Influence of Porosity on Thermal Free Vibration of Rotating Porous Sigmoid Functionally Graded Plate with Bi-Directional Thickness Variation

PurposeThe present work investigates the free vibration characteristics of rotating pre-twisted porous sigmoid functionally graded material (S-FGM) plate with bi-directional thickness variation, which can be deemed as the model of turbomachinery blades.MethodsThe temperature-dependent material properties of the plate with porosities are assumed to vary smoothly in the thickness direction according to sigmoid law. Two types of porosity distributions, namely, even and uneven distributions, are considered. The dynamic characteristics of S-FGM blades idealized as cantilever thin plates are studied using the finite element method (FEM) based on the first-order shear deformation theory (FSDT). The dynamic equilibrium equations are arrived at based on the Lagrange's equation of motion for moderate rotational speeds and the natural frequencies of the S-FGM plates are obtained by solving the standard eigenvalue problem through QR iteration technique.ResultsA comprehensive parametric study is carried out to analyze the influences of some critical parameters like gradient index, porosity distribution, taper ratios, pre-twist angle, aspect ratio, rotational speed, and temperature on the natural frequency of the S-FGM plates. The parametric study demonstrates that the frequencies of porous S-FGM cantilever plate decrease with the increase in gradient index and pre-twist angle. Furthermore, the frequencies of the pre-twisted S-FGM plate having even porosity distribution decrease with an increase in the porosity factor, while the reverse trend occurs for uneven porosity distribution.ConclusionsThe thickness variation ratio has a significant impact on the fundamental frequencies of the porous S-FGM plate. The NDFF decreases with an increase in thickness variation ratio along spanwise direction but shows an increasing tendency for an increase in thickness variation ratio along chordwise direction in both porous and perfect S-FGM plates. The natural frequencies are found to increase with an increase in the rotational speed for perfect and porous S-FGM plates, while the reverse trend is observed with temperature increment.