Application of the Geometrically Exact Intrinsic Beam Model on Rotor Blades

Abstract

With the Versatile Aeromechanic Simulation Tool (VAST), the German Aerospace Center (DLR) is developing a software framework for the simulation of rotary wing aircraft. One challenge consists of simulating the dynamic behaviour of rotor blades. In general, rotor blades can be considered as flexible beams for which numerous models have been developed in the past. One of them is the geometrically exact intrinsic beam model [2] which is represented by a time dependent hyperbolic system of partial differential equations (PDE) in one space dimension along a reference line of the considered beam. In contrast to other well-known models like the Euler-Bernoulli model or the Timoschenko model, the governing equations of the intrinsic beam model contain non-linearities which makes it a geometrically exact model. Furthermore, it allows for the modelling of initially curved and twisted anisotropic beams making it well-suited for the simulation of rotor blades. In [1], we used a practical formulation of the intrinsic beam model as a system of linear hyperbolic balance laws to derive a discontinuous Galerkin (DG) approach for its discretization. For boundary conditions describing the mechanical setup of a clamped-free beam, we found that this discretization approach is numerically stable if no energy comes from the boundaries of the considered domain. Choosing a DG approach for the discretization of the problem is not only senseful because it is very efficient and helps minimizing the degrees of freedom in the computationally intensive analysis of helicopters. It is also able to represent discontinuities accurately which is interesting for the simulation of rotor blades as for example material parameters might change discontinuously along the blade. For steady-state cases, we show that the intrinsic beam DG method is more accurate than our previous approach using experimental results for a rotating beam in vacuum. In addition, we show first numerical results for simulating the dynamic behaviour and discuss ongoing research and challenges concerning boundary conditions, stability and damping. REFERENCES [1] C. Bleffert. An Energy Stable Discontinuous Galerkin Discretization Approach for the Geometrically Exact Intrinsic Beam Model. Master thesis, University of Cologne, 2022. [2] D. H. Hodges. Geometrically exact, intrinsic theory for dynamics of curved and twisted anisotropic beams. AIAA Journal, 41(6):1131-1137, 2003.