| The study of nonlinear vibration involves not only mathematics and physics,but also engineering practice and scientific research.The complex phenomena exhibited in nonlinear vibration systems have always been a hot topic of research,and these phenomena have many potential research implications in various disciplinary fields.The main purpose of this thesis is to explore the application scenarios of nonlinear vibration theory and the common synchronization behavior in nonlinear vibration systems through a combination of theoretical deduction and experimental research.The main content includes two basic experiments,one to study the vibration of guitar strings near the resonance frequency and the other to study the frequency and phase characteristics of synchronized candles.In the experiment of string vibration,two different types of vibrations can be observed: one-dimensional planar vibration and two-dimensional non-planar vibration.For planar vibration in the force plane,this thesis explains the experiment from the perspective of solving the linear vibration equation.For the non-planar vibration that appears in the experiment,the thesis first derives two different nonlinear vibration equations in two directions,namely,the two-dimensional nonlinear vibration equation.Considering the coupling between the two directions of vibration,the approximate solution of the transverse vibration is obtained by seeking the intrinsic connection between the square coupling force and parameter resonance,explaining the reason for the appearance of transverse vibration.Finally,under the condition of variable equivalent damping coefficient,the relationship between frequency and amplitude is given,and the reason for the formation of stable vibration is explained.In the experiment of candle burning,the method of spectrum analysis was used to analyze the candle oscillator,and the spectra of various oscillation structures were obtained,confirming that the flame vibration of the candle oscillator belongs to typical nonlinear vibration.Then,the experiment was designed to explore the formation process of the candle oscillator and its frequency change relationship.Finally,the synchronous in-phase and synchronous anti-phase vibrations that occur when two identical coupled candle oscillators were investigated in combination with experiments. |
