Fourier p- element simulation and experimental validation of frequencies for rotating blade in flexure

A novel method based on Fourier-p discretization is proposed for analyzing the flapping motion of the free vibration of a uniform blade. The Fourier-p element approach involves utilizing a single element with a limited number of degrees of freedom (DOF) to describe the beam deformations. In the Fourier-p element approach, the displacement functions are formulated by combining polynomials and trigonometric shape functions, which describe the spatial variation of the displacement within the element. By incorporating trigonometric shape functions, internal nodal degrees of freedom are shown, leading to a more accurate depiction of the beam’s deformation and vibration behavior. Combining polynomials and trigonometric functions in the displacement functions provides a broad coverage of deformation patterns, resulting in a comprehensive representation of the beam’s displacement. Lagrange’s equations are employed to formulate the differential equations that govern the free vibrations of the rotating blade. Numerical predictions are then computed for various hub radii, rotational speeds, and different end conditions. Whenever possible, these predictions are compared with relevant results from existing literature enabling a validation and evaluation of the proposed method’s accuracy and effectiveness. The model is consolidated and validated by both experimental work as well as commercial Finite element Abaqus package. The Fourier-p element discretization method demonstrates its ability to yield accurate beam frequencies by incorporating a small number of trigonometric sine terms. This approach achieves results that align with exact solutions, surpassing the accuracy achieved by conventional finite element methods.