An innovative generalized Layer-Wise (LW) approach is proposed for the modal analysis of anisotropic doubly-curved shells with an arbitrary shape by employing the Generalized Differential Quadrature (GDQ) method. The geometrical description of shell structures can be traced from both the differential geometry and mapping technique based on a proper definition of the blending functions.

The kinematic field is described in each lamina by employing several interpolating polynomials in a generalized setting, while developing a LW theory that involves different orders of kinematic expansion. The Equivalent Single Layer (ESL) generalized formulation is, thus, derived as particular case of the LW theory. Angle-ply generally anisotropic laminated shells are here investigated, as well as layups with a thick foam softcore. Several numerical examples are illustrated, including different boundary conditions of the mapped geometry, different geometric curvatures for both unmapped and mapped paths, along with a variety of interpolating polynomials and expansion orders of the kinematic field. The accuracy of the proposed model is well-established by a comparative evaluation between our solutions in terms of frequencies and mode shapes and predictions based on classical 3D finite elements.

提出了一种创新的广义逐层 (LW) 方法，通过采用广义微分正交 (GDQ) 方法对具有任意形状的各向异性双曲面壳进行模态分析。壳结构的几何描述可以从基于混合函数的适当定义的微分几何和映射技术进行追踪。

通过在广义设置中使用多个插值多项式，同时开发涉及不同运动学展开阶数的 LW 理论，在每个层中描述了运动学场。因此，等效单层 (ESL) 广义公式是作为 LW 理论的特例推导出来的。这里研究了角层一般各向异性的层压壳，以及具有厚泡沫软芯的叠层。说明了几个数值示例，包括映射几何的不同边界条件、未映射和映射路径的不同几何曲率，以及运动场的各种插值多项式和展开阶数。