Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory
In this paper, nonlinear free vibration analysis of micro-beams resting on the viscoelastic foundation is investigated by the use of the modified couple stress theory, which is able to capture the size effects for structures in micron and sub-micron scales. To this aim, the gov-erning equation of mo...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2017-06-01
|
| Series: | Archive of Mechanical Engineering |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/meceng.2017.64.issue-2/meceng-2017-0015/meceng-2017-0015.xml?format=INT |
| _version_ | 1818758436055154688 |
|---|---|
| author | Jam Jafar Eskandari Noorabadi Milad Namdaran Nader |
| author_facet | Jam Jafar Eskandari Noorabadi Milad Namdaran Nader |
| author_sort | Jam Jafar Eskandari |
| collection | DOAJ |
| description | In this paper, nonlinear free vibration analysis of micro-beams resting on the viscoelastic foundation is investigated by the use of the modified couple stress theory, which is able to capture the size effects for structures in micron and sub-micron scales. To this aim, the gov-erning equation of motion and the boundary conditions are derived using the Euler–Bernoulli beam and the Hamilton’s principle. The Galerkin method is employed to solve the governing nonlinear differential equation and obtain the frequency-amplitude algebraic equation. Final-ly, the effects of different parameters, such as the mode number, aspect ratio of length to height, the normalized length scale parameter and foundation parameters on the natural fre-quency-amplitude curves of doubly simply supported beams are studied. |
| first_indexed | 2024-12-18T06:26:48Z |
| format | Article |
| id | doaj.art-f0aa3436e2c0487db7624d81239bb471 |
| institution | Directory Open Access Journal |
| issn | 2300-1895 |
| language | English |
| last_indexed | 2024-12-18T06:26:48Z |
| publishDate | 2017-06-01 |
| publisher | Polish Academy of Sciences |
| record_format | Article |
| series | Archive of Mechanical Engineering |
| spelling | doaj.art-f0aa3436e2c0487db7624d81239bb4712022-12-21T21:18:00ZengPolish Academy of SciencesArchive of Mechanical Engineering2300-18952017-06-0164223925610.1515/meceng-2017-0015meceng-2017-0015Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress TheoryJam Jafar Eskandari0Noorabadi Milad1Namdaran Nader2Composite Materials and Technology Center, Malek Ashtar University of Technology, Tehran, Iran (Islamic Republic of).Composite Materials and Technology Center, Malek Ashtar University of Technology, Tehran, Iran (Islamic Republic of).Composite Materials and Technology Center, Malek Ashtar University of Technology, Tehran, Iran (Islamic Republic of).In this paper, nonlinear free vibration analysis of micro-beams resting on the viscoelastic foundation is investigated by the use of the modified couple stress theory, which is able to capture the size effects for structures in micron and sub-micron scales. To this aim, the gov-erning equation of motion and the boundary conditions are derived using the Euler–Bernoulli beam and the Hamilton’s principle. The Galerkin method is employed to solve the governing nonlinear differential equation and obtain the frequency-amplitude algebraic equation. Final-ly, the effects of different parameters, such as the mode number, aspect ratio of length to height, the normalized length scale parameter and foundation parameters on the natural fre-quency-amplitude curves of doubly simply supported beams are studied.http://www.degruyter.com/view/j/meceng.2017.64.issue-2/meceng-2017-0015/meceng-2017-0015.xml?format=INTnonlinear free vibrationsize dependentthe modified couple stress theoryEuler-Bernoulli beam modelGalerkin method |
| spellingShingle | Jam Jafar Eskandari Noorabadi Milad Namdaran Nader Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory Archive of Mechanical Engineering nonlinear free vibration size dependent the modified couple stress theory Euler-Bernoulli beam model Galerkin method |
| title | Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory |
| title_full | Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory |
| title_fullStr | Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory |
| title_full_unstemmed | Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory |
| title_short | Nonlinear Free Vibration Analysis of Micro-beams Resting on Viscoelastic Foundation Based on the Modified Couple Stress Theory |
| title_sort | nonlinear free vibration analysis of micro beams resting on viscoelastic foundation based on the modified couple stress theory |
| topic | nonlinear free vibration size dependent the modified couple stress theory Euler-Bernoulli beam model Galerkin method |
| url | http://www.degruyter.com/view/j/meceng.2017.64.issue-2/meceng-2017-0015/meceng-2017-0015.xml?format=INT |
| work_keys_str_mv | AT jamjafareskandari nonlinearfreevibrationanalysisofmicrobeamsrestingonviscoelasticfoundationbasedonthemodifiedcouplestresstheory AT noorabadimilad nonlinearfreevibrationanalysisofmicrobeamsrestingonviscoelasticfoundationbasedonthemodifiedcouplestresstheory AT namdarannader nonlinearfreevibrationanalysisofmicrobeamsrestingonviscoelasticfoundationbasedonthemodifiedcouplestresstheory |