Advances in nano research

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Dynamic characteristics of viscoelastic nanobeams including cutouts

  • Rabab A., Shanab (Engineering Mathematics Department, Faculty of Engineering, Zagazig University) ;
  • Norhan A., Mohamed (Engineering Mathematics Department, Faculty of Engineering, Zagazig University) ;
  • Mohamed A., Eltaher (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University) ;
  • Alaa A., Abdelrahman (Mechanical Design and Production Dept., Faculty of Engineering, Zagazig University)
  • Received : 2022.01.19
  • Accepted : 2022.06.07
  • Published : 2023.01.25
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Abstract

This paper aimed to investigate the nonclassical size dependent free vibration behavior of regularly squared cutout viscoelastic nanobeams. The nonlocal strain gradient elasticity theory is modified and adopted to incorporate the viscoelasticity effect. The Kelvin Voigt viscoelastic model is adopted to model the linear viscoelastic constitutive response. To explore the influence of shear deformation effect due to cutout, both Euler Bernoulli and Timoshenko beams theories are considered. The Hamilton principle is utilized to derive the dynamic equations of motion incorporating viscoelasticity and size dependent effects. Closed form solutions for the resonant frequencies for both perforated Euler Bernoulli nanobeams (PEBNB) and perforated Timoshenko nanobeams (PTNB) are derived considering different boundary conditions. The developed procedure is verified by comparing the obtained results with the available results in the literature. Parametric studies are conducted to show the influence of the material damping, the perforation, the material and the geometrical parameters as well as the boundary and loading conditions on the dynamic behavior of viscoelastic perforated nanobeams. The proposed procedure and the obtained results are supportive in the analysis and design of perforated viscoelastic NEMS structures.

Keywords

Acknowledgement

This research was funded by the Institutional Fund Projects under grant no. IFPIP (10-135-1443). The authors gratefully acknowledge technical and financial support provided by the Ministry of Education and King Abdulaziz University, DSR in Jeddah, Saudi Arabia.

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