Flexible multibody dynamics using joint coordinates and the Rayleigh‐Ritz approximation: The general framework behind and beyond Flex

This article presents a general framework to set up the equations of motion for flexible multibody system using joint coordinates and Rayleigh‐Ritz approximation. The framework covers in particular the underlying formulation behind the aeroelastic code Flex developed by Øye. This formulation is strongly related to the one used in the module ElastoDyn of the code OpenFAST. The approach results in models with few degrees of freedom thanks to carefully selected shape functions and the direct account of the constraints. The specificities of the method for open‐loop systems and thin beams are presented. The inclusion of torsion and couplings with finite element methods or superelements are discussed. Simple validations cases are used. A four degrees of freedom model of a two‐bladed wind turbine is developed to illustrate the method.