Three-dimensional vibration behavior of FGM doubly-curved laminated structures

This paper investigates a new spectral solution technique to accurately and efficiently predict the dynamics of laminated doubly curved structures that includes functionally graded materials (FGM). To describe the effective material properties, Mori-Tanaka method is used. The integral boundary value problem of FGM curved structures, three-dimensional (3D) elasticity equations are used together with extended Hamilton’s principle. For the numerical solution, Tchebychev polynomials are used and the system matrices are calculated through the exact evaluation of differentiation and inner-product operations using the Tchebychev matrix operators. Finally, to impose the essential boundary conditions on the boundary value problem, the projection matrices approach is used; therefore the necessity of applying different basis/trial functions for each different structure and boundary conditions is eliminated. To validate and demonstrate the performance of the presented technique, various case studies are performed on laminated doubly-curved composite structures.