Dynamic deformation of a beam at sudden structural transformation of foundation

The article presents a methodic for analytical determining forces, displacements, modes and frequencies of natural flexural vibrations of a beam on elastic foundation. The beam consists of two sections: the first one supports on Winkler elastic foundation, and next one is free. Equations for flexural natural and forced vibrations were written in dimensionless variables and parameters and solved using the initial parameters method and Krylov functions. At the same time second and higher frequencies of natural vibrations of the beam were determined assuming unknown frequency is higher than “conventional” frequency which characterizes generalized stiffness of a system “beam–foundation”. Using numerical analysis, authors showed dependencies between the first three dimensionless frequencies of natural vibrations of the beam and a generalized stiffness of the system “beam–foundation” when foundation suddenly partially failure under the beam. Investigation established that effect of a sudden structural transformation leads to five-time moment increasing in the system “beam–foundation” at sudden foundation failure under the second half of the beam.