Large amplitude nonlinear vibration analysis of functionally graded Timoshenko beams with porosities

• We study the large-amplitude nonlinear vibration of FG porous beams.
• Galerkin׳s method and the method of multiple scales are employed.
• Numerical simulations shows the effectiveness of proposed method.
• Effects of several significant parameters are examined.

In this paper, the large-amplitude nonlinear vibration characteristics of functionally graded (FG) Timoshenko beams made of porous material is investigated for the first time. Material properties of FG porous beam are supposed to vary continuously along the thickness according to the rule of mixture which modified to approximate material properties with porosity phases. The governing equations are derived based on Timoshenko beam theory through Hamilton׳s principle and they are solved utilizing both Galerkin׳s method and the method of multiple scales. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG porous beams as compared to the literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as material distribution profile, porosity volume fraction, aspect ratio and mode number on the normalized natural frequencies of the FG porous beams in detail. It is explicitly shown that the vibration behavior of a FG beams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG porous beams.