Vibration suspension of Euler-Bernoulli-von Karman beam subjected to oppositely moving loads by optimizing the placements of visco-elastic dampers

Possibilities of control and suspension of bending vibrations of a geometrically nonlinear Euler-Bernoulli beam subjected to two oppositely moving point loads in given finite time are considered. It is assumed that the beam undergoes large deformations and the nonlinear von Karman strains are considered. The suspension is carried out by means of optimizing the placements of visco-elastic dampers under the beam. By applying the modified Bubnov-Galerkin procedure, it becomes possible to avoid linearization of the state equation. The validation of the theory is carried out on the example of a finite simply supported beam. It is observed that by optimizing the dampers placements, both the maximal absolute value of the beam transverse displacements and the vibration reduction time can be reduced.