Importance of Higher Order Modes and Refined Theories in Free Vibration Analysis of Composite Plates

This paper evaluates frequencies of higher-order modes in the free vibration response of simply-supported multilayered orthotropic composite plates. Closed-form solutions in harmonic forms are given for the governing equations related to classical and refined plate theories. Typical cross-ply (0 deg/90 deg) laminated panels (10 and 20 layers) are considered in the numerical investigation (these were suggested by European Aeronautic Defence and Space Company (EADS) in the framework of the “Composites and Adaptive Structures: Simulation, Experimentation and Modeling” (CASSEM) European Union (EU) project. The Carrera unified formulation has been employed to implement the considered theories: the classical lamination theory, the first-order shear deformation theory, the equivalent single layer model with fourth-order of expansion in the thickness direction $z$⁠, and the layerwise model with linear order of expansion in $z$ for each layer. Higher-order frequencies and the related harmonic modes are computed by varying the number of wavelengths $(m,n)$ in the two-plate directions and the degrees of freedom in the plate theories. It can be concluded above all that—refined plate models lead to higher-order frequencies, which cannot be computed by simplified plate theories—frequencies related to high values of wavelengths, even the fundamental ones, can be wrongly predicted when using classical plate theories, even though thin plate geometries are analyzed.