Dynamic loading of the beam on the Pasternak base initiated by the sudden settlement of part of the base

Abstract

Abstract The article presents a methodology for the analytical assessment of the dynamic loading of a beam based on a mathematical model of a transient dynamic process in a loaded structure resting on an elastic two-parameter Pasternak base, initiated by sudden settlement of a part of the base. Determine that the sudden formation of a defect leads to a decrease in the overall rigidity of the structure and a violation of the static balance of the beam-base system. The arising inertia forces cause a dynamic response, redistribution and growth of deformations and stresses. As a result, there may be a violation of the regular functioning of the structure, loss of bearing capacity and destruction. From the standpoint of structural mechanics, the problem boils down to an analysis of the manifestations of structural nonlinearity of a loaded elastic system. It is shown that the factor of sudden formation of a defect significantly increases internal forces compared with the quasistatic formation of the same defect. It is also shown that taking into account the Pasternak parameter reduces (compared with the one-parameter Winkler base) the level of dynamic bending moments during sudden partial destruction of the base.