A Two-Stage Mathematical Model for Evaluating the Modes of Forced Vibrations of an Aircraft Skin Element with the Use of Fiber-Optic Technologies

The purpose of research is development of a mathematical model of vibration vibrations of an aircraft skin element made in the form of a plate with a two-stage transformation "vibration load parameters – deformation of the plate - change in the wavelength of the optical signal" in order to take into account the number of loading cycles and their characteristics, accumulated fatigue deformation of the plate and its life before the critical state in order to optimize planned repairs and reducing the risks of unpredictable failures associated with fatigue phenomena in the skin material and supporting structures of the aircraft.Methods. The described mathematical model uses the parameters of a harmonic vibration signal as input data and includes a two-stage transformation, firstly, of the parameters of the vibration signal (frequency, amplitude) into the amplitude of the vibration vibrations of the aircraft skin element made in the form of a plate, secondly, the amplitude of the vibrations of the plate in question into a change in the wavelength of the optical signal, the presence of which is caused by the use of fiber-optic technologies that are promising for the construction of modern systems for monitoring and diagnostics of aircraft.Results. The proposed mathematical model allows calculating and analytical methods to estimate the amplitude of forced vibration vibrations of the aircraft skin element, which causes the absence of plate resource consumption due to the effects of loading cycles (there is only natural aging of the material), plate resource consumption in elastic deformation mode, accumulation of fatigue deformation of the sample. The method of evaluating the plate for the resonant effect is given, which indirectly affects the processes of designing the elements of the aircraft skin in terms of weight and size indicators, which largely determine the frequency of natural vibrations of the plate. The resulting deformation of the plate is expressed in a change in the wavelength of the light beam for detection and analysis by the control and diagnostic system of the aircraft, made on the basis of fiber-optic technologies.Conclusion. The proposed mathematical model is designed to assess the residual life of a specific element of the aircraft skin, involves subsequent software modeling to confirm the correctness or refinement of the resulting calculation algorithm.