The resonance phenomenon is for the first time investigated in anisotropic and functionally graded anisotropic nano-size structure. The structure is considered as a doubly curved shell which is modeled exploiting a quasi-three-dimensional model and nonlocal strain gradient theory in order to predict the small-size effects. The doubly-curved nanoshell is made from aragonite with an orthorhombic crystal system. The corresponding governing equations and boundary conditions, which include simply supported edges, are obtained using Hamilton principle. Then, an analytical technique based Navier solution procedure is used for the dynamic problem in which the double Fourier series has been applied to satisfy the conditions in edges. The extended numerical examples have been shown the sensitivity of resonance position to geometrical parameters, small-size parameters, and the shape of shell panels. Furthermore, we provide a comparison between the present anisotropic model with its isotropic one to ignore the complexity in equations.

首次在各向异性和功能梯度各向异性纳米尺寸结构中研究了共振现象。该结构被认为是双曲壳，它是利用准三维模型和非局部应变梯度理论建模的，以预测小尺寸效应。双重弯曲的纳米壳由具有正交晶系晶体的文石制成。使用汉密尔顿原理获得相应的控制方程和边界条件，其中包括简单支撑的边。然后，基于解析技术的Navier求解程序用于动力学问题，在该动力学问题中，已应用双重傅里叶级数来满足边缘条件。扩展的数值示例已经表明共振位置对几何参数的敏感性，小尺寸的参数，以及壳面板的形状。此外，我们在当前各向异性模型与其各向同性模型之间进行了比较，以忽略方程的复杂性。