A Multiscale Model of Mass-Functionally Graded Beam-Fluid System Under Bending and Vibration Responses

In this paper, a multiscale model is developed for the mass functionally graded (FG) beam-fluid system to investigate its static and dynamic responses based on 3D printed porous beam free vibration tests, which are determined by two aspects. At the microstructural level, the gradient variation is realized by arbitrary distribution of matrix pores, and the effective moduli under specific distribution are obtained using the micromechanics homogenization theory. In the meantime, at the structural level, the mechanical responses of FG porous beams subjected to mass loading are considered in a static fluid environment. Then, the explicit expressions of local finite-element (FE) expressions corresponding to the static and dynamic responses are given in the appendices. The present results are validated against numerical and experimental results from the literature and mechanical tests of 3D printed structures, with good agreement generally obtained, giving credence to the present model. On this basis, a comprehensive parametric study is carried out, with a particular focus on the effects of boundary conditions, fluid density, and slenderness ratio on the bending and vibration of FG beams with several different gradations.