Nonlinear Hybrid Control Of Elastic Beam Based On Time Delay Technology And Energy Sink

With the development of modern materials and construction technology,modern bridges possess the advantages of large span,strong flexibility,light weight and low damping.In recent years,the national infrastructure construction has been continuously strengthened,and amount of large-span bridges has also increased.However,due to its low damping and large flexibility,it is prone to large vibrations under the action of earthquakes,vehicles,wind and rain.Therefore,the vibration control of long-span bridges has become an urgent problem in practical engineering applications.Time-delay damping technology and nonlinear energy sink are popular vibration control methods in recent years.They have attracted widespread attention due to their advantages such as real-time feedback,strong tunability,robustness,and bandwidth of working frequency.In this thesis,based on the hybrid control of time-delay feedback technology and nonlinear energy sink,the nonlinear resonance response of elastically supported beams is studied.The specific content is as follows:1.Based on the nonlinear energy sink control strategy,a nonlinear dynamic model of a single-degree-of-freedom Duffing vibrator coupled with the nonlinear energy sink is established.Through numerical simulation,the dynamic response of the controlled vibrator under different parameters is analyzed.Based on the Hamilton principle,the nonlinear vibration control equation of the elastic support beam is established,the Galerkin method is used to discretize the motion equation,the time history curve and energy graph of beam under different nonlinear energy sink control parameters is obtained through numerical integration and energy method.2.Research on hybrid control mechanism of time-delay damping technology and nonlinear energy sink.A single-degree-of-freedom Duffing vibrator dynamic model under hybrid control is established,and the nonlinear main resonance and 1/3 subharmonic resonance response of the vibrator under dual-frequency excitation are solved by the multi-scale/harmonic balance method.Through theoretical analysis and numerical simulation,the influence of different control forms and parameters on the vibration reduction effect is studied,and the hybrid control vibration reduction mechanism under the action of displacement and velocity time delay feedback is further contrasted and analyzed.3.Vibration control analysis of elastic support beam under hybrid control of time-delay damping technology and nonlinear energy sink.A motion model of elastic support beam coupled with time-delay feedback control and nonlinear energy sink is established,the multi-scale/harmonic balance method is used to analyze the main resonance dynamic response of the beam under hybrid control,and through numerical simulation,the influence of each parameter on the nonlinear response of the beam is analyzed,and the vibration reduction mechanism of the elastic support beam under the action of hybrid control is revealed.