Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory
On the basis of modified couple stress theory, the postbuckling behavior of the Euler-Bernoulli microscale FG beams is investigated by means of an exact solution method. The modified couple stress theory as a nonclassical continuum theory is capable of interpreting the size dependencies which become...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/654640 |
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| _version_ | 1849685367567941632 |
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| author | R. Ansari M. A. Ashrafi T. Pourashraf M. Hemmatnezhad |
| author_facet | R. Ansari M. A. Ashrafi T. Pourashraf M. Hemmatnezhad |
| author_sort | R. Ansari |
| collection | DOAJ |
| description | On the basis of modified couple stress theory, the postbuckling behavior of the Euler-Bernoulli microscale FG beams is investigated by means of an exact solution method. The modified couple stress theory as a nonclassical continuum theory is capable of interpreting the size dependencies which become more significant at micro/nanoscales. The Von-Karman type nonlinear strain-displacement relationships are employed. The thermal effects are also incorporated into formulation. The governing equation of motion and the corresponding boundary conditions are derived using Hamilton’s principle. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A closed-form solution is obtained for the postbuckling deformation which is beyond the critical buckling load. To study the vibrations taking place in the vicinity of a buckled equilibrium position, the linear vibration problem is exactly solved around the first three buckled configurations. The natural frequencies of the lowest vibration modes around each of the first three buckled configurations are obtained. The influences of power-law exponent, boundary condition, length scale parameter, and thermal environment changes on the static deflection and free vibration frequencies are studied. A comparison is also made between the present results and those obtained via the classical beam theories. |
| format | Article |
| id | doaj-art-c409546feb5049d19c765ffbc368e661 |
| institution | DOAJ |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-c409546feb5049d19c765ffbc368e6612025-08-20T03:23:11ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/654640654640Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress TheoryR. Ansari0M. A. Ashrafi1T. Pourashraf2M. Hemmatnezhad3Department of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, IranDepartment of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, IranDepartment of Mechanical Engineering, University of Guilan, P.O. Box 3756, Rasht, IranDepartment of Mechanical Engineering, Islamic Azad University, Takestan Branch, Takestan, IranOn the basis of modified couple stress theory, the postbuckling behavior of the Euler-Bernoulli microscale FG beams is investigated by means of an exact solution method. The modified couple stress theory as a nonclassical continuum theory is capable of interpreting the size dependencies which become more significant at micro/nanoscales. The Von-Karman type nonlinear strain-displacement relationships are employed. The thermal effects are also incorporated into formulation. The governing equation of motion and the corresponding boundary conditions are derived using Hamilton’s principle. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A closed-form solution is obtained for the postbuckling deformation which is beyond the critical buckling load. To study the vibrations taking place in the vicinity of a buckled equilibrium position, the linear vibration problem is exactly solved around the first three buckled configurations. The natural frequencies of the lowest vibration modes around each of the first three buckled configurations are obtained. The influences of power-law exponent, boundary condition, length scale parameter, and thermal environment changes on the static deflection and free vibration frequencies are studied. A comparison is also made between the present results and those obtained via the classical beam theories.http://dx.doi.org/10.1155/2014/654640 |
| spellingShingle | R. Ansari M. A. Ashrafi T. Pourashraf M. Hemmatnezhad Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory Shock and Vibration |
| title | Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory |
| title_full | Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory |
| title_fullStr | Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory |
| title_full_unstemmed | Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory |
| title_short | Vibration Analysis of a Postbuckled Microscale FG Beam Based on Modified Couple Stress Theory |
| title_sort | vibration analysis of a postbuckled microscale fg beam based on modified couple stress theory |
| url | http://dx.doi.org/10.1155/2014/654640 |
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