Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response

This paper presents the free vibration analysis of composite sandwich plates and doubly-curved shells with variable stiffness. The reinforcing fibers are located in the external skins of the sandwich structures according to curved paths. These curvilinear paths are described by a general expression that combines power-law, sinusoidal, exponential, Gaussian and ellipse-shaped functions. As a consequence, the reinforcing fibers are placed in these orthotropic layers in an arbitrary manner, in order to achieve the desired mechanical properties. The effect of this variable fiber orientation on the natural frequencies is investigated by means of several parametric studies. As far as the structural theory is concerned, an Equivalent Single Layer (ESL) approach based on the well-known Carrera Unified Formulation (CUF) is employed. The Murakami’s function is added to the kinematic model to capture the zig-zag effect, when the soft-core effect is significant. Thus, several Higher-order Shear Deformation Theories (HSDTs) are taken into account in a unified manner. The differential geometry is employed to describe the reference surface of doubly-curved shells and panels, which are characterized by variable radii of curvature. The numerical solution is obtained using the Generalized Differential Quadrature (GDQ) method, due to its accuracy and stability features. The present solution is compared with the results available in the literature or obtained by finite element commercial codes.