Reduced-order model of geometrically nonlinear flexible structures for fluid-structure interaction applications

This paper deals with the numerical computation, via a reduced order models (ROM), of the vibrations of geometrically nonlinear structures triggered by the aeroelastic coupling with a fluid flow. The formulation of the ROM proposed in this paper is based on the projection on a basis of reduced dimension enhanced with dual modes. An explicit expression of the projected nonlinear forces is computed in a non-intrusive way based on the Implicit Condensation method. The resulting ROM is an improvement of the classical ICE method since the effects of membrane stretching are taken into account in the resolution of the dynamic equation of motion. Such a ROM aims to be adapted to follower aerodynamic unsteady loads. The construction of the ROM is first detailed and validated under several load cases on a Euler-Bernoulli beam with von Karman hypothesis. Then a fluid-structure partitioned coupling on a two-dimensional example involving vortex-induced vibrations is considered to demonstrate the capability of such ROM to replace a nonlinear FE solver. In this paper, the limitations of the ICE method are highlighted in the examples treated, while the ROM proposed overcomes such limitations and captures accurately the dynamics.

Automated summary

This paper focuses on the numerical computation of vibrations in geometrically nonlinear structures induced by aeroelastic coupling with fluid flow using reduced order models (ROM). The proposed ROM formulation utilizes projection on a basis of reduced dimension enhanced with dual modes, allowing for the accurate capture of dynamic characteristics and adaptation to unsteady aerodynamic loads. The limitations of the classical Implicit Condensation method are highlighted, while the ROM proposed overcomes these limitations and accurately captures the dynamics.