石墨烯增强复合材料板的静态分析
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摘要
将石墨烯片一致或随机地分布到基体中,形成石墨烯增强复合材料。基于考虑横向拉伸的位移场,利用哈密顿原理建立数学模型,对石墨烯增强复合材料板的弯曲行为进行分析。首先通过与已发表文献中板的自由振动频率一致性的比较,验证所建立数学模型与算法的正确性。在此基础上,对石墨烯含量、长宽比、长厚比、板的长宽比等对石墨烯的中心横向位移在厚度方向上变化的影响进行了探讨,并给出了相应的物理解释。
Multilayer graphene nanoplates was added to the matrix as reinforcements to form graphene reinforced composites. Based on the displacement field considering transverse tensile effect,a mathematical model is established by using Hamilton principle to analyze the bending behavior of graphene reinforced composites plate. Firstly,the validity of the mathematical model established in this paper is verified by comparing the frequency consistency of the free vibration with the results in published literature. Then,the effects of the aspect ratio of graphene and the length-width ratio of plate on the variation of the central transverse displacement deformation of graphene in the thickness direction are discussed,and the physical explanation of the response is given.
Multilayer graphene nanoplates was added to the matrix as reinforcements to form graphene reinforced composites. Based on the displacement field considering transverse tensile effect,a mathematical model is established by using Hamilton principle to analyze the bending behavior of graphene reinforced composites plate. Firstly,the validity of the mathematical model established in this paper is verified by comparing the frequency consistency of the free vibration with the results in published literature. Then,the effects of the aspect ratio of graphene and the length-width ratio of plate on the variation of the central transverse displacement deformation of graphene in the thickness direction are discussed,and the physical explanation of the response is given.
引文
[1] Hao Y X,Chen L H,Zhang W,et al.Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate[J],Journal of Sound and Vibration,2008,312:862-892.
[2] Zhang W,Hao Y X,Yang J. Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges[J]. Composite Structures,2012,94:1075-1086.
[3] Yang J,Chen D,Kitipornchai S. Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method[J].Composite Structures,2018,193:281-294.
[4] Wang Y Q,Ye C,Zu J W.Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets[J]. Aerospace Science and Technology,2019,85:359-370.
[5] Mao J J,Zhang W.Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces[J].Composite Structures,2019,216:392-405.
[6] Thai C H,Ferreira A J M,Tran T D,et al.Free vibration,buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation[J]. Composite Structures,2019,220.749-759.
[7] Polit O,Anant C,Anirudh B,et al.Functionally graded graphene reinforced porous nanocomposite curved beams:Bending and elastic stability using a higher-order model with thickness stretch effect[J]. Composites Part B,2019,166:310-327.
[8] Li K Y,Wu D,Chen X J.Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets[J]. Composite Structures,2018,204:114-130.
[9] Guo H L,Cao S Q,Yang T Z,et al.Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method[J].International Journal of Mechanical Sciences,2018,142-143:610-621.
[10]陈鸿燕,王爱文,郝育新,等.考虑横向拉伸影响的FGM板的静态分析[J].应用力学学报,2018,35(4):918-924.
[11] Chen H Y,Wang A W,Hao Y X,et al. Free vibration of FGM sandwich doubly-curved shallow shell based on a new shear deformation theory with stretching effects[J]. Composite Structures,2017,179:50-60.
[12] Wang A W,Chen H Y,Hao Y X,et al.Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets[J].Results in Physics,2018,9:550-559.
[13] Song M T,Kitipornchai S,Yang J. Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets[J]. Composite Structures,2017,159:579-588.
[14] Puneet K,Srinivas J. Vibration,buckling and bending behavior of functionally graded multiwalled carbon nanotube reinforced polymer composite plates using the layer-wise formulation[J]. Composite Structures,2017,177:158-170.
[2] Zhang W,Hao Y X,Yang J. Nonlinear dynamics of FGM circular cylindrical shell with clamped-clamped edges[J]. Composite Structures,2012,94:1075-1086.
[3] Yang J,Chen D,Kitipornchai S. Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method[J].Composite Structures,2018,193:281-294.
[4] Wang Y Q,Ye C,Zu J W.Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets[J]. Aerospace Science and Technology,2019,85:359-370.
[5] Mao J J,Zhang W.Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces[J].Composite Structures,2019,216:392-405.
[6] Thai C H,Ferreira A J M,Tran T D,et al.Free vibration,buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation[J]. Composite Structures,2019,220.749-759.
[7] Polit O,Anant C,Anirudh B,et al.Functionally graded graphene reinforced porous nanocomposite curved beams:Bending and elastic stability using a higher-order model with thickness stretch effect[J]. Composites Part B,2019,166:310-327.
[8] Li K Y,Wu D,Chen X J.Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets[J]. Composite Structures,2018,204:114-130.
[9] Guo H L,Cao S Q,Yang T Z,et al.Vibration of laminated composite quadrilateral plates reinforced with graphene nanoplatelets using the element-free IMLS-Ritz method[J].International Journal of Mechanical Sciences,2018,142-143:610-621.
[10]陈鸿燕,王爱文,郝育新,等.考虑横向拉伸影响的FGM板的静态分析[J].应用力学学报,2018,35(4):918-924.
[11] Chen H Y,Wang A W,Hao Y X,et al. Free vibration of FGM sandwich doubly-curved shallow shell based on a new shear deformation theory with stretching effects[J]. Composite Structures,2017,179:50-60.
[12] Wang A W,Chen H Y,Hao Y X,et al.Vibration and bending behavior of functionally graded nanocomposite doubly-curved shallow shells reinforced by graphene nanoplatelets[J].Results in Physics,2018,9:550-559.
[13] Song M T,Kitipornchai S,Yang J. Free and forced vibrations of functionally graded polymer composite plates reinforced with graphene nanoplatelets[J]. Composite Structures,2017,159:579-588.
[14] Puneet K,Srinivas J. Vibration,buckling and bending behavior of functionally graded multiwalled carbon nanotube reinforced polymer composite plates using the layer-wise formulation[J]. Composite Structures,2017,177:158-170.