Three-dimensional solutions for free vibration of variable stiffness laminated sandwich plates with curvilinear fibers

Abstract

This paper is concerned with the free vibration of variable stiffness laminated sandwich plates with curvilinear fibers. The three-dimensional elasticity theory and the p-version of the finite element method are adopted for the analysis. The skin is composed of one or more plies with curvilinear fibers. The fiber path orientation angle in a ply is assumed to vary linearly with the x coordinate. The plies may be stacked symmetrically or anti-symmetrically with respect to the middle surface of the plate. Each layer is modeled as one brick p-element. The principle of virtual displacements is used to derive the element stiffness and mass matrices. The generalized displacements at vertices, edges, and faces shared by elements are matched to ensure inter-element compatibility. Since no solutions are available for the free vibration of such variable stiffness laminated sandwich plates, the validity, convergence, and accuracy of the present three-dimensional method are established by comparing with existing three-dimensional frequencies for constant stiffness laminated sandwich plates with rectilinear fibers. The study reveals that inter-layer modal bending stresses are discontinuous; modal transverse shearing stresses are constant in the core; the sign of modal transverse shearing stresses can change through the thickness of the skin; and the shape of modal cross-sectional warping is influenced by the mode number and stacking sequence of plies. Three-dimensional frequencies are presented for different fiber orientation angles, boundary conditions, aspect ratios, thickness ratios, core/skin thickness ratios, and stacking sequences of plies. The accurate results presented here will serve as a benchmark for future investigations.

Elasticity solution for a sandwich plate having composite facesheets with in-plane grading

“…Karamanli [32] presented a quasi-three dimensional shear deformation theory to study the bending response of a bi-directionally graded sandwich beam subjected to transverse loading; a power-law variation was chosen for the volume fraction along both the in-plane as well as thickness direction and simple rule of mixtures was employed to calculate the effective properties. Using p-version finite elements, Houmat [33] presented a three-dimensional vibration solution for sandwich plates having laminated composite non-homogeneous facesheets with curvilinear fibres and a homogeneous isotropic or orthotropic core; the fibre orientation of any facesheet layer was taken to vary linearly along an in-plane direction. Very recently, Heshmati and Jalali [34] studied the free vibration behaviour of sandwich circular plates with uniform facesheets and an isotropic core made up of a porous material with radial variation of porosity using the FSDT.…”