On vibrations of FG nanobeams

Abstract

In the current study, the vibration behavior of axially functionally graded nanobeams is investigated in the framework of Eringen's two-phase local-nonlocal model which considers both local and nonlocal phases in modelling nano-scale structures. Material properties are varied through the length using power-law functions. By employing the Hamilton's principle and a conversion between integral-differential, higher order equation of motion with two additional higher order non-classical boundary conditions are achieved. A modified differential quadrature method is used to solve the problem and the accuracy of the current methodology is approved by comparing the results with previous studies for simplified models. In order to indicate the influence of different parameters such as nonlocal term, phase coefficients, material varying function, etc., a comprehensive parametric study is presented and nanobeam with different boundary conditions are discussed. For different boundary conditions, variation of frequency terms is presented especially for cantilever axially functionally graded nanobeams in which differential form of Eringen's nonlocal theory is unable to model accurately. It is shown that the two-phase nonlocal model has the capability to model the axially functionally graded nanobeams with different boundary conditions and material varying terms.