State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads
This paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distri...
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MDPI AG
2024-03-01
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| Online Access: | https://www.mdpi.com/1996-1944/17/6/1296 |
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| author | Dongying Liu Junxiang Su Li Zhao Xudong Shen |
| author_facet | Dongying Liu Junxiang Su Li Zhao Xudong Shen |
| author_sort | Dongying Liu |
| collection | DOAJ |
| description | This paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distributed throughout the polymer matrix against microbeam length, and the improved Halpin–Tsai micromechanics model and the rule of mixture are adopted to evaluate the effective material properties. Eigenvalue equations of the microbeams governing the static stability and vibration are derived based on the modified couple stress Euler–Bernoulli beam theory via the state-space method, and are analytically solved with the discrete equilong segment model. The effects of axial distribution patterns, weight fraction, and geometric parameters of GPLs, as well as different types of AVLs, on the size-dependent buckling load and natural frequency are scrutinized in detail. The results show that the synchronized axial distributions of GPLs and AVLs could improve the buckling resistance and natural frequency more powerfully. |
| first_indexed | 2024-04-24T18:03:30Z |
| format | Article |
| id | doaj.art-b6970f6eb723482ab4069b9db48549ca |
| institution | Directory Open Access Journal |
| issn | 1996-1944 |
| language | English |
| last_indexed | 2024-04-24T18:03:30Z |
| publishDate | 2024-03-01 |
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| spelling | doaj.art-b6970f6eb723482ab4069b9db48549ca2024-03-27T13:52:27ZengMDPI AGMaterials1996-19442024-03-01176129610.3390/ma17061296State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying LoadsDongying Liu0Junxiang Su1Li Zhao2Xudong Shen3School of Civil Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Civil Engineering, Guangzhou University, Guangzhou 510006, ChinaSchool of Civil Engineering and Architecture, Zhejiang University of Science & Technology, Hangzhou 310023, ChinaHuanjiang Laboratory, No. 7 Wenzhong Road, Taozhu Street, Zhuji 311816, ChinaThis paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distributed throughout the polymer matrix against microbeam length, and the improved Halpin–Tsai micromechanics model and the rule of mixture are adopted to evaluate the effective material properties. Eigenvalue equations of the microbeams governing the static stability and vibration are derived based on the modified couple stress Euler–Bernoulli beam theory via the state-space method, and are analytically solved with the discrete equilong segment model. The effects of axial distribution patterns, weight fraction, and geometric parameters of GPLs, as well as different types of AVLs, on the size-dependent buckling load and natural frequency are scrutinized in detail. The results show that the synchronized axial distributions of GPLs and AVLs could improve the buckling resistance and natural frequency more powerfully.https://www.mdpi.com/1996-1944/17/6/1296axially functionally graded GPL-reinforced microbeamaxially varying applied loadbucklingvibrationmodified couple stress theory |
| spellingShingle | Dongying Liu Junxiang Su Li Zhao Xudong Shen State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads Materials axially functionally graded GPL-reinforced microbeam axially varying applied load buckling vibration modified couple stress theory |
| title | State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads |
| title_full | State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads |
| title_fullStr | State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads |
| title_full_unstemmed | State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads |
| title_short | State-Space Formulation for Buckling and Free Vibration of Axially Functionally Graded Graphene Reinforced Nanocomposite Microbeam under Axially Varying Loads |
| title_sort | state space formulation for buckling and free vibration of axially functionally graded graphene reinforced nanocomposite microbeam under axially varying loads |
| topic | axially functionally graded GPL-reinforced microbeam axially varying applied load buckling vibration modified couple stress theory |
| url | https://www.mdpi.com/1996-1944/17/6/1296 |
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