The present paper provides a general formulation of a 2D higher-order equivalent single layer theory for free vibrations of thin and thick doubly-curved laminated composite shells and panels with different curvatures. The theoretical framework covers the dynamic analysis of shell structures by using a general displacement field based on the Carrera’s Unified Formulation (CUF), including the stretching and zig-zag effects. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order formulation is the proposal of a kinematic assumption, with an arbitrary number of degrees of freedom, which is suitable to represent most of the displacement field presented in literature. The main aim of this work is to determine the explicit fundamental operators that can be used not only for the Equivalent Single Layer (ESL) approach, but also for the Layer Wise (LW) approach. Such fundamental operators, expressed in the orthogonal curvilinear co-ordinate system, are obtained for the first time by the authors. The 2D free vibration shell problems are numerically solved using the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. GDQ results are compared with recent papers in the literature and commercial codes.
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