Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams
The purpose of this research is to initiate an investigation of the nonlinear material strain-rate damping effects on the amplitude and frequencies of some Euler-Bernoulli Beams. It is well known that the dynamic behaviors of most heat-treated metals can be modelled by using the power-law strain-rat...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823005963 |
| _version_ | 1797736888464834560 |
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| author | Dongming Wei Almir Aniyarov Dichuan Zhang Christos Spitas Daulet Nurakhmetov Andas Amrin |
| author_facet | Dongming Wei Almir Aniyarov Dichuan Zhang Christos Spitas Daulet Nurakhmetov Andas Amrin |
| author_sort | Dongming Wei |
| collection | DOAJ |
| description | The purpose of this research is to initiate an investigation of the nonlinear material strain-rate damping effects on the amplitude and frequencies of some Euler-Bernoulli Beams. It is well known that the dynamic behaviors of most heat-treated metals can be modelled by using the power-law strain-rate dependent constitutive equations. Lumped parameter models for approximations of dynamic vibration of the power-law Euler-Bernoulli Beam subject to power-law strain-rate damping and concentrated loads are formulated. Analytic formulas of the lumped parameters, including effective the train-rate damping, are derived. The lumped-parameters are also evaluated numerically by a low-order Galerkin Method to validate and compare the lumped parameter model with another numerical model. Numerical examples made of some heat-treated aluminum and stainless-steel alloys are presented to illustrate the implications of the aforementioned lumped-parameter models on the dynamics of the beams. The results obtained in this work cover with the classical results in the literature for linear the materials as special cases. The novel lumped parameter models can provide useful insights for crashworthiness analysis of structures of heat treated metals and thermal plastics. |
| first_indexed | 2024-03-12T13:20:48Z |
| format | Article |
| id | doaj.art-cea2cd1d30e94fd7ab8794c08e992843 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-03-12T13:20:48Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-cea2cd1d30e94fd7ab8794c08e9928432023-08-26T04:42:51ZengElsevierAlexandria Engineering Journal1110-01682023-09-0178246255Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beamsDongming Wei0Almir Aniyarov1Dichuan Zhang2Christos Spitas3Daulet Nurakhmetov4Andas Amrin5Nazarbayev University, School of Sciences and Humanities, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, Kazakhstan; Corresponding author.Nazarbayev University, School of Engineering and Digital Sciences, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, KazakhstanNazarbayev University, School of Engineering and Digital Sciences, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, KazakhstanNazarbayev University, School of Engineering and Digital Sciences, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, KazakhstanNazarbayev University, School of Engineering and Digital Sciences, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, KazakhstanNazarbayev University, School of Engineering and Digital Sciences, Kabanbay Batyr Ave. 53, 010000 Nur-Sultan, KazakhstanThe purpose of this research is to initiate an investigation of the nonlinear material strain-rate damping effects on the amplitude and frequencies of some Euler-Bernoulli Beams. It is well known that the dynamic behaviors of most heat-treated metals can be modelled by using the power-law strain-rate dependent constitutive equations. Lumped parameter models for approximations of dynamic vibration of the power-law Euler-Bernoulli Beam subject to power-law strain-rate damping and concentrated loads are formulated. Analytic formulas of the lumped parameters, including effective the train-rate damping, are derived. The lumped-parameters are also evaluated numerically by a low-order Galerkin Method to validate and compare the lumped parameter model with another numerical model. Numerical examples made of some heat-treated aluminum and stainless-steel alloys are presented to illustrate the implications of the aforementioned lumped-parameter models on the dynamics of the beams. The results obtained in this work cover with the classical results in the literature for linear the materials as special cases. The novel lumped parameter models can provide useful insights for crashworthiness analysis of structures of heat treated metals and thermal plastics.http://www.sciencedirect.com/science/article/pii/S1110016823005963Power-law Euler-Bernoulli beamLumped-parameter modelDamping ratiosNonlinear strain-rate dampingVibration |
| spellingShingle | Dongming Wei Almir Aniyarov Dichuan Zhang Christos Spitas Daulet Nurakhmetov Andas Amrin Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams Alexandria Engineering Journal Power-law Euler-Bernoulli beam Lumped-parameter model Damping ratios Nonlinear strain-rate damping Vibration |
| title | Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams |
| title_full | Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams |
| title_fullStr | Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams |
| title_full_unstemmed | Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams |
| title_short | Kelvin-Voigt lumped parameter models for approximation of the Power-law Euler-Bernoulli beams |
| title_sort | kelvin voigt lumped parameter models for approximation of the power law euler bernoulli beams |
| topic | Power-law Euler-Bernoulli beam Lumped-parameter model Damping ratios Nonlinear strain-rate damping Vibration |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823005963 |
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