Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates
In this paper, the free vibration behavior of post-buckled functionally graded (FG) Mindlin rectangular microplates are described based on the modified couple stress theory (MCST). This theory enables the consideration of the size-effect through introducing material length scale parameters. The FG m...
| Main Authors: | , , , , |
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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=S1679-78252014001300003&lng=en&tlng=en |
| _version_ | 1819019045492490240 |
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| author | R. Ansari M. FaghihShojaei V. Mohammadi R. Gholami M. A. Darabi |
| author_facet | R. Ansari M. FaghihShojaei V. Mohammadi R. Gholami M. A. Darabi |
| author_sort | R. Ansari |
| collection | DOAJ |
| description | In this paper, the free vibration behavior of post-buckled functionally graded (FG) Mindlin rectangular microplates are described based on the modified couple stress theory (MCST). This theory enables the consideration of the size-effect through introducing material length scale parameters. The FG microplates made of a mixture of metal and ceramic are considered whose volume fraction of components is expressed by a power law function. By means of Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-plates in the postbuckling domain. The governing equations and boundary conditions are then discretized by using the generalized differential quadrature (GDQ) method before solving numerically by the pseudo-arclength continuation technique. In the solution procedure, the postbuckling problem of microplates is investigated first. Afterwards, the free vibration of microplates around the buckled configuration is discussed. The effects of dimensionless length scale parameter, material gradient index and aspect ratio on the on the postbuckling path and frequency of FG microplates subject to arbitrary edge supports are thoroughly discussed. |
| first_indexed | 2024-12-21T03:29:04Z |
| format | Article |
| id | doaj.art-21dc9c70459a42dea89db56348eb6926 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-21T03:29:04Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-21dc9c70459a42dea89db56348eb69262022-12-21T19:17:30ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-782511132351237810.1590/S1679-78252014001300003S1679-78252014001300003Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplatesR. Ansari0M. FaghihShojaei1V. Mohammadi2R. Gholami3M. A. Darabi4University of GuilanUniversity of GuilanUniversity of GuilanUniversity of GuilanUniversity of GuilanIn this paper, the free vibration behavior of post-buckled functionally graded (FG) Mindlin rectangular microplates are described based on the modified couple stress theory (MCST). This theory enables the consideration of the size-effect through introducing material length scale parameters. The FG microplates made of a mixture of metal and ceramic are considered whose volume fraction of components is expressed by a power law function. By means of Hamilton's principle, the nonlinear governing equations and associated boundary conditions are derived for FG micro-plates in the postbuckling domain. The governing equations and boundary conditions are then discretized by using the generalized differential quadrature (GDQ) method before solving numerically by the pseudo-arclength continuation technique. In the solution procedure, the postbuckling problem of microplates is investigated first. Afterwards, the free vibration of microplates around the buckled configuration is discussed. The effects of dimensionless length scale parameter, material gradient index and aspect ratio on the on the postbuckling path and frequency of FG microplates subject to arbitrary edge supports are thoroughly discussed.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014001300003&lng=en&tlng=enMindlin plate theorySmall scale effectModified couple stress theoryFree vibrationPost-buckled FG rectangular microplateGeneralized differential quadrature |
| spellingShingle | R. Ansari M. FaghihShojaei V. Mohammadi R. Gholami M. A. Darabi Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates Latin American Journal of Solids and Structures Mindlin plate theory Small scale effect Modified couple stress theory Free vibration Post-buckled FG rectangular microplate Generalized differential quadrature |
| title | Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates |
| title_full | Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates |
| title_fullStr | Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates |
| title_full_unstemmed | Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates |
| title_short | Size-dependent vibrations of post-buckled functionally graded Mindlin rectangular microplates |
| title_sort | size dependent vibrations of post buckled functionally graded mindlin rectangular microplates |
| topic | Mindlin plate theory Small scale effect Modified couple stress theory Free vibration Post-buckled FG rectangular microplate Generalized differential quadrature |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252014001300003&lng=en&tlng=en |
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