Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

Abstract

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

Modelling and Parametric Study for Panel Flutter Problem using Functionally Graded Materials

“…Analyses show the approaches efficiently optimize material distribution to reduce peak stress and mass while improving computational performance. [11][12][13][14] put forward plate formulations specialized for stability and vibration analysis in rotating blades, porous sandwich composites and bi-directionally graded materials using shear and thickness deformation assumptions. [15] derived analytical flutter solutions for porous functionally graded plates to quantify porosity effects on frequencies and speed, enabling design optimization.…”

Transient analysis of variable thickness multi-directional functionally graded plates using isogeometric analysis

“…Taped plates with one way wedged shapes (Lotfi et al, 2011) or two-way prismatic geometries (Cheung and Zhou, 2003;Rajagopal and Hodges, 2015) are the most common type of variable-thickness plates (Cheung and Ding, 1999;Leissa, 1969;Tweet et al, 1997;Wang, 1997;Wang et al, 1995Wang et al, , 2018. However, nonlinear variable thickness plates are also investigated recently for practical applications (Ansari and Setoodeh, 2020;Zenkour, 2003Zenkour, , 2018. Recently, various investigations have been conducted in the literature to study the mechanical behavior of variable-thickness FGM/MFGM plates in terms of linear bending and free vibration behavior.…”

“…, 1995, 2018). However, nonlinear variable thickness plates are also investigated recently for practical applications (Ansari and Setoodeh, 2020; Zenkour, 2003, 2018). Recently, various investigations have been conducted in the literature to study the mechanical behavior of variable-thickness FGM/MFGM plates in terms of linear bending and free vibration behavior.…”

Investigate the bending and free vibration responses of multi-directional functionally graded plates with variable thickness based on isogeometric analysis

“…Therefore, investigations on their mechanical behaviour have been extensively conducted by various researchers in the literature [5][6][7][8][9][10][11][12]. In addition, other types of variable thickness plates with nonlinear thickness variation have been investigated for practical application recently [13,14], especially in the adoption of Functionally Graded Materials (FGMs) for such structures.…”