A collocation model based on a Generalized Differential Quadrature Method (GDQM) is proposed for the dynamic analysis of anisotropic curved laminated structures with a central lattice core and different external constraints. The theory is based on the Equivalent Single Layer (ESL) approach, together with higher-order kinematic assumptions. The reliability of the proposed method is checked with respect to classical 3D FEM-based solutions, for different shell geometries, lamination schemes and unit cell configurations. Based on the numerical investigation, the proposed formulation reveals to be computationally performing even for complicated shapes and structural members, compared to more expensive commercial finite-element-based packages.