Free vibration analysis of fg curved nanobeam resting on elastic foundation using Rayleigh-Ritz method

Abstract

    In this paper, an analytical solution using Chebyshev polynomials based on the Rayleigh-Ritz method to analyze the free vibration analysis of functionally graded porous (FGP) curved nanobeams embedded in an elastic medium. Hamilton’s principle is based on the Quasi 3D higher-order shear deformation beam theory, in conjunction with nonlocal elasticity theory, the governing equation of nanobeam is derived. Material properties of beam continuously change through the thickness via a power-law distribution and porosity distributions are described by two laws including even porosity distribution and uneven porosity distribution, respectively. Thermal and moisture subject on structures is assumed to cause tension load in the plane and do not change the material’s mechanical properties. The accuracy of the proposed method is verified by comparing the obtained numerical
results with those of the published works in the literature. In addition, the influence of the curve of the beam, nonlocal coefficient, porosity coefficient, stiffness foundation of the beam on the vibration response of the nanobeam is examined in detail