Study On Dynamic Behavior Of A Class Of Nonlinear Coveyer Belt Impact-friction System Under Different Constraint

Scholars have a long history of studying the vibration system with gap coupling,and the conveyor belt model is also one of the traditional research models studied.The former is non-smooth due to collision factors,while the latter is non-smooth due to friction.And the non-smooth dynamical systems are universal in daily life and various research fields.Therefore,more and more scholars begin to study the dynamical models containing both friction and collision.The most commonly used analysis methods are: Filippov convex method,the G function theory,and so on.The relatively advanced simulation methods are: path tracking method and cell mapping,and so on.This paper tries to combine Filippov convex method and G function theory to construct a new method,and then use new methods to study specific dynamical models.Filippov convex method and G function theory have advantages and focus in studying collision-friction systems.Filippov convex method mainly studies sliding bifurcation when discussing collision-friction system,but because the theoretical analysis is difficult,it is realized by simulation and continuation.G function theory can be used to carefully discuss the transformation of the specific moving state of the oscillator and the existence conditions of the periodic motion of the oscillator,the local stability and so on.By introducing the concept of G function in the Filippov convex method,our new method can not only obtain the advantages of the original two research methods,but also can obtain the conditions of special periodic solution that containing bifurcation points faster and more accurately.Then,we can conduct the simulation and continuation of sliding bifurcation.Using the new method,the single degree of freedom conveyor belt collision-friction system with rigid or elastic constraint is analyzed,and the main researches include:1.The switching conditions of motions of the single-degree-of-freedom belt collision-friction system with unilateral rigid constraint under the new method are discussed and verified numerically.The mapping structure of vibrator motion and all possible periodic motions of vibrator are discussed and corresponding conditions are given.The special periodic motion with sliding bifurcation points is directly located by the new method and corresponding conditions are given.On this basis,the one-parameter and two-parameter numerical continuation is carried out to find the influence of each parameter on the motion state of the oscillator.2.The switching conditions of motions of the single-degree-of-freedom belt collision-friction system with unilateral elastic constraint under the new method are discussed and verified numerically.The switching condition of vibrator motion at the intersection point(d,V)of the discontinuous boundary is discussed,and the mapping structure of vibrator motion and all possible periodic motions of vibrator are discussed and corresponding conditions are given.The special periodic motion with sliding bifurcation points is directly located by the new method and corresponding conditions are given.At the same time,numerical continuation is carried out on this basis to find the influence of each parameter on the motion state of the oscillator.