Simulation of beating modes during the rotary-oscillating movement of complex aerodynamic engineering with determination of the conditions of their occurrence

Abstract

The aim of the article is to determine the conditions of occurrence of beating modes in a nonlinear high-order dynamic system with subsequent computer simulation of these modes. Methods of research of nonlinear oscillatory systems are applied with consideration of two cases of interrelation on rotation (weak and strong) between oscillatory circuits.

In the first of them, the conditions for the existence of beating modes are approximately the same values of the partial frequencies of longitudinal and lateral oscillating motions with a constant increase in the modulus of the phase shift between these oscillations (phase motion is unstable).

At strong forces of interconnection (coefficients of interrelation of various signs) modes of beating arise at close values of sizes of the main frequencies of the interconnected fluctuations lying in a range between partial frequencies. Such modes (in the absence of parametric interaction between the circuits) are possible when the conditions of stability of the biharmonic process are observed.

The study of the complex form of rotational-oscillating motion of an aerodynamic object at the initial stage includes the selection from the complete dynamic system of two interconnected self-oscillating contours of longitudinal and lateral motions as a basis (necessary conditions) for the existence of beating modes.

In cases of observance of existence conditions of single-frequency self-oscillating processes at occurrence of parametric interaction these processes can also pass to beating modes.

In practice (outside the resonant region of the main frequencies) this is often realized when the functional frequency of the contour of lateral motion includes components proportional to the parameters of longitudinal motion.

All these cases are supported by numerous model experiments.