Dynamic analysis of viscoelastic functionally graded porous beams using an improved Bernstein polynomials algorithm

Functionally graded porous (FGP) materials have significant application potential because they can achieve many specific applications by controlling porosity and material composition. However, most current research has little emphasis on the vibration characteristics of FGP materials with viscoelastic properties. To address this issue, this article presents an improved Bernstein polynomials algorithm to establish the governing equation for analyzing the vibration response of fractional-order viscoelastic FGP beams. This method effectively resolves instability problems associated with boundary conditions. Single step Adams scheme and Newmark-β method are then utilized to solve the governing equation of the viscoelastic FGP beams. The accuracy of the proposed method is confirmed through comparison with the results obtained from the finite element method. A parametric investigation is conducted to explore the impact of porosity and its distribution pattern, power law index, boundary condition, fractional order, and viscoelasticity coefficient on the vibration characteristics of the viscoelastic FGP beams. These findings suggest that desirable dynamic properties for FGP beams can be achieved through tailoring their material gradient and porosity distribution.