Higher-order theories for the free vibrations of doubly-curved laminated panels with curvilinear reinforcing fibers by means of a local version of the GDQ method

The aim of this paper is to investigate the dynamic behavior of singly and doubly-curved panels reinforced by curvilinear fibers. The Variable Angle Tow (VAT) technology allows the placement of fibers along curvilinear paths with the purpose of improving dynamic performance of plates and shells. The effect of the variation of constants which define analytically the fiber orientation is also investigated by several parametric studies. The Carrera Unified Formulation (CUF) with different thickness functions along the three orthogonal curvilinear directions is the basis of the present theoretical model. Various doubly-curved laminated panels reinforced by curvilinear fibers are analyzed using several structural theories. The Local Generalized Differential Quadrature (LGDQ) method is employed to solve numerically free vibration problems. Compared to the well-known GDQ method from which it descends, the LGDQ is characterized by banded matrices instead of full ones, since the current technique considers only few points of the whole domain. Therefore, the solution of the equation system needs a lower computational effort.