Variable Cross-section Simply Supported Beam Subject To Rigid Block Multiple Impact Dynamic Response

The multiple elastic-plastic mini impacts is a complex mechanics phenomenon relating to the dynamic mechanic capability of the material, the transmission of the elastic-plastic stress wave and the plastic dynamic response of the structure. The structure with variable cross-section has been increasingly applied to aviation, aerospace, mechanical and transportation. Meanwhile, its elastic-plastic dynamic response by the impact of the mass has become the focus of many fields.This paper has modified and used the Winkler model to simulate the local contact between a mass and an elastic-plastic simplely supported beam. The relationship between the impact force and the indentation in the process of loading and unloading is obtained. Dynamic equations of the beam are dispersed in space. Combining dynamic equations of the mass and using the time difference method, the dynamic response of the variable cross-section beam is educed.By researching the dynamic response of the beam with variation in width and the one with variation in height, it concluded that the variation of width and height not only affects the amplitude of the impact force, but also affects the starting and ending time and the duration of the impact cluster. Meanwhile, the variation of the cross-section in width and height has significant effect on the distribution of the moment and the deflection of the beam and on the displacement and the velocity of the mass. In addition, to the simple beams with equal sectional area but different sectional shape, the distribution of the moment and the deflection of the beam and on the displacement and the velocity of the mass are different.