Structural Modification of Nonlinear FEA Subcomponents Using Nonlinear Normal Modes

Abstract

Structural modification procedures are widely used to predict changes in the dynamics of a structure based on the addition of stiffeners, reinforcements, modifications of bolted joints, and payloads. A truncated modal basis of a linear dynamic system can be used to predict the changes of the mode shapes and frequencies due these modifications. This work proposes an extension of modal structural modification for geometrically nonlinear structures, by representing the structure with a set of nonlinear normal modes. An approximate quasi-linear modal model is defined from the fundamental frequency and maximum deformation shape of the nonlinear normal mode solutions. The resulting quasi-linear model has energy dependent mode shapes and natural frequencies. An iterative algorithm then applies modal structural modification to the quasi-linear modal model such that the modal parameters used in the substructuring routine are appropriate for each response level of interest. The method is demonstrated on a finite element model of a geometrically nonlinear beam with a variable elastic boundary condition. The model is meant to mimic the uncertain boundary conditions of a substructure in a hypersonic air vehicle. The nonlinear normal modes are computed for the unmodified beam, and a torsion spring is added to the boundary using the proposed method. It is found to give accurate predictions of the nonlinear modes of the assembly, potentially at a greatly reduced computational cost.