Influence of Mass Matrix Models on Flutter Computations

Abstract

For the computation of the dynamic properties and response of structures using the finite-element method (FEM), there are two main options for the mass matrix modeling: the lumped model and the consistent model. Both have their own advantages and drawbacks. This work focuses on the influence of mass matrix models on flutter computations of aircraft structures. Even nowadays, with high computational power resources at our disposal, a reduced and precise model for the flutter problem could be of great value given the large number of compilations required to solve it. In order to find the most suitable mass matrix to achieve this task, four different mass matrices have been considered in this work: consistent, lumped, and two optimal (proposed by the authors). Three different aircraft structures have been analyzed: a clean wing, a wing with a tip mass, and a wing with a large tip mass. For every case, the same conclusion was drawn: the result using the consistent mass matrix converges with significantly fewer elements than when using the lumped mass matrix. In addition, the proposed optimal mass matrices, which are a weighted linear combination of the lumped and consistent mass matrices, do not improve the results obtained by the consistent mass approach either computationally or in accuracy. These conclusions contradict the usual procedure followed for flutter computations within the industry, where the lumped mass model is widely spread.