In this article, the natural vibration investigation of a functionally graded material sandwich plate with initial geometrical imperfection of the exponential function is conducted. Two face sheets of the sandwich plate are composited by functionally graded material. Their material coefficients are affected by temperature and vary in the direction of thickness following the power law. The core layer is only the metal. With the aid of Reddy’s displacement fields, a quasi-three-dimensional model is used, in which the effects of transverse stretching on natural vibration are considered. The natural frequencies and model shapes of the system are calculated on the basis of Rayleigh–Ritz method and Chebyshev polynomials. A comparison of these results with those of the existing three-dimensional theory results shows the validity and computability of present method. The influences of various parameters on the natural frequencies are researched in detail.

在本文中，对具有梯度函数的初始几何缺陷的功能梯度材料夹心板进行了固有振动研究。夹心板的两个面板由功能渐变材料复合而成。它们的材料系数受温度影响，并且在厚度方向上遵循幂定律变化。核心层仅是金属。在雷迪位移场的帮助下，使用了准三维模型，其中考虑了横向拉伸对自然振动的影响。系统的固有频率和模型形状是根据Rayleigh-Ritz方法和Chebyshev多项式计算的。将这些结果与现有的三维理论结果进行比较，表明了本方法的有效性和可计算性。详细研究了各种参数对固有频率的影响。