic foundations by nonlocal continuum mechanics

Moustafa S. Taima, Tamer El Sayed* (Corresponding Author), Michael I. Friswell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
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Abstract

Understanding the mechanical behavior of nanoscale structures is crucial in the development of advanced nanotechnologies. In this study, a novel approach to investigate the thermal lateral vibration of cracked nanobeams immersed in an elastic matrix is investigated. For this purpose, Reddy’s third-order shear deformation theory (TSDT) is considered. In contrast to Timoshenko beam theory (First-order Shear Deformation Theory, FSDT), TSDT does not depend on a shear correction coefficient. The nano-scale effect is modeled using Eringen’s nonlocal continuum mechanics theory. The nonlocal form of the governing equation is obtained through the application of Hamilton’s principle. The weak form of the finite element global mass and stiffness matrices are obtained using Lagrange linear and Hermitian cubic interpolation. To model the crack in bending vibration, two rotational springs are used for TSDT, unlike the use of a single rotational spring in traditional Bernoulli–Euler (Classical Beam Theory, CBT) and FSDT. The stiffness of the springs is adjusted based on the severity of the crack. The influences of the nonlocal parameter, beam slenderness, position of crack, crack severity, Pasternak and Winkler foundation parameters, thermal effects and boundary conditions on the natural frequencies are investigated. The model’s outcomes are compared with findings from prior publications, demonstrating a strong level of agreement. This study contributes to the growing research on nanostructures by presenting a novel approach to understanding the dynamics of cracked nanobeams using Reddy beam analysis-based solutions.
Original languageEnglish
Article number111249
Number of pages15
JournalThin-walled Structures
Volume193
Early online date15 Nov 2023
DOIs
Publication statusPublished - 1 Dec 2023

Bibliographical note

Funding information
The authors declare that they do not receive any funds from any organization for this research.

Data Availability Statement

Data will be made available on request.

Keywords

  • Third-order shear deformation theory
  • Finite element method
  • Transverse vibration
  • Cracked nanobeam
  • Pasternak foundation
  • Thermal effect

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