Nonlinear free vibration analysis of FGP beams in thermal environment employing PIB mesh-free method
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https://doi.org/10.15625/0866-7136/23898Keywords:
functionally graded porous beam, mesh-free method, point interpolation, nonlinear free vibration, thermally induced vibrationAbstract
A free vibration analysis of functionally graded porous (FGP) beams considering geometrically nonlinear and thermal effects using the point interpolation-based (PIB) mesh-free method is presented in this paper. Uniform and symmetric porosity distributions across the beams’ thickness are assumed. Temperature-dependent properties of the matrix material are estimated using a nonlinear function of temperature. The displacement and strain fields of the beams are modelled by the Timoshenko beam theory and the von Kármán’s nonlinearity assumption. The nonlinear governing equations are derived based on the virtual work principle. A robust mesh-free method in which polynomial basis functions combined with the point interpolation technique are utilized to construct shape functions in influence domains is employed to discretize the governing equations. The mesh convergence is tested, and the accuracy of the study is confirmed by comparison with previous works. The effects of important parameters, such as temperature change, porosity coefficient, porosity distributions, and boundary conditions, on the natural frequency are investigated. The study results provide a robust computational tool and scientific knowledge for designing FGP beams exposed to thermal environments.
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