Dynamic response analysis of the vertical elastic impact of the spherical rock on the metal plate.

Highlights • Based on the Flores contact model, we establish the dynamic model of spherical rocks vertical impact on the metal plate with the considering the energy absorbed and consumed by the compression of the rock and energy absorbed by the bending deformation of the metal plate. • Based on the Drucker–Prager criterion, we obtain the function of maximum comprehensive stress ε 0 (α, μ 1) and deduced the initial yield stress and initial yield impact velocity for the consideration of principal stress σ2. • We propose the approximate theoretical formula of the maximum contact compression of spherical rocks based on recursive solution. Influence law of impact velocity, material parameters and structure size on the dynamic response of the impact system is obtained. • The combining simulation based on ADAMS and Hypermesh was used to verify the correctness of the theoretical model. Abstract In the process of top coal caving mining, the metal sheet of the tail beam of the hydraulic support will vibrate when coal and rock particles start to impact the tail beam. In the impact between the particles and the metal plate of finite dimension, there are many complicated problems such as short duration of impact, rapid enhancement of transient stress, local large deformation of particles and macroscopic deflection of the metal plate are involved. However, the analysis of the contact force between the spherical particles and other objects is still simplified to the ideal Hertz contact problem. In order to study the real contact states of coal and rock particles impact on the metal plate, we simplified the working conditions from the coal and rock particles impact the tail beam in top coal caving mining to the system that spherical particles have similar properties to coal or rocks impact vertically on the metal plate. Based on the Flores contact theory and the energy absorbed by the bending deformation of the metal plate, the contact model of spherical rock at the compression stage was established. At the same time, we researched the initial yield stress and initial yield impact velocity of spherical rock that obeys the Drucker–Prager (D–P) criterion and proposed the approximate theoretical calculation method of maximum contact compression of spherical rocks. In the range of elastic impact velocity, the influence of impact velocity, restitution coefficient, material parameters and structure sizes on the dynamic response of the system were also analyzed. Finally, the correctness of the theoretical model has been verified by the virtual prototype simulation combined by ADAMS and Hypermesh. The research will provide the basic theory reference for the recognition technology of a single particle of coal or rock that based on the impact vibration of the tail beam. [ABSTRACT FROM AUTHOR]