کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
777991 | 1463195 | 2015 | 10 صفحه PDF | دانلود رایگان |
• Nonlinear governing equations of nanobeams in presence of the small scale and surface effects are derived.
• The nonlinear governing equation is solved using the exact analytical solution called elliptic integrals.
• The surface effects increase natural frequencies of aluminum nanobeam for all values of amplitude ratio.
• The surface effects increase natural frequencies of silicon nanobeams only at low amplitude ratios.
• The fundamental natural frequencies of silicon and aluminum nanobeams vary linearly with respect to the nonlocal parameter.
In this paper, nonlinear free vibration analysis of simply-supported nanoscale beams incorporating surface effects, i.e. surface elasticity, surface tension and surface density, is studied using the nonlocal elasticity within the frame work of Euler–Bernoulli beam theory with von kármán type nonlinearity. A linear variation for the component of the bulk stress, σzz, through the nanobeam thickness is used to satisfy the balance conditions between the nanobeam bulk and its surfaces. An exact analytical solution to the governing equation of motion is presented for natural frequencies of nanobeams using elliptic integrals. The effect of the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the normalized natural frequencies of aluminum and silicon nanobeams with positive and negative surface elasticity, respectively, is investigated. It is observed that the surface effects increase natural frequencies of the aluminum nanobeam for all values of the amplitude ratio and the silicon nanobeam at low amplitude ratios while at higher amplitude ratios the surface effects decrease the natural frequencies of the silicon nanobeam. Also, for all values of amplitude ratios, the normalized fundamental natural frequencies of silicon and aluminum nanobeams vary linearly with respect to the nonlocal parameter while this is not the case at higher mode numbers.
Journal: European Journal of Mechanics - A/Solids - Volume 52, July–August 2015, Pages 44–53