proposal of a viscous model for nonviscously damped beams based on fractional derivatives

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ID: 158168
2018
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Abstract
Viscoelastic materials are widely used in structural dynamics for the control of the vibrations and energy dissipation. They are characterized by damping forces that depend on the history of the velocity response via hereditary functions involved in convolution integrals, leading to a frequency-dependent damping matrix. In this paper, one-dimensional beam structures with viscoelastic materials based on fractional derivatives are considered. In this work, the construction of a new equivalent viscous system with fictitious parameters but capable of reproducing the response of the viscoelastic original one with acceptable accuracy is proposed. This allows us to take advantage of the well-known available numerical tools for viscous systems and use them to find response of viscoelastic structures. The process requires the numerical computation of complex frequencies. The new fictitious viscous parameters are found to be matching the information provided by the frequency response functions. New mass, damping, and stiffness matrices are found, which in addition have the property of proportionality, so they become diagonal in the modal space. The theoretical results are contrasted with two different numerical examples.
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lzaro2018shockproposal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors ;Mario Lázaro;Jose M. Molines-Cano;Ignacio Ferrer;Vicente Albero
Journal Nano letters
Year 2018
DOI
10.1155/2018/5957831
URL
http://dx.doi.org/10.1155/2018/5957831
Keywords
physics

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