Surface and nonlocal effects on the free vibration of nanobeam by differential transformation method

This paper is proposed to study surface and nonlocal elasticity of Eringen on the free vibration of nanobeam.To incorporate surface effects, Gurtin-Murdoch model is used. The motion equation is derived using Hamilton’s principlebased on Euler-Bernoli beam theory (EBT) with different boundary conditions which are solved by differentialtransformation method (DTM). It is shown that by increasing size of beam the influence of surface effect on frequenciesreduces to zero, which in macroscale it can removed and the natural frequency of beam is identical as a classical beam.But at nanoscale, the surface effects will increase by buckling energy and surface effect should be considered in equations.

کلیدواژه ها:

nonlocal elasticity ، surface effect ، nanobeam ، free vibration ، differential transformation method