Crack Effects on the Dynamic Behavior of Orthotropic Composite Pre-Twisted Blades Using Radial Basis Function Model Paul Juinn Bing Tan National Penghu University of Science and Technology, Magong, Penghu, Taiwan e-mail:pashatan@yahoo.com.tw Ming-Hung Hsu National Penghu University of Science and Technology, Magong, Penghu, Taiwan e-mail:hsu.mh@msa.hinet.net Abstract—The eigenvalue problem of a tapered pre-twisted orthotropic composite blade is studied using a radial basis function model. The pre-twisted orthotropic composite blade is characterized with an Euler-Bernoulli beam model. The radial basis function model is used to transform the partial differential equations of a tapered pre-twisted orthotropic composite blade into a discrete eigenvalue problem. This study also investigated the effects of fiber orientation, crack, incline angle and rotation speed on the frequencies of a tapered pre-twisted orthotropic composite blade. Integrity and computational efficiency were compared in the radial basis function model in numerous case studies. Numerical results confirmed that the radial basis function model is accurate and efficient for modeling a pre-twisted orthotropic composite blade. Keywords—orthotropic composite blade; radial basis function model; frequency; vibration; crack; numerical method I. FORMATION OF THE EIGENVALUE PROBLEM Fiber-reinforced composites and isotropic materials are widely used in fan or compressor machinery designs. Fiber reinforced composite material in blade applications has been studied extensively. Figure 1 shows a tapered pre-twisted orthotropic composite blade structure. The pre-twisted blade is attached to a rigid hub. Axes 1, 2 and 3 are the global axes, and axes x, y and z are the local blade axes. The b and h denote the breadth and thickness, respectively, at the root of the tapered blade. The f θ is the fiber orientation, t θ is the total pre-twisted angle from the blade root to the tip, and i θ is the inclined angle of the blade. In an orthotropic composite beam simultaneously subjected to a bending moment (,) B M zt and a torsion moment (,) T M zt , the respective bending and torsion moments are [1-5] ( ) 2 2 , zz xx t zz xx B mt E I CE I u M zt C z z φ η η ∂ ∂ = + ∂ ∂ (1) ( ) 2 2 , t zz xx T mt C E I u M zt C z z φ η ∂ ∂ = + ∂ ∂ (2) where ( ) , uzt and ( ) , zt φ are the displacement and the twist angle of the blade, respectively. For an orthotropic composite blade, the above parameters are[1-5] () 3 3 2 xx t 1 z z z I z bh (1 )(1 ) cos ( ) 12 L L L α β θ = − − 3 3 2 t 1 z z z b h(1 ) (1 )sin ( ) 12 L L L α β θ + − − (3) () () () [ ( )] zz xx t 2 mt E I zC z z 1 C z η = − (4) () () xx mt 35 2I z C z S = (5) zz 4 4 f f 2 31 f 11 33 13 33 1 E sin cos 2 1 1 sin 2 E E 4 G E θ θ ν θ = + + − (6) 2 2 f f 35 f 11 33 sin cos S sin 2 E E θ θ θ = − 31 f 13 33 2 1 1 sin4 4 G E ν θ + − (7) 1463 978-1-4673-8644-9/16/$31.00 c 2016 IEEE