Modal analysis of a 20-degree-of-freedom model of a transport aircraft wing

Abstract

The subject of the study is the modal analysis of natural frequencies and vibration modes of a regional transport aircraft wing. The proposed model utilizes predefined functions of aerodynamic forces and moments to compute the wing’s resonance frequencies and analyze vibration stability under resonance conditions.  The study presents finite element analysis examples based on a 20-degree-of-freedom wing model with variable bending and torsional parameters along the span. Numerical methods were used to determine the natural frequencies and corresponding mode shapes, enabling the identification of the most critical modes for further analysis of the structure's dynamic behavior. This study aims to develop a reduced-order model and a computational algorithm for wing vibration analysis with fewer degrees of freedom compared to the original high-fidelity model, and to validate the accuracy of the dynamic characteristics for subsequent evaluation of vibration stability and flutter boundaries. The objectives include: developing a model that accounts for spanwise variations in bending and torsion; considering the partial-span location of the aileron; and incorporating the positions of the wing’s stiffness axis and mass center axis. The research methodology is based on numerical schemes for mathematical modeling and dynamic system analysis, with an emphasis on finite element analysis to determine the wing's frequency characteristics. The analysis accounts for spanwise variations in stiffness and torsional moments within the mechanical control linkage. Results and conclusions: The study substantiates and applies key assumptions for constructing a computational model of a regional transport aircraft wing. Based on these assumptions, a finite element model with 20 degrees of freedom was developed. Unlike existing models, the proposed model incorporates not only the bending and torsional angles of the wing and aileron but also the spanwise variation of all structural parameters. Scientific novelty of the obtained results: for the first time, a novel method has been developed for constructing a reduced-order model of an aircraft wing with a significantly lower number of degrees of freedom, while maintaining a high level of agreement with the dynamic characteristics of the full-scale wing structure.