Bài báo khoa học

This work presents solutions for the nonlinear dynamic features of beams with a Winkler-Pasternak foundation under a traveling mass, employing Reddy’s beam theory. The beam is made from a functionally graded porous material (FGPM) with three patterns of porosity distribution considered, including symmetric, asymmetric, and uniform distributions. The system of governing equations of the beam is developed based on the Ritz procedure and Lagrange’s equation. The nonlinear responses of the FGPM beam are then obtained via the Runge–Kutta scheme. Verifications are presented to confirm the accuracy and reliability of the present model with the literature. The effects of material parameters, geometry parameters, elastic foundation, boundary conditions, and moving mass parameters on the dynamic features of the FGPM beam are studied via parametric studies. The linear and nonlinear responses of the beam also are compared. Based on numerical results, it can be disclosed that the porosity distribution patterns and coefficient play an important role in the nonlinear dynamic response. The non-uniform symmetric porosity distribution pattern offers the best performance, i.e. the highest fundamental frequency and the lowest dynamic deflection.