A Jacobi–Ritz Approach for Aeroelastic Analysis of Swept Distributed Propulsion Aircraft Wing

Abstract

This article presents a Jacobi–Ritz approach for conducting flutter and divergence analysis of a complex distributed propulsion aircraft wing similar to that of NASA X-57. The general orthogonal Jacobi polynomials are used to approximate the bending displacement and torsional rotation angle in the Ritz method-based structural and aeroelastic analysis. The Jacobi polynomials satisfy the orthogonality condition using weight functions, which are easily modified to satisfy different essential and natural boundary conditions. Compared to simple polynomials, Jacobi polynomials can eliminate the well-known ill-conditioning numerical issues when considering higher-order polynomial terms during the eigenvalue analysis. The Jacobi–Ritz method is also found to alleviate mode switching, which is often encountered in tracking the changes of modes with the varying airspeed. The Jacobi–Ritz method is later used to investigate the flutter and divergence speeds under different parameters including distributed propulsor mass and their locations, nonuniform aerodynamic model for the wing in the presence of multiple propulsors, and the sweep angle. Results show that placing the distributed propulsors on the wing’s leading edge increases the flutter speed even though the bending and torsion modal frequencies are decreased compared to those of the wing without propulsors. The presence of pods for the middle high-lift motors causes an extra aerodynamic moment, which reduces the flutter speed. Parametric studies also show that the divergence speed is lower than the flutter speed for a uniform and straight distributed propulsor wing. Using swept-back wing configuration and placing the tip propulsor near the wing’s leading edge can help to increase both flutter and divergence speeds.