Surface Stress Effects on the Bending Wave Propagation of Nanobeams Resting on a Pasternak Foundation

چکیده مقاله

A new frontier of research in the area of computational nanomechanics is to study the behavior of structures at very small length scales. As the dimensions of a structure approach the nanoscale, the classical continuum theories may fail to accurately predict the mechanical behavior of nanostructures. Among these nanostructures, nanobeams are attracting more and more attention due to their great potential engineering applications. One of the most important factors that influence the behavior of such submicron-sized structures is surface stress effect because of their high surface to volume ratio.In the current study, a non-classical continuum model based on Gurtin–Murdoch elasticity theory is presented to develop closed-form solutions corresponding to the Euler-Bernoulli beam model for transverse waves propagating analyses of nanobeams including surface stress effects. The effects of the surrounding elastic medium are considered using the spring constant of the Winkler-type and the shear constant of the Pasternak-type. Explicit formulas are proposed to evaluate the surface stress effects on the phase speed of the nanobeams. Numerical results are presented to demonstrate the difference between the behaviors of the nanobeam predicted by the classical and non-classical solutions which depends on the magnitudes of the surface elastic constants. Furthermore, the influences of the surrounding medium and rotary inertia on the phase speed for nanobeams are analyzed. Obtained results turn out that the surrounding medium plays an significant role in phase speed of the nanobeams.