Parameterization of nonlinear aeroelastic reduced order models via direct interpolation of Taylor partial derivatives

Abstract

The identification of optimally sparse Taylor partial derivatives presents a new opportunity in efficient nonlinear aerodynamic model reduction for complex aeroelastic systems. Unfortunately, for this class of reduced order model (ROM), the robustness that is observed in the linear regime to parameters including; dynamic pressure, control hinge linear stiffness, or even freeplay, is quickly forfeited given the amplitude (or velocity) dependency of the aerodynamic loading on the structure. In this paper, nonlinear sensitivity is addressed by interpolating a library of nonlinear unsteady aerodynamic ROMs across a compact subspace in dynamic pressure and freeplay magnitude. The ROM, based on Lagrange interpolation of sparse higher-order Taylor partial derivatives, demonstrates excellent precision in modelling high amplitude transonic limit cycle oscillations for an all-movable wing with freeplay, capturing the nonlinear instability region (up to 96% of the linear flutter boundary), and for a range of freeplay values. Mathematics Subject Classification (2020) MSC code1 · MSC code2 · more