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

Abstract

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 Kármán 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.

Nonlinear coupled moving-load excited dynamics of beam-mass structures

“…Zupan and Zupan [15] employed a three-dimensional framework for the dynamic analysis of beams with a moving mass through use of a finite element formulation. Khurshudyan and Ohanyan [16] considered a nonlinear Bernoulli-Euler beam excited by two moving loads in opposite directions and analysed the nonlinear vibrations using the Bubnov-Galerkin procedure.…”

Min(max)imization of horizontal and vertical displacements of a fibre‐reinforced magneto‐elastic cantilever rod

“…Applying the Newton‐Raphson algorithm, we express these coefficients in terms of u making the rigorous analysis more simple. Note that the Bubnov‐Galerkin procedure has been used in control and optimization problems earlier . The developed method can be straightforwardly applied to study more complicated equations of magneto(thermo)‐elasticity …”

“…Note that the Bubnov-Galerkin procedure has been used in control and optimization problems earlier. [2,3] The developed method can be straightforwardly applied to study more complicated equations of magneto(thermo)-elasticity. [4]…”