Abstract
The free vibration analysis of moderately thick functionally graded (FG) sector plates resting on two-parameter elastic foundation with general boundary conditions is presented via Fourier-Ritz method, which is composed of the modified Fourier series approach and the Ritz procedure. The material properties are assumed to vary continuously along the thickness according to the power-law distribution. The bilayered and single-layered functionally graded sector plates are obtained as the special cases of sandwich plates. The first-order shear deformation theory (FSDT) is adopted to construct the theoretical model. Under current framework, regardless of boundary conditions, each displacement and each rotation of plates is represented by the modified Fourier series consisting of a standard Fourier cosine series and several closed-form auxiliary functions introduced to ensure and accelerate the convergence of the series representation. Then, the accurate solutions are obtained by using the Ritz procedure based on the energy function of sector plates. The present method shows good convergence, reliability, and accuracy by comprehensive investigation with some selected classical boundary conditions. Numerous new vibration results for moderately thick FG sandwich sector plates are provided. The effects of the elastic restraint parameters and so forth on free vibration characteristic of sector plates are presented.
Highlights
The sector plates have been widespread in many branches of engineering applications such as architectural structures, bridges, hydraulic structures, containers, airplane, missiles, ships, and instruments due to the excellent performance like light weight and an effective form with high loadcarrying capacity, economy, and technological effectiveness
The aim of this paper is to propose a benchmark solution for the vibration characteristics of the functionally graded (FG) sandwich sector plates with general boundary conditions and resting on elastic foundation
The aim of this paper is to study the vibration analysis of moderately thick functionally graded sector plates resting on two-parameter elastic foundation with general boundary conditions
Summary
The sector plates have been widespread in many branches of engineering applications such as architectural structures, bridges, hydraulic structures, containers, airplane, missiles, ships, and instruments due to the excellent performance like light weight and an effective form with high loadcarrying capacity, economy, and technological effectiveness. As is known to us all, the functionally graded material and the fiber-reinforced composite laminated structures possess outstanding characteristics such as the high specific strength and stiffness, good corrosion resistance, and long fatigue life. A large quantity of research efforts has been devoted to the vibration analysis of composite laminated and functionally graded sector plates [1–39] in the literature. In these researches, the scope of the boundary conditions and accuracy of solution for the vibration information of the plate rest on the plate theories and the numerical method. Thereafter, the moderately thick plate theory including the first-order shear deformation theory and higher-order shear deformation theory is developed which, z r
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