压电集成石墨烯增强功能梯度多孔板的等几何建模与分析

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (2) : 280-290.

论文

刘庆运1，刘康仁1，张红一1，刘涛1,2

作者信息 +

Isogeometric modeling and analysis of piezoelectric integrated functionally graded porous plates reinforced by graphene platelets

LIU Qingyun1, LIU Kangren1, ZHANG Hongyi1, LIU Tao1,2

Author information +

文章历史 +

摘要

基于等几何分析方法和一种仅含有4自由度的简化一阶剪切变形理论（Simple first-order shear deformation theory, S-FSDT）建立了压电集成石墨烯增强功能梯度多孔（Piezoelectric integrated graphene platelets reinforced functionally graded porous, P-GPLs-FGP）板的数值分析模型。首先，利用Halpin-Tsai微观力学模型、闭胞体高斯随机场理论和混合定律得到了石墨烯增强功能梯度多孔板的有效材料属性；其次，基于等几何分析方法、S-FSDT和哈密顿原理推导了P-GPLs-FGP板的运动控制方程，并通过与已有算例对比验证了模型的准确性和有效性；最后，利用所建模型分析了孔隙分布形式、孔隙系数、石墨烯分布形式、石墨烯质量分数、边界条件和宽厚比对P-GPLs-FGP板固有频率和机-电载荷作用下静态弯曲响应的影响。研究结果表明：板的刚度与孔隙系数成反比，而在基体材料中添加少量的石墨烯可以有效地增强结构的刚度；与其他组合形式相比，板的刚度在孔隙PD-S分布和石墨烯GPL-S分布时最大。

Abstract

Based on the isogeometric analysis method and a simple first-order shear deformation theory (S-FSDT) with only four degrees of freedom per node, the numerical analysis model of piezoelectric integrated graphene platelets reinforced functionally graded porous (P-GPLs-FGP) plates is established. Firstly, the effective material properties of graphene platelets reinforced functionally graded porous plates are determined by using the Halpin-Tsai micromechanical model, the closed cell theory under Gaussian random field and the rule of mixture. Then, the governing equations of P-GPLs-FGP plates are derived based on the isogeometric analysis method, S-FSDT and Hamilton’s principle. The accuracy and effectiveness of developed model are demonstrated through numerical experiment with comparison. Finally, the effects of porosity distribution types, porosity coefficient, graphene platelets distribution patterns, graphene platelets weight fraction, boundary conditions and width-thickness ratio on natural frequencies and static bending response of P-GPLs-FGP plates under electro-mechanical loads are analyzed. The results show that the stiffness of the plates is inversely proportional to the porosity coefficient and can be effectively enhanced by adding a small amount of GPLs into the matrix material. Compared with other considered combinations, the plates with PD-S and GPL-S possess the highest stiffness.

导出引用

刘庆运1，刘康仁1，张红一1，刘涛1,2. 压电集成石墨烯增强功能梯度多孔板的等几何建模与分析[J]. 振动与冲击, 2024, 43(2): 280-290

LIU Qingyun1, LIU Kangren1, ZHANG Hongyi1, LIU Tao1,2. Isogeometric modeling and analysis of piezoelectric integrated functionally graded porous plates reinforced by graphene platelets[J]. Journal of Vibration and Shock, 2024, 43(2): 280-290

参考文献

[1] 李双蓓，吴海，莫春美. 基于样条无网格法的厚/薄压电功能梯度板动力分析[J].振动与冲击, 2017, 36(07):116-122+198. Li shuangbei, Wu hai, Mo chunmei. Dynamic analysis of thick/thin piezoelectric FGM plates with spline meshless method [J]. Journal of vibration and shock, 2017, 36(07): 116-12+198. [2] Zhang S Q, Wang Z X, Qin X S, et al. Geometrically nonlinear analysis of composite laminated structures with multiple macro-fiber composite (MFC) actuators[J]. Composite Structures, 2016, 150: 62-72. [3] Rafiee M, Liu X F, He X Q, et al. Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates[J]. Journal of Sound and Vibration, 2014, 333(14): 3236-3251. [4] 刘涛，李朝东，汪超，等. 基于三阶剪切变形理论的压电功能梯度板静力学等几何分析[J]. 振动与冲击, 2021, 40(01):73-85. Liu Tao, Li Chaodong, Wang Chao, et al. Static iso-geometric analysis of piezoelectric functionally graded plate based on third-order shear deformation theory [J]. Journal of vibration and shock, 2021, 40(01): 73-85. [5] Singh V K, Mahapatra T R, Panda S K. Nonlinear transient analysis of smart laminated composite plate integrated with PVDF sensor and AFC actuator[J]. Composite Structures, 2016, 157: 121-130. [6] 袁丽芸，向宇，陆静. 多孔吸声矩形薄板声振特性分析的一种新模型[J]. 振动与冲击, 2016, 35(13): 106-113. Yuan Liyun, Xiang Yu, Lu Jing. A new model for analysis on the vibroacoustic performance of a thin rectangular porous plate. Journal of vibration and shock, 2016, 35(13): 106-113. [7] Chen D, Kitipornchai S, Yang J. Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core[J]. Thin-Walled Structures, 2016, 107: 39-48. [8] Smith B H, Szyniszewski S, Hajjar J F, et al. Steel foam for structures: A review of applications, manufacturing and material properties[J]. Journal of Constructional Steel Research, 2012, 71: 1-10. [9] Phung-Van P, Ferreira A J M, Nguyen-Xuan H, et al. Scale-dependent nonlocal strain gradient isogeometric analysis of metal foam nanoscale plates with various porosity distributions[J]. Composite Structures, 2021, 268: 113949. [10] 高英山，张顺琦，黄钟童. CNT纤维增强功能梯度复合板非线性建模与仿真[J]. 机械工程学报, 2019, 55(8): 80-87. Gao Yingshan, Zhang Shunqi, Huang Zhongtong. Nonlinear modeling and simulation of carbon nanotube fiber reinforced composite plate[J]. Journal of mechanical engineering, 2019, 55(8): 80-87.(in Chinese) [11] Zhao Y F, Zhang S Q, Wang X, et al. Nonlinear analysis of carbon nanotube reinforced functionally graded plates with magneto-electro-elastic multiphase matrix[J]. Composite Structures, 2022, 297: 115969. [12] 陈碧静，黄永辉，杨智诚，等. 功能梯度石墨烯增强复合材料拱在脉冲荷载下的动力屈曲分析[J]. 工程力学，2022, 39(S1): 370-376. Chen Bijing, Huang Yonghui, Yang Zhicheng, et al. Dynamic buckling of functionally graded graphene nanoplatelets reinforced composite arches under pulse load[J]. Engineering Mechanics, 2022, 39(S1): 370-376. [13] 罗东晖，黄友钦，杨振宝. 功能梯度石墨烯增强复合板的自由振动分析[J]. 科学技术与工程，2020, 20( 26) : 10674-10682. Luo Donghui, Huang Youqin, Yang Zhenbao. Free vibration of functionally graded graphene reinforced composite plates[J]. Science Tech-nology and Engineering, 2020, 20(26): 10674-10682. [14] Yang B, Mei J, Chen D, et al. 3D thermo-mechanical solution of transversely isotropic and functionally graded graphene reinforced elliptical plates[J]. Composite Structures, 2018, 184: 1040-1048. [15] Song M, 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. [16] Kitipornchai S, Chen D, Yang J. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets[J]. Materials & Design, 2017, 116: 656-665. [17] Chen D, Yang J, Kitipornchai S. Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams[J]. Composites Science and Technology, 2017, 142: 235-245. [18] Li Z, Chen Y, Zheng J, et al. Thermal-elastic buckling of the arch-shaped structures with FGP aluminum reinforced by composite graphene platelets[J]. Thin-Walled Structures, 2020, 157: 107142. [19] Gao K, Gao W, Chen D, et al. Nonlinear free vibration of functionally graded graphene platelets reinforced porous nanocomposite plates resting on elastic foundation[J]. Composite Structures, 2018, 204: 831-846. [20] Li Q, Wu D, Chen X, et al. Nonlinear vibration and dynamic buckling analyses of sandwich functionally graded porous plate with graphene platelet reinforcement resting on Winkler–Pasternak elastic foundation[J]. International Journal of Mechanical Sciences, 2018, 148: 596-610. [21] Teng M W, Wang Y Q. Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets[J]. Thin-Walled Structures, 2021, 164: 107799. [22] Xu M, Li X, Luo Y, et al. Thermal buckling of graphene platelets toughening sandwich functionally graded porous plate with temperature-dependent properties[J]. International Journal of Applied Mechanics, 2020, 12(08): 2050089. [23] Arshid E, Amir S, Loghman A. Thermal buckling analysis of FG graphene nanoplatelets reinforced porous nanocomposite MCST-based annular/circular microplates[J]. Aerospace Science and Technology, 2021, 111: 106561. [24] Yas M H, Rahimi S. Thermal buckling analysis of porous functionally graded nanocomposite beams reinforced by graphene platelets using Generalized differential quadrature method[J]. Aerospace Science and Technology, 2020, 107: 106261. [25] 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. [26] Anamagh M R, Bediz B. Free vibration and buckling behavior of functionally graded porous plates reinforced by graphene platelets using spectral Chebyshev approach[J]. Composite Structures, 2020, 253: 112765. [27] Li Z, Zheng J. Structural failure performance of the encased functionally graded porous cylinder consolidated by graphene platelet under uniform radial loading[J]. Thin-Walled Structures, 2020, 146: 106454. [28] Genao F Y, Kim J, Żur K K. Nonlinear finite element analysis of temperature-dependent functionally graded porous micro-plates under thermal and mechanical loads[J]. Composite Structures, 2021, 256: 112931. [29] Nguyen N V, Nguyen-Xuan H, Lee D, et al. A novel computational approach to functionally graded porous plates with graphene platelets reinforcement[J]. Thin-Walled Structures, 2020, 150: 106684. [30] Li K, Wu D, Chen X, et al. Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets[J]. Composite Structures, 2018, 204: 114-130. [31] Nguyen Q H, Nguyen L B, Nguyen H B, et al. A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets[J]. Composite Structures, 2020, 245: 112321. [32] Al-Furjan M S H, Habibi M, Ebrahimi F, et al. A coupled thermomechanics approach for frequency information of electrically composite microshell using heat-transfer continuum problem[J]. The European Physical Journal Plus, 2020, 135(10): 1-45. [33] Moradi-Dastjerdi R, Behdinan K. Stability analysis of multifunctional smart sandwich plates with graphene nanocomposite and porous layers[J]. International Journal of Mechanical Sciences, 2020, 167: 105283. [34] Nguyen L B, Nguyen N V, Thai C H, et al. An isogeometric Bézier finite element analysis for piezoelectric FG porous plates reinforced by graphene platelets[J]. Composite Structures, 2019, 214: 227-245. [35] Nguyen N V, Nguyen L B, Nguyen-Xuan H, et al. Analysis and active control of geometrically nonlinear responses of smart FG porous plates with graphene nanoplatelets reinforcement based on Bézier extraction of NURBS[J]. International Journal of Mechanical Sciences, 2020, 180: 105692. [36] Thai H T, Choi D H. A simple first-order shear deformation theory for the bending and free vibration analysis of functionally graded plates[J]. Composite Structures, 2013, 101: 332-340. [37] Thai H T, Choi D H. A simple first-order shear deformation theory for laminated composite plates[J]. Composite Structures, 2013, 106: 754-763. [38] Roberts A P, Garboczi E J. Computation of the linear elastic properties of random porous materials with a wide variety of microstructure[J]. Proceedings Mathematical Physical & Engineering Sciences, 2002(2021).