Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation
Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation
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DOI：
10.1016/j.compstruct.2018.06.076
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发表时间：
2018-11-01
影响因子：
6.3
通讯作者：
Zhang, Wei
中科院分区：
文献类型：
--
作者：
Mao, Jia-Jia;Zhang, Wei
石墨烯增强可以显著提高聚偏氟乙烯(PVDF)的压电性和力学性能。研究了均匀分散和非均匀分散石墨烯片层增强智能压电复合板的线性和非线性振动行为。有效杨氏模数由Halpin-Tsai平行模型预测，有效质量密度、泊松比和压电性由混合物法则计算。基于一阶剪切变形板理论、von Karman非线性几何关系和哈密顿原理，推导了智能压电复合板在不同边界条件下的运动控制方程。用微分求积法求解运动控制方程，得到了系统的非线性特征方程。并与现有的智能压电复合板的计算结果进行了比较，验证了分析的正确性。详细讨论了GPL的分布方式、层数、GPL的浓度和几何形状、板的几何形状、外电压和压电性能以及边界条件对GPL线性和非线性振动行为的影响。数值结果清楚地表明，利用广义最小二乘法来实现结构刚度显著提高的智能结构具有很大的潜力。
Graphene reinforcements can obviously enhance the piezoelectric properties as well as the mechanical properties of the polyvinylidene fluoride (PVDF). This paper investigates the linear and nonlinear vibration behaviors of the smart piezoelectric composite plate reinforced by uniformly and non-uniformly dispersing graphene platelets (GPLs). The effective Young's modulus is predicted by the Halpin Tsai's parallel model while the effective mass density, Possion's ratio and piezoelectric properties are calculated by the rule of the mixture. Based on the first-order shear deformation plate theory, von Karman nonlinear geometric relationship and Hamilton's principle, the governing equations of motion under different boundary conditions are derived for the smart piezoelectric composite plate. The governing equations of motion are solved to obtain the nonlinear eigenvalue equations by the differential quadrature (DQ) method. The analysis is validated by comparing with the current results of the smart piezoelectric composite plate. The effects of the GPL distribution pattern, stratification number, concentration and geometry of GPLs, plate geometry, external voltage and piezoelectric properties of GPLs as well as boundary conditions on the linear and nonlinear vibration behaviors are discussed in detail. The numerical results clearly illustrate that there exists the great potential for using GPLs in achieving smart structures with significantly improved structural stiffness.