Forced vibrations of a box element of a multi-story building under dynamic impact

The article is devoted to the dynamic calculations of the elements of the box-shaped structure of buildings for seismic resistance, taking into account the spatial work of the elements of the box under the action of dynamic influences set by the movement of their lower part according to the sinusoidal law. The equations of motion are given for each of the plate and beam elements of the box-shaped structure of the building on the basis of the Kirchhoff-Love theory. Expressions are given for the forces, moments and stresses of the plate elements that equalize the movement of the box elements, and the boundary conditions, as well as the conditions for full contact in terms of displacements and force factors in the contact zones of plate and beam elements. The general solution of the problem is constructed by the method of decomposition of the movement of the elements of the box according to their own forms using the method of finite differences. The calculation results were obtained in the form of diagrams over the height of the box of bending moments, plate elements working in bending, as well as shear stresses of plate elements.