Abstract
This paper presents a variational formulation for the free vibration analysis of unsymmetrically laminated composite plates with elastically restrained edges. The study includes a micromechanics approach that allows starting the study considering each layer as constituted by long unidirectional fibers in a continuous matrix. The Mori-Tanaka method is used to predict the mechanical properties of each lamina as a function of the elastic properties of the components and of the fiber volume fraction. The resulting mechanical properties for each lamina are included in a general Ritz formulation developed to analyze the free vibration response of thick laminated anisotropic plates resting on elastic supports. Comprehensive numerical examples are computed to validate the present method, and the effects of the different mechanical and geometrical parameters on the dynamical behavior of different laminated plates are shown. New results for general unsymmetrical laminates with elastically restrained edges are also presented. The analytical approximate solution obtained in this paper can also be useful as a basis to deal with optimization problems under, for instance, frequency constraints.
Highlights
Fiber-reinforced composite laminated plates are extensively used in many engineering applications
This paper presents a variational formulation for the free vibration analysis of unsymmetrically laminated composite plates with elastically restrained edges
Among the numerous theories used for laminated plates that include the transverse shear strain, the first-order shear deformation theory (FSDT) [1, 2] is adequate for the computation of global responses and simultaneously has some advantages due to its simplicity and low computational cost
Summary
Fiber-reinforced composite laminated plates are extensively used in many engineering applications. Nallim and Grossi [23] studied the vibration of symmetric laminated plates resting on elastic support employing the Ritz method and beam orthogonal polynomials as approximated functions. These kind of approximate functions (in one or two variables) have been used by many authors to the free vibration analysis of, both homogeneous and nonhomogeneous, plates (Chakraverty et al [24,25,26] and Chow et al [27], among others). The dynamic response of the unsymmetrical laminated plate, with elastically restrained edges, is analyzed using the first-order shear deformation theory and the Ritz method with beam orthogonal polynomials as coordinate functions. The approximate analytical solution developed here is very useful to understand, both qualitatively and quantitatively, the behavior of complex laminated plates
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