Free Vibration Analysis of Laminated Doubly-Curved Shells with Arbitrary Material Orientation Distribution Employing Higher Order Theories and Differential Quadrature Method

In the present work, the dynamic behaviour of laminated anisotropic doubly-curved shells characterized by a generalized distribution of the material orientation angle is investigated employing higher order theories. The structural problem is developed following the Equivalent Single Layer (ESL) methodology, setting up a unified approach for the assessment of the displacement field variable with higher order theories. Accordingly, a generalized three-dimensional distribution of the material orientation angle is associated to each layer of the stacking sequence, accounting for an in-plane bivariate power distribution and out-of-plane symmetric and unsymmetric profiles described with both polynomial and non-polynomial analytical expressions. The funda-mental equations are derived from the Hamiltonian Principle, and they are numerically tackled employing the Generalized Differential Quadrature (GDQ) method directly in the strong form. Moreover, a generalized three-dimensional set of linear elastic springs is implemented for the assessment of con-conventional boundary con-ditions. Furthermore, a generalized isogeometric mapping of the physical domain accounts for arbitrarily-shaped structures. The model is validated successfully with respect to refined three-dimensional classical models, and it is, then, applied systematically to check for the sensitivity of the mechanical response to the structural curvature, external constraints, and material orientation angle distributions.