Abstract: Characteristic which a contain with a hopper filled with powder food is subjected vertical vibration is investigated. The powder food in the contain is divided into layers of the same mass, assuming each two adjacent layers connected by a spring and a frictional damper and the bottom of the contain subjected a vertical vibration. Vertical vibration of cohesion powder foodsystem is modeled as vibrator-spring-damper system. Choosing displacement of each layer regard as generalized coordinates of the system, Lagrang’s equations of the system are established. Furthermore, the methods of determination of parameters of the model are given, criterion for arch destruction during vertical vibration is derived. The numerical results of calculation of the model are given and are compared with the test data by Ge et al. The numerical results agree with the test data. The numerical results show the system possesses a resonant frequency, and during resonant vibration, the accelerations of layers of powder food are the largest. The numerical results also show during vertical vibration of the resonant frequency, the acceleration of each layer of powder food is not the same, and only when the layer that arch locate at vibrate in the largest acceleration the energy for arch destruction is the smallest.

Key words:  , powder food； contain with a hopper； arch destruction； vibration；