This paper studies the free vibration behavior of hybrid laminated plates using a layer-wise formulation. The laminated structures are made of graphite fiber-reinforced composite (GFRC) and multilayer functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plies. The internal single-walled carbon nanotubes (SWCNTs) are distributed in layer-wise form along the ply thickness direction either uniformly or functionally graded according to four separate patterns. Both the linear and nonlinear of the CNTs distributions form are considered. Theatrical formulations are based on the first-order shear deformation theory (FSDT), and finite element method is employed to obtain the nondimensional natural frequency. The elastic modulus of both GFRC and CNTRC plies composed the hybrid laminated plate is obtained by a micromechanics model. Initially, the provided results are validated by comparing it with the literature; thereafter, a parametric study is carried out the influences of laminates configuration, number of CNTRC plies layers, CNT volume fraction, CNT distribution patterns, linear and nonlinear distribution of CNTs, plate width-to-thickness ratio, plate aspect ratio, boundary conditions, stacking sequences, and number of plies on the free vibration behavior of hybrid laminated plates. Some final remarks considering the laminated plate configuration and the distribution form of the CNT fillers are presented in order to provide a useful observation on the design criteria of the laminated composite plate structures.

本文使用分层公式研究混合层压板的自由振动行为。层压结构由石墨纤维增强复合材料（GFRC）和多层功能梯度碳纳米管增强复合材料（FG-CNTRC）制成。内部单壁碳纳米管（SWCNT）沿着层厚度方向以分层形式分布，或者根据四个单独的图案在功能上渐变。同时考虑了CNTs分布形式的线性和非线性。戏剧的表达是基于一阶剪切变形理论（FSDT），并采用有限元方法获得了无量纲的固有频率。通过微力学模型获得了由混合层压板组成的GFRC和CNTRC层的弹性模量。原来，通过与文献进行比较来验证所提供的结果；此后，进行了参数研究，研究了层压板结构，CNTRC层数，CNT体积分数，CNT分布模式，CNT的线性和非线性分布，板宽厚比，板长宽比，边界条件的影响，堆叠顺序以及层数取决于混合层压板的自由振动行为。提出了一些考虑层压板结构和CNT填料分布形式的最后评论，以便对层压复合板结构的设计标准提供有用的观察。CNTRC层的数量，CNT的体积分数，CNT的分布模式，CNT的线性和非线性分布，板的宽厚比，板的长宽比，边界条件，堆叠顺序和层数取决于混合体的自由振动行为层压板。提出了一些考虑层压板结构和CNT填料分布形式的最后评论，以便对层压复合板结构的设计标准提供有用的观察。CNTRC层的数量，CNT的体积分数，CNT的分布模式，CNT的线性和非线性分布，板的宽厚比，板的长宽比，边界条件，堆叠顺序和层数取决于混合体的自由振动行为层压板。提出了一些考虑层压板结构和CNT填料分布形式的最后评论，以便对层压复合板结构的设计标准提供有用的观察。