Free Vibrational Behaviour of Multi‑Directional Porous Functionally Graded Structures

摘要

The free vibrational frequencies of a multi-directional functionally graded (FG) structure are investigated for the first time inthis paper considering the influences of variable grading (power-law, sigmoid, exponential) and porosity distribution (evenand uneven type). Also, the structural properties (Young’s modulus, density and Poisson’s ratio) varied along with two differentdirections simultaneously, i.e., the longitudinal and transversional ones, respectively. The present multi-directionalgrading model of the FG structure is reconstructed mathematically for the numerical analysis by considering adequatestate-space deformation kinematics with the help of higher-order displacement functions and shear stress continuity. Thegeneral motion equation of a multi-graded structure is expressed using Hamilton’s principle and the finite element methodincluding the necessary porosity effect. Initially, model consistency is verified and the eigenvalues obtained in the analysisare compared with the ones found in the literature. The comparison also includes the directional grading effect on theirfrequencies. Further, the influence of different parameters, i.e., power exponents (n_z and n_x), aspect ratio, thickness ratio,geometry, end support conditions, curvature ratio, porosity index, porosity distribution and material grading patterns, on thevibration characteristics of the multi-directional FG structure is computed. The analysis of the numerical results confirmsthat material grading; porosity distribution pattern and other design parameters have a significant influence on the frequencyresponse characteristics of a single/multi-directional porous FG structure.