Modeling the dynamics of multiply connected nonlinear mechanical systems using a new numerical method

Аuthors

Kondratenko L. A.^*, Mironova L. I.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: kondrat.leonid@yandex.ru
**e-mail: mironova_lub@mail.ru

Abstract

The article regards the initial stage of an aircraft landing, particularly the Yak-42 aircraft, as a dynamic process of a multi connected nonlinear mechanical system. Despite the measures taken by pilots on dampening vertical speed and angular oscillations of the aircraft during landing under the impact of the external factors, such as wind, or factors determined by the design properties of the aircraft or its components, there is a possibility that the landing speed may be exceeded and unacceptable angular oscillations occur. Such deviations, arising at the initial stage of the process under consideration, affect significantly the subsequent aircraft movement along the airfield.
A numerical method developed by the authors, based on the 4-th order Runge-Kutta method, was applied for this process dynamics studying. This method allows studying dynamic processes in almost any system containing any number of nonlinearities, including significant ones. To develop a mathematical model of the process, the method developed by the authors for analyzing motion speeds and stresses is used as well.
A system of linear differential equations has been compiled to describe the movement of different parts of the aircraft airframe. Based on this system of equations, a system of right-hand sides of the equations was compiled. When developing the computational programm the system was supplemented with nonlinearities, such as nonlinear friction in the supports (chassis), nonlinear aerodynamic impact on the aircraft airframe parts.
The movement of the consoles was considered from the conditions of deformation under the action of concentrated forces, reduced to the position of the average aerodynamic chord. The article presents the modeling algorithm. Computed oscilloscope patterns, characterizing the initial stage of landing, were obtained while modeling. Computing process is limited by the physical time for the object in question, equal to one second. Besides, the computation did not account for the change in the supports elasticity caused by the specific dynamics of the aircraft landing gear.

Keywords:

mechanical systems, airframe, friction, elasticity, speed, stress, nonlinearity

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