Hygro-thermo-mechanical vibration analysis of functionally graded porous curved nanobeams resting on elastic foundations

This paper presents an analytical solution using Chebyshev polynomials based on Rayleigh–Ritz method and Navier's solution to analyze the free vibration response of functionally graded porous (FGP) curved nanobeams embedded resting on an elastic medium under hygro-thermo-mechanical load. Applying Hamilton's principle based on the quasi-3D higher-order shear deformation beam theory and the nonlocal elasticity theory, the governing equation of FGP curved nanobeam is derived. Material properties of nanobeam continuously change through the thickness via a power-law distribution and porosity distribution is described by two laws including even porosity distribution and uneven porosity distribution, respectively. The impact of thermal and moisture on structures are assumed to cause tension load in the plane and do not change the material properties. The elastic foundation used in this work is the Winkler–Pasternak type. 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 curvature radius, nonlocal coefficient, porosity coefficient, stiffness of foundation, and boundary conditions on the free vibration of the nanobeam are examined in detail.