New mathematical model from SPbU scientists will improve flight safety

The model, based on the principles proposed by a Soviet mathematician, describes all possible modes of oscillation

Scientists from St. Petersburg State University (SPbU) and Khalifa University in Abu Dhabi have developed a mathematical model to combat flutter - dangerous vibrations in aircraft wings. The research will allow for accurate analysis of oscillations and the creation of effective damping devices.

Flutter is rapidly increasing oscillations in aircraft structures, such as wings and tail, which accelerate the wear of parts and can lead to their destruction in flight. The new model, created on the basis of principles proposed by Soviet mathematician Mstislav Keldysh, describes all possible modes of oscillation, including hidden ones that are not detected by standard methods. The scientists retained part of the Keldysh equations describing the behavior of the wing, but simplified the damper characteristic, replacing it with a V-shaped mathematical function. This allowed for a more accurate analysis and identification of all oscillation options.

The research is supported by a grant from the Russian Science Foundation and published in the International Journal of Robust and Nonlinear Control. According to Nikolay Kuznetsov, Head of the Department of Applied Cybernetics at SPbU, the model will help engineers design reliable dampers that dampen vibrations, which will improve flight safety. In the future, scientists plan to compare the results with full-scale tests.

Our analysis will be useful for engineers. By understanding the exact mechanisms of the emergence and suppression of nonlinear oscillations, they will be able to design more reliable and efficient damping devices for wings and other elements of aircraft.

Nikolay Kuznetsov, Head of the Department of Applied Cybernetics at SPbU, Head of the Laboratory of Information and Control Systems of the Institute of Mechanical Engineering Problems of the Russian Academy of Sciences, Corresponding Member of the Russian Academy of Sciences

SPbU has been studying flutter since 2021, when a scientific review on this topic was published. Nikolay Kuznetsov, the head of the research, is the author of more than 400 scientific papers and the laureate of the 2024 State Prize of the Russian Federation for his contribution to the study of oscillations. The development is already used in fundamental and applied science, including navigation and communication systems.