Reasearch On Nonlinear Dynamics Of Beam-Slider Structure

In the last decades,the studies on the nonlinear structure were developed rapidly,which also thrived the application widely in vibration suppression and energy harvesting.However,the frequency response function of the nonlinear structure may be a multi-value function.For a given frequency,there coexist multiple energy orbits corresponding to different vibration states of the structure.In reality,for the specific requirements of the application,it is often hoped that the nonlinear structure can maintain the vibration state on the desired energy orbit.At present,the active and semi-active methods are mostly used for obtaining the certain energy orbit by researchers in global.But it is inevitable to increase the complexity of the system significantly.Furthermore,these methods lacking the theoretical quantitative analysis cannot supply a control algorithm quantitatively.In the beam-slider structure,there is a distinctive coupling between the beam vibration and slider movement.If the coupling is engaged properly,the modulation of the parameters can be realized in a passive way.When the beam in the structure is nonlinear,the movement of the slider can even help it capture the high-energy orbit.To investigate the dynamics of the beam-slider structure comprehensively and draw out a quantitative method for obtaining the desired energy orbit of the nonlinear structure,the works in this thesis are carried out as below:First,the dynamics of the clamped-clamped beam-slider structure are investigated in this thesis.Through the theoretical modeling,numerical simulation and experiments,the results reveal that the nonlinearity of the beam in this structure broadens the resonant bandwidth of the structure and the movement of the free movable slider assists the nonlinear beam obtain the high-energy orbit.However,the vibration state on the high-energy orbit is not reliable.The disturbance can make it jump to the low-energy orbit easily.To address this issue,the clamped-clamped beam-slider structure is improved by introducing a small inclination angle.As a result,the movement of the slider also depends on gravity apart from the inertial force,which enhances the correlation between the moving direction of the slider and the vibration state of the beam.Ultimately,the movement of the slider not only helps the nonlinear beam capture the high-energy orbit but also makes the vibration state on the high-energy orbit anti-interference.Second,the clamped-clamped beam-slider structure is further improved to overcome the drawback that the nonlinearity of the structure is not adjustable.The clamped-clamped beam in the structure is replaced by a cantilever beam with two magnets fixed at the free end.The appropriate axial repulsion between the magnets enable the beam obtain the hardening nonlinearity.The piezoelectric element that can transfer the kinetic energy to the electricity is attached on the clamped side of the beam to achieve vibration energy harvesting.After the improvement,the results of simulations and experiments agree well.It indicates that the nonlinear cantilever beam-slider structure can ensure that the energy harvester has advantages of broadband,high efficiency,and anti-interference.The overall performances of the structure significantly exceed the linear beam-slider structure and nonlinear beam with fixed slider structure.Third,the effects of different parameters including mass ratio,nonlinearity,and natural frequency ratio of the nonlinear dynamic vibration absorber on the vibration suppression bandwidth of the primary structure are analyzed comprehensively.The results show that compared to the changes in these parameters,the different vibration states on different energy orbits have a stronger influence.When the nonlinear cantilever beam-slider structure is applied as the vibration absorber,the theoretical analysis and the experiments verified that the nonlinear beam can obtain the high-energy orbit passively even in the tow-degree-of-freedom system and the vibration suppression are improved significantly.Finally,after the essence of the slider helps capture high-energy orbits is revealed and considering the process of the sweep frequency excitation for obtaining different energy orbits,a Duffing oscillator model with time-varying parameters is established to explore the in-depth theoretical mechanism of these methods quantitatively.The harmonic balance method,multiple scales method and 4th Runge-Kuta numerical method are used to solve the time response of the oscillator.The results show that when the parameters such as excitation frequency,linear stiffness or mass of the structure change,both the response of the oscillator and the basin of attraction will change accordingly.Whether the nonlinear system can finally obtain the high-energy orbit depends on whether the phase trajectory of the oscillator is always maintained in the basin of attraction of the high-energy orbit.Furthermore,a method of temporary modulation of the natural frequency is proposed for obtaining the high-energy orbit in a specific frequency range.Quantitative analysis of the temporary linear stiffness modulation and mass modulation based on this method are carried out,which provides a reliable theoretical support for the nonlinear structure obtaining the certain energy orbit in practical application.