Research On Dynamic Characteristics Of Nonlinear Coupled Vibration System Granular Materials Under Unilateral Vibration

With the development of the treatments of granular materials toward high efficiency,intelligentialize and energy saving and emission reductio,current unloading equipments can't meet the stable and automated unloading to some extent,and the unloading equipment easily occurs locally abnormal vibration,fatigue wear and a certain degree of damage of granular materials caused by the discontinuous and stochastic friction and collision between granular materials and vibration unloading surface,high dust,high noise and other complex and changeable working environment.Besides,due to the nonlinear vibration of unloading equipment and nonlinear characteristics of granular materials,the motion state of granular materials becomes a little more complex.A novel design of unilateral vibration vehicle-vibration platform coupled system is presented,and the operating performance directly affects the unloading efficiency and flow characteristics of the granular materials.Therefore,it is necessary to analyze the dynamic properties of granular materials under nonlinear vibration condition and nonlinear dynamical characteristics of local and overall structure for the unilateral vibration vehicle-vibration platform-granular materials coupled system,which can explore the flow regularity of granular materials,develop vibration flow aiding mechanism,estimate the complex nonlinear vibration of the unloading equipment and reveal the interaction between mechanical system and granular materials.Taking the dynamic characteristic of nonlinear coupled vibration system granular materials under unilateral vibration as a research object,based on Lagrange's equation and Euler beam theory,the local dynamic models(vibration platform system with intermediate nonlinearity support and geometric nonlinearity,a unilateral vibration vehicle system with square and cubic nonlinearities)and overall dynamic models(unilateral vibration vehicle-vibration platform coupled system,simplified unilateral vibration vehicle-vibration platform-granular materials coupled system)of the coupled are established.The numerical integration method(Newmark-? method),semi-analysis and semi-numeric method(modified incremental harmonic balance method)and experimental verification are used to investigate local and overall nonlinear dynamics simultaneously,the mechanism of vibration generation and the propagation rule and nonlinear dynamic behaviors with the influences on the dynamic parameters and structural parameters.On the basis of the interaction between granular materials and combination with the slippage theory,the discriminate condition of motion state of granular materials relative to the nonlinear vibration unloading surface and the transformation discriminate condition among each motion state are further investigated.The main research results are as follows:(1)The incremental harmonic balance method(IHBM)is modified by arc length extension technique,which can be used to more quickly and accurately obtain arbitrarily approximate analytic solution,the contribution of each harmonic to nonlinear vibration and the dynamic performances of primary resonance and super-harmonic resonance.Taking a 2-DOF nonlinear vehicle system with square and cubic nonlinearities as an example,the correctness and veracity of modified IHBM are verified by Newmark-? method.(2)Based on Lagrange's equation and Euler beam theory,the continuous equations of the vibration platform system considering intermediate nonlinearity support and geometric nonlinearity are derived,which is dispersed by Galerkin method.Through the experimental verification,the bifurcation law,vibration response characteristics and resonance mechanism are studied with different system parameters,in order to further reveal the nonlinear dynamics of the vibration platform.It can be found that the increasing excitation amplitude and staying away from the middle position of nonlinear support make "increased stiffness" effects to vibration system in the primary resonance region,which have a theory guidance to structural parameter design and dynamic control of the vibration platform.(3)The global bifurcation and resonance mechanism of the unilateral vibration vehicle system with square and cubic nonlinearities are investigated.With increasing dynamic parameter,the jump discontinuous phenomenon and intermittency chaos enhance,the resonant hysteresis region broadens near primary resonance region and the softening nonlinear behavior strengthen in super-harmonic resonance region.As the suspension nonlinear stiffness increase,the unstable region widens,intermittency chaos gradually fades out and the critical excitation frequency of occurring continuous chaotic motion moves backward gradually.The amplitude-frequency curves move to the right,the hardening nonlinear behavior enhances in primary resonance region and the softening nonlinear behavior weakens in super-harmonic resonance region.(4)The mathematical model of the unilateral vibration vehicle-vibration platform coupled system is established by combining the equations of motion both the unilateral vibration vehicle and vibration platform using the displacement relationship and interaction force relationship at contact points,the nonlinear vibration responses and stable/unstable region of the approximate analytical solution are studied with the influence of different parameters.As a results,the unstable region widens firstly and then narrows,the hardening nonlinear behavior reinforces in primary resonance region and the softening nonlinear behavior weakens in super-harmonic resonance region with increasing excitation amplitude.Increasing inclined angle can induce the super-harmonic resonance,and larger residual mass ratio can decrease nonlinear resonance.(5)Based on the interaction between granular materials and combination with slippage theory,the discriminate condition of motion state of granular materials and the transformation discriminate condition among each motion state are analyzed under nonlinear coupled vibration system.As the inclined angle and friction coefficient to change,the granular materials exhibit different motion states:relative rest,unidirectional sliding,relative forward sliding-relative backward sliding,relative forward sliding-relative backward sliding-a single relative rest and relative forward sliding-relative backward sliding-multiple relative rest.In addition,the sliding "sluggishness" weakens with increasing inclined angle and decreasing friction coefficient at a certain excitation frequency.The studied results can give a theory guidance to further understanding flow characteristics of granular materials under nonlinear vibration and dynamic behaviors of the unilateral vibration vehicle-vibration platform coupled system.