Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives
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-depe...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/5957831 |
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| author | Mario Lázaro Jose M. Molines-Cano Ignacio Ferrer Vicente Albero |
| author_facet | Mario Lázaro Jose M. Molines-Cano Ignacio Ferrer Vicente Albero |
| author_sort | Mario Lázaro |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b329857cd7fa4301916a52218e4b2ce9 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-b329857cd7fa4301916a52218e4b2ce92025-08-20T03:39:18ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/59578315957831Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional DerivativesMario Lázaro0Jose M. Molines-Cano1Ignacio Ferrer2Vicente Albero3Department of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainViscoelastic 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.http://dx.doi.org/10.1155/2018/5957831 |
| spellingShingle | Mario Lázaro Jose M. Molines-Cano Ignacio Ferrer Vicente Albero Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives Shock and Vibration |
| title | Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives |
| title_full | Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives |
| title_fullStr | Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives |
| title_full_unstemmed | Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives |
| title_short | Proposal of a Viscous Model for Nonviscously Damped Beams Based on Fractional Derivatives |
| title_sort | proposal of a viscous model for nonviscously damped beams based on fractional derivatives |
| url | http://dx.doi.org/10.1155/2018/5957831 |
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