Huu Quoc Tran, Minh Tu Tran, Van Tham Vu
Faculty of Industrial and Civil Engineering, National University of Civil Engineering, Hanoi 100000, Vietnam.
Materials (Basel). 2019 Nov 7;12(22):3675. doi: 10.3390/ma12223675.
This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell's equation and Hamilton's principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.
本文提出了一种新的四变量精细板理论，用于层合压电功能梯度碳纳米管增强复合材料板（PFG-CNTRC）的自由振动分析。该理论包括沿板厚呈抛物线分布的横向剪应变，并满足板的两个自由表面处的零牵引边界条件。因此，不需要剪切修正因子。各功能梯度碳纳米管（FG-CNT）层厚度方向上碳纳米管的分布可以是功能梯度的或均匀分布的。此外，假设压电层中的电势沿厚度呈二次分布。利用麦克斯韦方程和哈密顿原理推导了PFG-CNTRC矩形板的运动方程。采用纳维技术计算了电边界条件为闭路和开路的简支混合板的固有频率。针对体积分数、碳纳米管分布、层数、碳纳米管纤维取向和压电层厚度对混合板自由振动响应的影响进行了新的参数研究。
