Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects
Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sarrami-Foroushani, Saeid [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014transfer abstract |
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| Umfang: |
13 |
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| Übergeordnetes Werk: |
Enthalten in: Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India - Desai, Akshatha G. ELSEVIER, 2021, Amsterdam [u.a.] |
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| Übergeordnetes Werk: |
volume:57 ; year:2014 ; pages:83-95 ; extent:13 |
| Links: |
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| DOI / URN: |
10.1016/j.physe.2013.11.002 |
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ELV027807886 |
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| 245 | 1 | 0 | |a Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects |
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| 520 | |a Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. | ||
| 520 | |a Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. | ||
| 650 | 7 | |a Free vibration |2 Elsevier | |
| 650 | 7 | |a Van der Waals forces |2 Elsevier | |
| 650 | 7 | |a Finite strip method |2 Elsevier | |
| 650 | 7 | |a Graphene sheets |2 Elsevier | |
| 650 | 7 | |a Nonlocal elasticity |2 Elsevier | |
| 650 | 7 | |a Buckling |2 Elsevier | |
| 700 | 1 | |a Azhari, Mojtaba |4 oth | |
| 773 | 0 | 8 | |i Enthalten in |n North-Holland, Elsevier Science |a Desai, Akshatha G. ELSEVIER |t Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India |d 2021 |g Amsterdam [u.a.] |w (DE-627)ELV006775543 |
| 773 | 1 | 8 | |g volume:57 |g year:2014 |g pages:83-95 |g extent:13 |
| 856 | 4 | 0 | |u https://doi.org/10.1016/j.physe.2013.11.002 |3 Volltext |
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10.1016/j.physe.2013.11.002 doi GBVA2014003000003.pica (DE-627)ELV027807886 (ELSEVIER)S1386-9477(13)00367-6 DE-627 ger DE-627 rakwb eng 530 530 DE-600 630 640 VZ Sarrami-Foroushani, Saeid verfasserin aut Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects 2014transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Free vibration Elsevier Van der Waals forces Elsevier Finite strip method Elsevier Graphene sheets Elsevier Nonlocal elasticity Elsevier Buckling Elsevier Azhari, Mojtaba oth Enthalten in North-Holland, Elsevier Science Desai, Akshatha G. ELSEVIER Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India 2021 Amsterdam [u.a.] (DE-627)ELV006775543 volume:57 year:2014 pages:83-95 extent:13 https://doi.org/10.1016/j.physe.2013.11.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U AR 57 2014 83-95 13 045F 530 |
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10.1016/j.physe.2013.11.002 doi GBVA2014003000003.pica (DE-627)ELV027807886 (ELSEVIER)S1386-9477(13)00367-6 DE-627 ger DE-627 rakwb eng 530 530 DE-600 630 640 VZ Sarrami-Foroushani, Saeid verfasserin aut Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects 2014transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Free vibration Elsevier Van der Waals forces Elsevier Finite strip method Elsevier Graphene sheets Elsevier Nonlocal elasticity Elsevier Buckling Elsevier Azhari, Mojtaba oth Enthalten in North-Holland, Elsevier Science Desai, Akshatha G. ELSEVIER Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India 2021 Amsterdam [u.a.] (DE-627)ELV006775543 volume:57 year:2014 pages:83-95 extent:13 https://doi.org/10.1016/j.physe.2013.11.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U AR 57 2014 83-95 13 045F 530 |
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10.1016/j.physe.2013.11.002 doi GBVA2014003000003.pica (DE-627)ELV027807886 (ELSEVIER)S1386-9477(13)00367-6 DE-627 ger DE-627 rakwb eng 530 530 DE-600 630 640 VZ Sarrami-Foroushani, Saeid verfasserin aut Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects 2014transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Free vibration Elsevier Van der Waals forces Elsevier Finite strip method Elsevier Graphene sheets Elsevier Nonlocal elasticity Elsevier Buckling Elsevier Azhari, Mojtaba oth Enthalten in North-Holland, Elsevier Science Desai, Akshatha G. ELSEVIER Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India 2021 Amsterdam [u.a.] (DE-627)ELV006775543 volume:57 year:2014 pages:83-95 extent:13 https://doi.org/10.1016/j.physe.2013.11.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U AR 57 2014 83-95 13 045F 530 |
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10.1016/j.physe.2013.11.002 doi GBVA2014003000003.pica (DE-627)ELV027807886 (ELSEVIER)S1386-9477(13)00367-6 DE-627 ger DE-627 rakwb eng 530 530 DE-600 630 640 VZ Sarrami-Foroushani, Saeid verfasserin aut Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects 2014transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Free vibration Elsevier Van der Waals forces Elsevier Finite strip method Elsevier Graphene sheets Elsevier Nonlocal elasticity Elsevier Buckling Elsevier Azhari, Mojtaba oth Enthalten in North-Holland, Elsevier Science Desai, Akshatha G. ELSEVIER Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India 2021 Amsterdam [u.a.] (DE-627)ELV006775543 volume:57 year:2014 pages:83-95 extent:13 https://doi.org/10.1016/j.physe.2013.11.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U AR 57 2014 83-95 13 045F 530 |
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10.1016/j.physe.2013.11.002 doi GBVA2014003000003.pica (DE-627)ELV027807886 (ELSEVIER)S1386-9477(13)00367-6 DE-627 ger DE-627 rakwb eng 530 530 DE-600 630 640 VZ Sarrami-Foroushani, Saeid verfasserin aut Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects 2014transfer abstract 13 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. Free vibration Elsevier Van der Waals forces Elsevier Finite strip method Elsevier Graphene sheets Elsevier Nonlocal elasticity Elsevier Buckling Elsevier Azhari, Mojtaba oth Enthalten in North-Holland, Elsevier Science Desai, Akshatha G. ELSEVIER Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India 2021 Amsterdam [u.a.] (DE-627)ELV006775543 volume:57 year:2014 pages:83-95 extent:13 https://doi.org/10.1016/j.physe.2013.11.002 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U AR 57 2014 83-95 13 045F 530 |
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Enthalten in Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India Amsterdam [u.a.] volume:57 year:2014 pages:83-95 extent:13 |
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Enthalten in Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India Amsterdam [u.a.] volume:57 year:2014 pages:83-95 extent:13 |
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Characterization of a 7 bp indel in MARCH1 promoter associated with reproductive traits in Malabari and Attappady Black goats of India |
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nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der waals effects |
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Nonlocal vibration and buckling analysis of single and multi-layered graphene sheets using finite strip method including van der Waals effects |
| abstract |
Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. |
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Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. |
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Detailed studies on the nanoscale vibration and buckling characteristics of rectangular single and multi-layered graphene sheets (SLGSs and MLGSs) are carried out using semi-analytical finite strip method (FSM), based on the classical plate theory (CPT). The displacement functions of the sheets are evaluated using continuous harmonic function series which satisfy the boundary conditions in one direction and a piecewise interpolation polynomial in the other direction. Nonlocal continuum mechanics is employed to derive the differential equation of the system. The weighted residual method is employed to obtain stiffness, stability and mass matrices of the graphene sheets. The effects of van der Waals (vdW) forces which are present as bonding forces between the layers are considered in the stiffness matrix of the system. The analysis of MLGSs is much more complex due to the influence of vdW forces. The mechanical properties of the graphene sheet are assumed in two ways as orthotropic or isotropic materials. A matrix eigenvalue problem is solved to find the natural frequency and critical stress of GSs subjected to different types of in-plane loadings including uniform and non-uniform uniaxial loadings. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a comprehensive parametric study is performed to investigate the effects of various parameters such as boundary conditions, nonlocal parameter, aspect ratio and the type of loading on the results. |
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