Abstract
Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.
Highlights
The laminated composites are widely used in various engineering applications—such as aerospace, mechanical, civil, and automotive engineering—due to high specific strength and stiffness, light weight, and good thermal stability
The results showed that only the bending stiffness formulations of functionally graded materials (FGMs) plates are not similar with homogeneous plates due to their more complicated combination of material properties
The results showed that the artificial neural network (ANN) method is a useful method to predict natural frequency, and the statespace-based differential quadrature method (SSDQM) has fast convergence speed
Summary
The laminated composites are widely used in various engineering applications—. Such as aerospace, mechanical, civil, and automotive engineering—due to high specific strength and stiffness, light weight, and good thermal stability. In order to overcome the adverse effects of laminated composites in mechanical properties, the engineering application of functionally graded materials (FGMs) was first proposed in 1984 by a group of aerospace scientists, due to a need for a type of material that can withstand high temperature difference in a space plane project [3]. The FGMs are a new type of advanced composite materials which are generally formed by two materials with smooth and continuous variation in specific direction from one surface to another, eliminating inter-laminar problems.
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