Abstract
A double-ended cantilever beam as a distributed parameter dynamic vibration absorber has been applied to a single-degree-of-freedom system subjected to harmonic forces.In this investigation, the beam has been analyzed under the well known model of Timoshenko and the computation of best parameters is based on the Chebyshev’s optimality criterion.This is somewhat novel in the field since:The design of cantilever beams as dynamic vibration absorbers is usually made under the hypotheses of the Euler-Bernoulli theory;It is the first time that the Chebyshev’s criterion is applied to the design of a double-ended cantilever beam used as a dynamic vibration absorber.For a ready use of the results herein presented, design charts allow a quick choice of optimal parameters such as tuning ratio and mass ratio.
Highlights
The classical dynamic vibrations absorber is made up of two masses
The first one is subjected to an harmonic load which lead to a vibrational motion of this mass, the second mass is connected to the main mass by means of a spring element
When an absorbing mass-spring system is attached to the main mass and the resonance of the absorber is tuned to match that of the main mass, the motion of the main mass is reduced to zero at its resonance frequency (Fig. 1)
Summary
The classical dynamic vibrations absorber is made up of two masses. The first one is subjected to an harmonic load which lead to a vibrational motion of this mass, the second mass is connected to the main mass by means of a spring element. As a consequence the parameters to be set in order to reduce the vibrations of the main mass are the intrinsic elasticity of the beam and its weight. For a more faithful modeling of the beam behavior, the authors have deduced the dynamic equations of the system under analysis by means of the Timoshenko’s model [7]. These equations have been used under the conditions set by the Chebyshev’s theorem in order to define the optimal features of the beam (e.g. cross section area, length, thickness) [9]. Vita / Optimal cantilever dynamic vibration absorbers by Timoshenko Beam Theory
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