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General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels

机译：双曲层合复合材料壳体和面板自由振动的一般高阶等效单层理论

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摘要

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.
机译：本文提供了二维的高阶等效单层理论的一般公式，该理论用于薄且厚的双曲层压复合壳和具有不同曲率的面板的自由振动。该理论框架涵盖了使用基于Carrera统一公式（CUF）的一般位移场对壳结构进行的动力学分析，包括拉伸和之字形效果。沿厚度方向的膨胀顺序被视为自由参数。当前一般高阶公式的起点是运动学假设的提议，该运动学假设具有任意数量的自由度，适合于代表文献中提出的大多数位移场。这项工作的主要目的是确定显式基本运算符，该运算符不仅可用于等效单层（ESL）方法，而且可用于层明智（LW）方法。作者首次获得了用正交曲线坐标系表示的这种基本算子。使用广义差分正交（GDQ）和广义积分正交（GIQ）技术以数值方式解决了二维自由振动壳问题。将GDQ结果与文献和商业法规中的最新论文进行比较。

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