Buckling and Nonlinear Vibration of Functionally Graded Porous Micro-beam Resting on Elastic Foundation

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Dang V.H.; Nguyen T.H.

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Journal Paper

Paper Information

Journal: MECHANICS OF ADVANCED COMPOSITE STRUCTURES Year:2022 | Volume:9 | Issue:1 Page(s): 75-88

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Information Journal Paper

Title

Buckling and Nonlinear Vibration of Functionally Graded Porous Micro-beam Resting on Elastic Foundation

Author(s)

Dang V.H. | Nguyen T.H. | Issue Writer Certificate

Keywords

Micro-beams

Nonlocal strain gradient theory

Functionally graded porous

Buckling

Nonlinear vibration

Abstract

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.

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