Demedetska V. Dynamics of a viscoelastic Timoshenko beam with dampers and dynamic vibration absorbers

The thesis for the scientific degree of a candidate of technical sciences (doctor of philosophy) in speciality 05.23.17 “Structural Mechanics” (19 – architecture and constructing). – Oles Honchar Dnipro National University; State Higher Educational Establishment “Prydniprovs’ka State Academy of Civil Engineering and Architecture”, Dnipro, 2019. The thesis is devoted to studying bending vibrations of beams equipped with dampers and dynamic vibration absorbers (DVA), using a non-classical beam model, proposed by S.P. Timoshenko (TB) and Focht model of viscoelastic material. Using the Timoshenko model allows to consider shear deformations and inertia of rotation, that is necessary for consideration for a wide class of bridge and tower structures. Taking into account internal and external friction allows one to give a realistic description of the beam dynamics near the resonance. A mathematical model of forced oscillations of Timoshenko beam made from a viscoelastic material with attached masses, dampers and dynamic vibration dampers, under arbitrary distributed load is obtained using a convenient set of dimensionless variables and parameters. An analytical solution was obtained for the problem of forced oscillations of a viscoelastic Timoshenko beam with the concentrated effects (dampers, DVAs, point masses) under the action of a harmonic load using an expansion in eigenfunctions of Timoshenko's elastic beam without these effects. The problem is reduced to solving a system of linear algebraic equations with complex coefficients with respect to generalized coordinates coefficients of the indicated expansion. Applying dampers and dynamic vibration absorbers intensifies the tendency for the occurrence of running waves at forced oscillations of beams, especially under the action of local forces and dampers displaced with respect to these forces. The running component significantly depends on the location of the damper or DVA and increases with increasing excitation frequency. This component of dynamic deflection can lead to significant changes in the curvature of the bent axis and, accordingly, in bending stresses, which should be considered when analyzing dynamic stresses and choosing DVA parameters.