Determination of frequency of free vibrations of hard foundation on the resilient founding under the action of impulse of explosion

Abstract

The aim of the research was to create reliable methods for calculating foundations that ensure the safe operation of stamping parts using shock-impulse loading (electro-hydraulic shock, explosive loading, pneumatic and static-dynamic shock). For calculation, we consider a foundation located on the surface of an elastic base and loaded with an asymmetric load P (r, t). Considering the foundation to be rigid, a differential equation for the movement of the foundation without vibrations is obtained. Further, we assume that there is no horizontal displacement, then this assumption and the asymmetric nature of the problem make it possible to use the variational solution method. This allows you to write a differential equation, then the oscillatory motion of the elastic base under load is equal to the magnitude of the reaction of the soil located under the foundation. The obtained equation describes the movement of the elastic element outside the base and allows you to take into account the influence of the elastic and inertial forces of the soil in this area on the parameters of the movement of the foundation.
It is assumed that the vibrational shape of the elastic base corresponds to a static draft. A general solution of the oscillation equation is obtained in the form of a modified Bessel function. Having completed the necessary transformations, we find that under the action of an instantaneous impulse, a rigid foundation on an elastic base performs harmonic oscillations with a circular frequency. To calculate the coefficients, you must know the nature of the movement along the depth of the base. The expressions obtained in the article for determining the frequency of free vibrations of a rigid foundation on an elastic foundation under the influence of pulsed loading allow us to solve a number of problems in choosing the modes of foundations of technological installations for shock- pulse loading carried out by the explosion energy in a hydraulic medium.