Dynamic behaviors of single- and multi-span functionally graded porous beams with flexible boundary constraints

This paper investigates the dynamic behaviors of single- and multi-span functionally graded porous (FGP) beams with flexible boundary constraints modelled by a combination of two-dimensional translational springs and a rotational spring. It is assumed that the pores are distributed either non-uniformly or uniformly according to four porosity distributions and that the material properties vary smoothly along the thickness direction of the beam. The dynamic governing equations are derived from Hamilton's principle within the framework of Timoshenko beam theory and solved by using discrete singular convolution element method (DSCEM) in conjunction with Taylor series expansion (TSE) method. To validate the accuracy of the proposed method, the present results are compared with those in open literature and obtained by finite element method (FEM). A comprehensive parametric study is conducted to investigate the effects of spring constants, boundary condition, porosity distribution, porosity coefficient and beam span ratio on the dynamic behaviors.