Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches
The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/9/7/1409 |
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| author | Małgorzata Chwał Aleksander Muc |
| author_facet | Małgorzata Chwał Aleksander Muc |
| author_sort | Małgorzata Chwał |
| collection | DOAJ |
| description | The buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations. |
| first_indexed | 2024-12-20T04:48:22Z |
| format | Article |
| id | doaj.art-eea5299bc90742c69000025d3447cf9c |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-12-20T04:48:22Z |
| publishDate | 2019-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-eea5299bc90742c69000025d3447cf9c2022-12-21T19:52:56ZengMDPI AGApplied Sciences2076-34172019-04-0197140910.3390/app9071409app9071409Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress ApproachesMałgorzata Chwał0Aleksander Muc1Institute of Machine Design, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, PolandInstitute of Machine Design, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, PolandThe buckling and free vibrations of rectangular nanoplates are considered in the present paper. The refined continuum transverse shear deformation theory (third and first order) is introduced to formulate the fundamental equations of the nanoplate. Besides, the analysis involve the nonlocal strain and stress theories of elasticity to take into account the small-scale effects encountered in nanostructures/nanocomposites. Hamilton’s principle is used to establish the governing equations of the nanoplate. The Rayleigh-Ritz method is proposed to solve eigenvalue problems dealing with the buckling and free vibration analysis of the nanoplates considered. Some examples are presented to investigate and illustrate the effects of various formulations.https://www.mdpi.com/2076-3417/9/7/1409nonlocal stress theorynonlocal strain theorybucklingfree vibrationsnanoplateshigher order shear deformation theories |
| spellingShingle | Małgorzata Chwał Aleksander Muc Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches Applied Sciences nonlocal stress theory nonlocal strain theory buckling free vibrations nanoplates higher order shear deformation theories |
| title | Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches |
| title_full | Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches |
| title_fullStr | Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches |
| title_full_unstemmed | Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches |
| title_short | Buckling and Free Vibrations of Nanoplates—Comparison of Nonlocal Strain and Stress Approaches |
| title_sort | buckling and free vibrations of nanoplates comparison of nonlocal strain and stress approaches |
| topic | nonlocal stress theory nonlocal strain theory buckling free vibrations nanoplates higher order shear deformation theories |
| url | https://www.mdpi.com/2076-3417/9/7/1409 |
| work_keys_str_mv | AT małgorzatachwał bucklingandfreevibrationsofnanoplatescomparisonofnonlocalstrainandstressapproaches AT aleksandermuc bucklingandfreevibrationsofnanoplatescomparisonofnonlocalstrainandstressapproaches |