Research On Sticking Vibration And Bifurcation Characteristics Of Vibro-impact System

The reserarch on the vibro-impact problems has important significance in the dynamical optimization design of mechanical system with clearance and dynamical analysis of the high-speed train. The vibro-impact systems generally have the following feature as multi-parameters, high-dimensional and strong non-linearity, so the parameter variation will cause the change of dynamics constitutionally and its dynamical performance will directly affect the overall function and performance of the system, which is the key factor to determine whether the system can operate safely, efficiently and harmoniously or not. Given a large number of practical engineering problems, deeper and more comprehensive understanding of dynamical behavior of vibro-impact system helps to improve the effectiveness of our work and to reach the anticipated goal. Furthermore, in order to optimize the parameters and dynamically design the system, it is very necessary to understand the correlative relationship and matching law between the dynamic characteristics and the parameters. Therefore, the study of vibro-impact systems not only have theoretical significance, but also have important value for engineering application. The main respects of the research are followings:（1） Two-degree-of-freedom vibro-impact system with symmetrical rigid constraints is considered. The influence of each parameter on the impact sequences and the sticking times of 1-（?）-（?） complete chatting-impact motion in a motion period is discussed. Taking the criterion parameters, existence regions and distribution laws of different types of periodic motions of the system are obtained in the （ω,δ）-parameter plane based on bifurcation analysis of two-dimensional parameters, and the mutual transitions between 1-p-p（p≥0） motion and 1-（p+1）-（p+1） motion, between 1-（?）-（?） incomplete chattering-impact motion and 1-（?）-（?） complete chatting-impact motion are studied. Based on the transition irreversibility of adjacent fundamental motions, a series of singular points and two types of transition regions, named hysteresis region and tongue-shaped regions on the boundary between adjacent regions of 1–p–p and 1–（p+1）–（p+1） motions are studied. The singular point is the point of intersection of four bifurcation boundaries. Attractors can coexist in the hysteresis region. Periodic motions in the tongue-shaped regions present diversity and regularity. Based on the two-dimensional parameters bifurcation, the influence of variation of parameters on existence regions, distribution laws and impact velocities of different types of periodic motions is analyzed.（2） Two-degree-of-freedom vibratory system with plastic impacts is considered. Taking the criterion parameters, existence regions and distribution laws of different types of periodic motions of the system are obtained in the（ ω,δ）-parameter plane based on bifurcation analysis of two-dimensional parameters. The transitions from 1/n （n=1,2,3,4） motion to 1/（n+1） subharmonic motion and two types of non-smooth bifurcations, including Sliding bifurcation and Grazing bifurcation, are cxamined. Based on the transition irreversibility between 1/0 and 1/1 motions, a series of singular points and two types of transition regions, nameed hysteresis region and tongue-shaped regions on the left boundary of existence region of 1/1 motion are studied. 1/n（n≥2） subharmonic motions dominate in the tongue-shaped region.（3） A dynamical model of a small vibro-impact pile driver with oscillatory and progressive motions is established, and the conditions for judging sticking or non-sticking progressive motions of the system are put forward. Based on bifurcation analysis of two-dimensional parameters, existence regions, distribution laws and bifurcation characteristics of different types of periodic motions of the system are obtained in the low coefficient of restitution and a plastic impact case, the periodic motion forms and parameter reasonable matching corresponding to the the maximum progression is ascertained. two types of non-smooth bifurcations, incuding sliding bifurcation and grazing bifurcation, are examined in a plastic impact case. In the low coefficient of restitution case, transitions laws between two types of adjacent fundamental motions are studied, and the occurrence mechanism of fundamental motion, incomplete chattering-impact motion, complete chatting-impact motion and their influence on the progression rate of pile driver are studied. In a plastic impact case, the progression of （?）/1 motion is far better than that of other periodic motion. In an elastic impact case, the chattering impacts finally bring out the sticking progressive motion of a driver and a pile, and the best progression of a pile is achieved in the region of low forcing frequencies. In a finite time, the largest progressions in two different impact cases are almost equal, however, it is important to note, that the progression in the plastic impact case is more effective for practical engineering application.（4） A dynamical model of a small vibro-impact pile driver with viscoelastic properties of pile cushion and soil is established. The motion state presented probably by the system between two consecutive impacts and its conditions of judgment are put forward. The system equilibrium is vibrating and moving downwards of the components, the impact velocity and the progression of 1/1 motion is far better than that of other periodic motion. The best progression of 1/1 motion occurs near the peak value of the impact velocity of the vibration generator M₁. Based on bifurcation analysis of two-dimensional parameters, existence regions, distribution laws and bifurcation characteristics of different types of periodic motions of the system are obtained. The mutual transitions between two adjacent fundamental motions and bifurcation characteristics of 1/n （n=2,3,4）subharmonic motions are analyzed. The singular points and two types of transition regions, named hysteresis region and tongue-shaped regions on the boundary between two types of adjacent fundamental motions are studied. in the tongue-shaped region, the system exhibits （2p+2）/2 and （2p+1）/2 motion. Based on the two-dimensional parameters bifurcation, the influence of variation of parameters on existence regions, distribution laws, impact velocities and progression rate of pile driver of different types of periodic motions is analyzed.