Dynamic analysis of nanoscale beams including surface stress effects

Djamel Ould Youcef , Abdelhakim Kaci , Abdelnour Benzair , Abdelmoumen Anis Bousahla , Abdelouahed Tounsi

Abstract

In this article, an analytic non-classical model for the free vibrations of nanobeams accounting for surface stress effects is developed. The classical continuum mechanics fails to capture the surface energy effects and hence is not directly applicable at nanoscale. A general beam model based on Gurtin-Murdoch continuum surface elasticity theory is developed for the analysis of thin and thick beams. Thus, surface energy has a significant effect on the response of nanoscale structures, and is associated with their size-dependent behavior. To check the validity of the present analytic solution, the numerical results are compared with those obtained in the scientific literature. The influences of beam thickness, surface density, surface residual stress and surface elastic constants on the natural frequencies of nanobeams are also investigated. It is indicated that the effect of surface stress on the vibrational response of a nanobeam is dependent on its aspect ratio and thickness.

Key Words

surface stress effects; nanoscales; free vibration; Gurtin-Murdoch

Address

Djamel Ould Youcef and Abdelnour Benzair — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria
Abdelhakim Kaci — Université Dr Tahar Moulay, Faculté de Technologie, Département de Génie Civil et Hydraulique, BP 138 Cité En-Nasr 20000 Saida, Algeria Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria
Abdelmoumen Anis Bousahla — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Centre Universitaire Ahmed Zabana de Relizane, Algeria
Abdelouahed Tounsi — Laboratoire de Modélisation et Simulation Multi-échelle, Département de Physique, Faculté des Sciences Exactes, Département de Physique, Université de Sidi Bel Abbés, Algeria; Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department, Algeria; Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals,31261 Dhahran, Eastern Province, Saudi Arabia

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