Free Vibration Analysis of Functionally Graded Nanobeams Based on Different Order Beam Theories Using Ritz Method

Abstract

This paper presents the fundamental frequency analysis of functionally graded (FG) nanobeams using Ritz method subjected to different sets of boundary conditions. The vibration analysis is based on the classical, the first-order and different higher-order shear deformation beam theories while including rotary inertia. The material properties of FG nanobeams are assumed to vary through the thickness according to the power-law exponent form. Based on the nonlocal constitutive relations of Eringen, the frequencies equations are obtained by the weak forms of the governing differential equations. In this study, the effects of material distribution, nonlocal parameter, beam theories, slenderness ratios and boundary conditions on the fundamental frequency are discussed. The analysis is validated by comparing the obtained results with the available results from the existing literature.