Semnan University Press Mechanics of Advanced Composite Structures 2423-4826 9 1 2022 04 01 Buckling and Nonlinear Vibration of Functionally Graded Porous Micro-beam Resting on Elastic Foundation 75 88 5951 10.22075/macs.2021.24098.1350 EN Van Hieu Dang Department of Mechanics, Thai Nguyen University of Technology, Thainguyen, Vietnam 0000-0001-8789-7284 Thi Hoa Nguyen Department of Mechanics, Thai Nguyen University of Technology, Thainguyen, Vietnam 0000-0003-3658-5998 Journal Article 2021 07 30 The buckling and nonlinear free vibration problems of functionally graded porous (FGP) micro-beam resting on an elastic foundation are presented through the nonlocal strain gradient theory (NSGT) and the Euler-Bernoulli beam theory (EBT) with the von-Kármán’s geometrical nonlinearity. The micro-beam is made up of metal and ceramic in which the material properties are assumed to be varied continuously in the thickness direction through a simple exponential law. Two porosity distribution models, including even and uneven distributions, are considered. The governing equation of motion is derived by employing Hamilton’s principle. The analytical expressions of the critical buckling force and nonlinear frequency of the FGP micro-beam with simply supported (S-S) boundary conditions (BCs) are obtained by utilizing the Galerkin technique and the equivalent linearization method (ELM). The reliability of the obtained results has been checked. Effects of the power-law index, the porosity distribution factor, the length-thickness ratio, the material length scale parameter (MLSP), the nonlocal parameter (NP), and the coefficients of the elastic foundation on the buckling and nonlinear free vibration responses of the FGP micro-beam are investigated and discussed in this work. https://macs.semnan.ac.ir/article_5951_800b03685c22049f049801f6841861a2.pdf