Research On Broadband Vibration Reduction Of Beam Structures Under Moving Load

This thesis uses a nonlinear energy sink(NES)to study vibration suppression of a simply supported beam under a single moving load,multiple moving loads,and moving oscillators.NES is a strongly nonlinear(cubic)oscillator with zero linear stiffness.Dynamic equations for these three models are established,which is followed by a non-dimensionalization procedure,and discretizing the dimensionless equations by Galerkin method.Then,by focusing on a properly designed energy dissipation index and using optimization algorithm,the optimal parameters for NES are found.Finally,in order to highlight superiority of NES,a comparison is made with the traditional linear tuned mass damper(TMD).Subsequently,the optimization diagram,timehistory responses,and time-frequency diagram of the beam-damper system are analyzed,fully revealing NES vibration suppression performance and leading to a relatively comprehensive framework for broadband vibration suppression of beam under moving loads encompassing single/multiple moving loads and moving oscillator.The research results of this thesis are summarized as follows:(1)Sensitivity analysis is used to optimize the parameters of NES and TMD,and determine the parameters of the optimized damper.In the initial stage of transient response,NES/TMD transfers some energy from the low order mode of the beam to the high order mode.Under single moving load excitation at different speeds(or frequencies),linear dampers(TMD)or nonlinear energy traps(NES)exhibit excellent vibration suppression effects.Because the displacement response of the beam is significantly reduced by connecting linear/nonlinear dampers,and the performance of NES is better than that of TMD,while the nonlinear energy well has strong robustness to changes in moving load frequency.(2)While the other parameters of NES remain unchanged,the stiffness value of the optimized NES shows a negative correlation with the number of moving loads.Detailed time-frequency analysis demonstrates that,NES generates more frequency components in the initial stage of response than TMD,but the frequency components of NES are damped out in a shorter period of time.The resonant coupling between the beam and NES occurs over a wider frequency range,which allows oscillating energy of the beam to be transmitted to the dampers(NES)and ultimately dissipated through the NES.NES can absorb and dissipate the energy generated by the main beam over a wide frequency range,but TMD can only reduce vibration within a specific frequency range.(3)Under the excitation of moving oscillators with low speed,resonance speed,high speed(or frequency),additional linear dampers(TMD)or nonlinear energy traps(NES)can not only reduce the dynamic response of the main beam,but also have a good vibration reduction performance on the vehicle,and the performance of NES is better than that of TMD.When a beam is attached with a damper,the beam generates more frequency components in the initial stage than the case without a damper,with the frequency components of the beamNES system disappearing faster than its counterpart using a linear TMD.For the time-frequency analysis of the vehicle,when dampers(NES and TMD)are added,another frequency band arises near zero-frequency(the frequency band associated with NES disappears faster than TMD).NES and TMD mainly capture the vibration energy of the main beam through 1:1 resonance,and the resonance capture ability of NES is significantly stronger than that of TMD.