Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control
Abstract This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. Th...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
| Subjects: | |
| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000500964&lng=en&tlng=en |
| _version_ | 1819198807616782336 |
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| author | Raphael Henrique Madeira Humberto Breves Coda |
| author_facet | Raphael Henrique Madeira Humberto Breves Coda |
| author_sort | Raphael Henrique Madeira |
| collection | DOAJ |
| description | Abstract This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed technique |
| first_indexed | 2024-12-23T03:06:19Z |
| format | Article |
| id | doaj.art-8b9ae0bffafd47bb8648b4a5c04b6d91 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-23T03:06:19Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-8b9ae0bffafd47bb8648b4a5c04b6d912022-12-21T18:02:19ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782513596499110.1590/1679-78252624S1679-78252016000500964Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration ControlRaphael Henrique MadeiraHumberto Breves CodaAbstract This study proposes a new pure numerical way to model mass / spring / damper devices to control the vibration of truss structures developing large displacements. It avoids the solution of local differential equations present in traditional convolution approaches to solve viscoelasticity. The structure is modeled by the geometrically exact Finite Element Method based on positions. The introduction of the device's mass is made by means of Lagrange multipliers that imposes its movement along the straight line of a finite element. A pure numerical Kelvin/Voigt like rheological model capable of nonlinear large deformations is originally proposed here. It is numerically solved along time to accomplish the damping parameters of the device. Examples are solved to validate the formulation and to show the practical possibilities of the proposed techniquehttp://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000500964&lng=en&tlng=enNonlinear dynamicstruss structuresvibration controllarge strainKelvin/Voigt rheology |
| spellingShingle | Raphael Henrique Madeira Humberto Breves Coda Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control Latin American Journal of Solids and Structures Nonlinear dynamics truss structures vibration control large strain Kelvin/Voigt rheology |
| title | Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control |
| title_full | Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control |
| title_fullStr | Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control |
| title_full_unstemmed | Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control |
| title_short | Kelvin Viscoelasticity and Lagrange Multipliers Applied to the Simulation of Nonlinear Structural Vibration Control |
| title_sort | kelvin viscoelasticity and lagrange multipliers applied to the simulation of nonlinear structural vibration control |
| topic | Nonlinear dynamics truss structures vibration control large strain Kelvin/Voigt rheology |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000500964&lng=en&tlng=en |
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