Abstract
Chaotic vibrations in elastic mechanical systems are not stationary. In the considered case a transient induced vibration is discussed. Here the energy is concentrated in different varying frequency ranges. This contribution considers an experimental investigation of jumping phenomena in this system under chaotic vibrations, driven by cart under harmonic excitation. Using this system, the data of jumping phenomenon during the chaotic vibration are collected and analyzed. Here, time-frequency energy method can effectively show the characteristics of energy in time domain and perform the component analysis in specific frequency range. Applying a comparative study of jumping phenomenon discussing different equilibria, frequency range recognition, and energy characterization, the jumping phenomenon of the pendulum signal induced by chaotic vibration is characterized. A state transition model is established. Further, an additive impulsive control on the elastic system is considered to validate the model.
Highlights
Time and frequency domain analysis are two signal processing methods widely used for vibration analysis
The chaotic vibration of this elastic mechanical system is transient, so the energy is concentrated in different frequency range which vary
The authors experimentally explored and analyze the behavior of jumping event during chaotic vibration of the inverted flexible pendulum system subjected to harmonic excitation
Summary
Time and frequency domain analysis are two signal processing methods widely used for vibration analysis. As a popular example of a nonlinear system, an inverted flexible pendulum subjected to harmonic excitation is experimentally analyzed. The authors experimentally explored and analyze the behavior of jumping event during chaotic vibration of the inverted flexible pendulum system subjected to harmonic excitation. To define the different state of chaotic jumping, the experimental data will be analyzed in order to characterize the behavior of jumping between multiple equilibria by energy/power content in a specific frequency range, and states transition of the chaotic jumping. The experimental results of chaotic oscillations observed are presented in time behavior representation as well as 3D spectrogram and discussed in detail, concentrating on how signal energy/power changes in different frequency ranges during pendulum’s chaotic vibration, and how these take place upon. The research question is related to suitable characterization of the jumping phenomena, during the transition between different states of equilibria
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