Experimental Study On Nonlinear Dynamic Behaviors Of Elastic Plate In Granular Media

The macroscopic movement of particulate matter presents abundant nonlinear characteristics,which result from the collision and friction between the particles.It also makes the interaction between particulate matter and elastic structure show strong nonlinear dynamic characteristics.At present,the research about nonlinear dynamic behavior and coupling effect of elastic structure in granular medium has just begun.Relevant work mainly concentrate on the physic-mechanical characters and movement behavior of granular systems,which is under the effect of motion structure,but hardly study the nonlinear dynamic behavior of elastomer under the effect of dynamic coupling of structure and granule.This kind of problem widely exists in the engineering,so we need to do corresponding physical experiment and acting mechanisms research.This paper takes the square plate with two opposite edges simply supported and other two free which is under harmonic excitation and buried in the glass particles as the object of the research,and studies nonlinear characteristic of the plate’s vibration inside particle medium based on the strain measurement technology.Excitation strategies such as constant amplitude variable frequency sweep and constant frequency variable amplitude sweep are adopted during the process of test.The jump phenomena in amplitude-frequency and phase-frequency are found in the research,and also the period doubling bifurcation and chaos of the nonlinear strain response are found.On basis of principle of fiber brag grating sensor testing technology,the method of space surface reconstruction is introduced,plate’s vibration shape before and after jump phenomena are obtained.The main works of this paper are:1.In the vicinity of the plate’s low-order natural frequency,the plate’s jump phenomena in particle medium is studied by a sinusoidal excitation method of constant amplitude variable frequency sweep and constant frequency variable amplitude sweep considering parameter such as the diameter of the particle,the depth of granular layer,the exciting position,the amplitude and frequency of exciting force.The jump phenomena in amplitude-frequency and phase-frequency are found in the experiment.The experiment’s results show that,in the vicinity of different resonant frequency,the plate’s amplitude frequency curve behaved like‘soft feature’ and ’hard feature’ which is more remarkable when the diameter of particles is smaller.With the amplitude of force increasing,the amplitude of jump is increasing and the frequency of jump doesn’t change.Under the certain depth,the number of resonance peak is in relation to the route of frequency sweep.2.The bifurcation and chaos phenomena of the plate’s vibration inside particle medium are studied by a sinusoidal excitation method of equivalent vibrating frequency and different vibrating force considering parameter such as the diameter of the particle,the depth of granular layer,the exciting position,the amplitude and frequency of exciting force.The experiment data is analyzed by using phase diagram,Poincare map,Lyapunov exponent and power spectrum.The analysis shows that the vibration of the plate buried in the particle medium goes through bifurcation to chaos as the vibrating force becomes larger.Typically,the bifurcation path of the beam is 1P→2P→4P(8P)→chaos which is more remarkable when the diameter of particles is smaller and the depth of granular layer is thicker,and the active band of doubling bifurcation and chaos is 200-300Hz.3.On basis of principle of fiber brag grating sensor testing technology,the method of space surface reconstruction is introduced,the plate’s vibration shape before and after jump phenomena are obtained from the transformation of strain-displacement.The results show that,after the first jump,compared with the shape of plate exposed to the air(empty plate),the shape of the oscillating plate changes and the line of mode shape appears.After the first jump,the line of linear peak’s mode shape move to the center of the plate and the shape is similar to the second mode shape of empty plate.Compared with the shape of empty plate,the mode shape of the second jump and the next linear peak change a little.