Vibration damping for the problems of aircraft motion

Vibration damping for the problems of aircraft motion

V. N. Azarskov, D. D. Gristchak



Two-step hybrid asymptotic method based on perturbation methods and phase integrals (methodWKB) is used to obtain approximate analytical solutions of the nonlinear problem of the vibrations ofthe aircraft near the rough surface, which reduces the need for the integration of singular nonlinear differentialequation with time-variable periodic coefficients for given initial conditions. This solution is notlimited to the value of the dimensionless amplitude of perturbations and the nature of the order non-linearrestoring force. The resulting solution has the form of the sum, where each term consists of two functionsaccording to the method of perturbation (in scalar parameter when the nonlinear component of the originalequation) and the WKB-approximation, effective in the integration of singular differential equations withvariable coefficients. For specific numerical results, a comparison with the data of direct numerical integrationof the equations of the original problem


Dynamics of the aircraft; a wavy water surface; the hybrid asymptotic approach; approximate analytical solution


Olkov. V. V. and Gusev, I. N. Disturbance methods in mechanics. Novosibirsk. Nauka. 1982. pp. 105-111. (in Russian).

Panovko, Ya. T. and Gubanova, I. I. Stability and oscillations of elastic systems. Мoscow. Nauka, 1964, 355 p. (in Russian).

Gusev, I. N. Disturbance methods in mechanics. Irkutsk, 1979. pp. 171–180. (in Russian).

Bolotin, V. V. Dynamic stability of elastic systems. Мoscow, Gostechizdat, 1956. 504 p. (in Russian).

Goloskokov E. G. and Phillipov A. P. Unstationary oscillations of deformable systems. Kyiv. Naukova dumka, 1977. 244 p. (in Russian).

Gristchak, V. Z and Kabak, V. N. “Double Asymptotic Method for Nonlinear Forced Oscillations Problems of Mechanical Systems with

Time Dependent Parameters.” Technische Mechanik, Band 16, Heft 4, 1996, pp. 285–296.

Gristchak, V. Z. and Ganilova, O. A. “Application of a Hybrid WKB-Galerkin Method in Control of the Dynamic Instability of a Piezolaminated Imperfect Column.” Technische Mechanik, no. 26(2), 2006, pp. 106–116.

Gristchak, V. Z. Hybrid asymptotical methods. Zaporizhzha: ZNU, 2009. 225 p. in