TRANSVERSE VIBRATIONS OF A BEAM WITH FREE EDGES ON AN ELASTIC BASE UNDER DYNAMIC LOAD

Abstract

It is known that in the case of dynamic influences, the important dynamic characteristics of the structures of a structure are the frequencies and forms of natural vibrations, with which its response to dynamic effects is associated. These structures include structures lying on the ground, which can be considered when calculating them as beams on an elastic foundation. Using the method of initial parameters for a beam with free edges located on an elastic base, the problem of determining the influence of the attached mass m1 on the circular frequency of natural transverse vibrations (without taking into account the resistance forces) is solved, the first three frequencies and forms of natural transverse vibrations of the beam are determined. The problem of determining the efforts in the beam, taking into account its own weight and dynamic load (perturbing force) F (t), with the frequency of forced vibrations corresponding to the resonance and interresonance zones applied at an arbitrary point d, was solved. The conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the action of variable loads in various design situations.