Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Numerical Non-linear Structural Analysis of a Rotary Blade under Aerodynamic Load
Submission Author:
André Florentino Ribeiro , MG
Co-Authors:
André Florentino Ribeiro, Murilo Sartorato, Carlos Pagani
Presenter: André Florentino Ribeiro
doi://10.26678/ABCM.COBEM2021.COB2021-0478
Abstract
Beams is a structure element with high aspect rate widely used to efficiently model engineering structure components. In the aeronautical field, beams can be used to model lift components, such as helicopter blades. This work purposes the computational implementation of a geometrically nonlinear rotary beam formulation which stems from the variational asymptotic method (VAM). The method VAM proposes the representation of a three- dimensional formulation of a geometrically non-linear beam in terms of two complementary formulations: 1) a one-dimensional formulation (1D), compact and geometrically exact along the beam reference line, and 2) a two-dimensional analysis (2D), generally linear, set at each beam cross-section. The combination of the 1D and 2D formulations leads to an accurate beam formulation, with high computational performance in comparison with similar three-dimensional formulation. The finite element method, associated with the Newton-Raphson method, is applied to numerically solve the equations representing the one-dimensional beam formulation for obtaining both the static and dynamic beam responses in terms of geometric parameters, materials properties, rotary speed and external loading. This formulation will be used to describe the structural behavior of one helicopter blade made of composite material with the cross-section airfoil known as the VR-7. Although the mathematical model of this work is only focused on structural analysis, it’s possible to simulate the beam in software that uses the blade element model theory to obtain the lift line force along the length of the blade and export it to the model that was created in this work to obtain the structure analyses. The structure analyses involve obtaining either the internal forces and moments or linear and angular displacements, but also makes possible to verify the axial force that the beam’s rotation generates. Furthermore, the model allows describing the actual lift component generated by the deformed blade that is aligned to the helicopter’s weight, because, in the geometrically nonlinear analysis, the external forces are measured in the deformed coordinates, whereas the static equilibrium conditions are written in the undeformed coordinates. Also, the natural frequencies can be shown in function of the angular speed applied in the root of the blade, since the natural frequencies related to its vibrational modes are also induced by rotation. Therefore, the methods adopted in this research will give accurate structure results for helicopter composite blade modeled as a rotary beam and contributes for becoming more practice to numerically simulate structure components made of composite material.
Keywords
Beam theory, Variational Formulation, Rotary Blades, Finite Elements, Numerical Solutions, Non-linear analysis
