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Coupled free vibration analysis of rotating non-uniform cantilever beams by an element-wise Ritz method using local hierarchical functions
Date Issued
01-11-2023
Author(s)
Dangarwala, Rutvik K.
Nagendra Gopal, K. V.
Abstract
The coupled free vibration behaviour of rotating non-uniform cantilever beams is investigated by an efficient and accurate element-wise Ritz method using Bardell's polynomials as local hierarchical functions. Both bending-twisting and bending-extension coupling is included in the beam model. The same hierarchical set can be suitably modified to satisfy the essential boundary conditions and represent the stretching, bending and rotation of the beam. The global matrices are obtained by minimizing the Lagrangian functional. The inter-element compatibility conditions are satisfied, and a condensation procedure is used to obtain the condensed matrices for the eigenvalue problem. The procedure is validated with examples from published studies and various case studies are presented to demonstrate the accuracy and convergence of the proposed method. A parametric study is presented to show the effect of various parameters on the free vibration response of rotating non-uniform beams. The frequency veering phenomenon is observed during the study. The proposed approach provides a simple and efficient approach for analyzing the free vibrations of rotating structures such as wind turbine rotor blades, helicopter blades, propellers, and structures with strong discontinuities, especially in the preliminary design stage.
Volume
288