Abstract
Free in-plane vibrations of a scimitar-type nonprismatic rotating curved beam, with a variable cross-section and increasing sweep along the leading edge, are calculated using an innovative, efficient and accurate solver called the Adomian modified decomposition method (AMDM). The equation of motion includes the axial force resulting from centrifugal stiffening, and the boundary conditions imposed are those of a cantilever beam, i.e., clamped-free and simple-free. The AMDM allows the governing differential equation to become a recursive algebraic equation suitable for symbolic computation, and, after additional simple mathematical operations, the natural frequencies and corresponding closed-form series solution of the mode shapes are obtained simultaneously. Two main advantages of the application of the AMDM are its fast convergence rate to a solution and its high degree of accuracy. The design shape parameters of the beam, such as transitioning from a straight beam pattern to a curved beam pattern, are investigated. The accuracy of the model is investigated using previously reported investigations and using an innovative error analysis procedure.
Highlights
A scimitar rotor blade, with increasing sweep along the leading-edge and made of modern light-weight materials, can lead to the production of more thrust and a reduction of propeller noise
The Adomian modified decomposition method (AMDM) was first partially validated using the unsymmetrical nonprismatic, nonrotating arch shown on Figure 2, whose cross-sectional height varies as h0(1 + α(2x − 1))
Once the coding was written for the governing equations and boundary conditions, which were written compactly using coefficients which could be given zero or infinity, it was relatively to change from one type of boundary condition to another
Summary
A scimitar rotor blade, with increasing sweep along the leading-edge and made of modern light-weight materials, can lead to the production of more thrust and a reduction of propeller noise. Özdemir and Kaya [19] investigated the free vibrations of rotating beams using the differential transformation method, while Gunda et al [20] used a linear combination of terms for the functions derived from the exact solution of the governing static differential equation of a stiff-string and that of a nonrotating beam. They proposed these new hybrid-type functions to determine the free frequencies in both cases, i.e., with and without rotation. The governing equation for the tangential displacement of the beam becomes: d3 φ dθ
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