Influence of surface effects on vibration behavior of a rotary functionally graded nanobeam based on Eringen’s nonlocal elasticity

Abstract

This article presents a free vibration analysis of size-dependent functionally graded rotating nanobeams with all surface effects considerations on the basis of the nonlocal continuum model. By using constitutive differential model of Eringen, the nonlocal elastic behavior is described which enables the present model to become effective in design and analysis of nanoactuators and nanosensors. The material for this work is a functionally graded which according to power law distribution, it is assumed that its bottom surface is aluminum and the top one is silicon. Taking attention to Euler---Bernoulli beam theory, the modeled nanobeam and its equations of motion are derived using Hamilton's principle. Novillity of this work is considering the effects of rotation and surface effects in addition to considering various boundary conditions of the FG nanobeam. The generalized differential quadrature method is used to discretize the model and to get a numerical approximation of the equation of motion. The model is validated by comparing the benchmark results with the obtained ones. Then influence of surfaces effects, nonlocal parameter, angular velocity, volume fraction index and boundary conditions on natural frequency ratio of the rotating FG nanobeams are investigated.