Xue Kai, Huang Wenhao, Li Qiuhong
College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China.
Materials (Basel). 2020 Jul 13;13(14):3113. doi: 10.3390/ma13143113.
The main purpose of this paper is to establish an analysis model of laminated composite rectangular plate with/without cutouts on the basis of three-dimensional elasticity theory and provide the exact three-dimensional solution. In the present work, the effect of the cutout is considered by subtracting the energies of cutouts from the total energy of the entire plate. The standard three-dimensional trigonometric cosine Fourier series and auxiliary Fourier series are chosen as admissible functions, and the Hamilton's principle and Rayleigh-Ritz procedure are used to obtain the exact solution. In order to verify the effectiveness and reliability of the proposed method, some numerical results are obtained, and the results are compared with the ones available in the literature or finite element analysis. Finally, the effects of some key parameters which will affect the vibration characteristics are analyzed, and the non-dimensional frequency parameters are obtained, which can serve as benchmark data for the future research.
本文的主要目的是基于三维弹性理论建立带/不带切口的层合复合矩形板的分析模型，并给出精确的三维解。在当前工作中，通过从整个板的总能量中减去切口的能量来考虑切口的影响。选择标准的三维三角余弦傅里叶级数和辅助傅里叶级数作为容许函数，并利用哈密顿原理和瑞利 - 里兹法来获得精确解。为了验证所提方法的有效性和可靠性，得到了一些数值结果，并将结果与文献中的结果或有限元分析结果进行了比较。最后，分析了一些影响振动特性的关键参数的影响，并得到了无量纲频率参数，可为未来的研究提供基准数据。
