Abstract
The paper presents a mathematical model of a dynamic process initiated in a constructively nonlinear system – a statically loaded beam on an elastic Pasternak foundation – by the sudden formation of a defect in the form of subsidence of a part of the foundation. The equations of static deflection, natural and forced vibrations are presented in matrix form using multicomponent state vectors and matrices of the influence of the initial parameters on the state of the beam sections. It is shown that a certain combination of mechanical characteristics of the «beam – two–parameter foundation» system and parameters of damage to the foundation (localization and dimensions) leads to forced nonharmonic vibrations with a frequency expressed in fractions of the frequency of a free or fully supported beam. The values of the increments of internal efforts, caused by the factor of suddenness of the formation of damage, have been determined.
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