Determining the influence of higher harmonics of nonlinear technological load in dynamic action systems

Abstract

This paper considers the influence of higher harmonics in dynamic action systems due to their complex movement in the process of interaction with the technological load. The object of research is the process of propagation of oscillations in complex dynamic systems. One of the problems in the application of oscillatory processes is the consideration of higher harmonics in the overall movement of systems. To solve the problem, the idea of using a hybrid model that takes into account both discrete and distributed parameters was proposed. The resulting mathematical discrete model in the analytical equations of motion of the dynamic system preserves continuous properties in the form of wave coefficients. These coefficients in their analytical form take into account the contribution of higher harmonics of both the reactive (elastic-inertial) and active (dissipative) components of the resistance force. The studies were carried out on a model of a plant with a multimode spectrum of oscillations and a nonlinear dynamic system, which is a system with piecewise linear characteristics.A series of experimental studies with a wide variation of the change in the frequency of oscillations was carried out on the installation with a multimode spectrum of oscillations. Zones of manifestation of higher harmonics along the vertical axis of force action were revealed. The given spectrum at the exciter frequency of 35 Hz showed the manifestation of the spectrum component (around 70 Hz) along the X axis, which is an important result for practical application. For a system with piecewise linear characteristics, the manifestation of multimode, which manifests itself in the form of subharmonic and superharmonic oscillations, was determined. The contribution of each harmonic is determined by applying the obtained dependences. The results were used in the development of algorithms and calculation methods of a new class of dynamic action systems taking into account the contribution of higher harmonics