Abstract
Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton’s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures.
Highlights
Tapered thin-walled structures have been widely used in wind turbine, helicopter, and fix-wing aircraft due to their weight-saving and aerodynamic load carrying capabilities [1]
DFM is different from the conventional finite element methods (CFEMs); the corresponding shape function is semianalytical solutions of the governing equations. e iterative calculation for the terms of transformed function Wa(k), Ua(k), Va(k), and φa(k) and modal frequencies of rotor blade can be quickly solved with a symbolic computational software
The spectral finite element model is comprehensively validated by comparing modal frequency and mode shape predictions of a tapered cylinder beam and a wind turbine by the ANSYS
Summary
Tapered thin-walled structures have been widely used in wind turbine, helicopter, and fix-wing aircraft due to their weight-saving and aerodynamic load carrying capabilities [1]. Wang [31] and Banerjee [32] applied the Frobenius method to obtain the semianalytical solutions for linearly tapered rotating beams under bending vibration and formulated the spectral finite element. E differential transform method (DTM) has been applied to solve the dynamic equation of a double tapered Timoshenko beam considering flapwise bending-torsion coupling recently [34]. A spectral finite element model is developed to investigate tapered thin-walled rotor blade structures, in which torsion related warping effect is included. En, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element.
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