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Vibration suspension of Euler‐Bernoulli‐von Kármán beam subjected to oppositely moving loads by optimizing the placements of visco‐elastic dampers
Author(s) -
Khurshudyan Asatur Zh.,
Ohanyan Sergey K.
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201800056
Subject(s) - beam (structure) , suspension (topology) , vibration , linearization , damper , nonlinear system , structural engineering , bernoulli's principle , physics , mathematics , mechanics , engineering , acoustics , quantum mechanics , homotopy , pure mathematics , thermodynamics
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.