Abstract
The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.
Highlights
The definition of Functionally Graded Materials (FGM), which was considered in Japan in 1984 firstly by materials scientists, is to make a class of composite materials that varies the material properties from one surface to the other based on a specific gradient [1,2,3]
Increase, especially Functionally Graded Material plates (FGM plates), FGM is often exposed to a variety of thermal conditions resulting in non-uniform and uniform thermal loads, which cause variation in the vibration characteristics of structures [8]
We assessed the influences of various boundary conditions, temperature change, and the material graded index on the dynamic response
Summary
The definition of Functionally Graded Materials (FGM), which was considered in Japan in 1984 firstly by materials scientists, is to make a class of composite materials that varies the material properties from one surface to the other based on a specific gradient [1,2,3]. As the demands of FGM increase, especially Functionally Graded Material plates (FGM plates), FGM is often exposed to a variety of thermal conditions resulting in non-uniform and uniform thermal loads, which cause variation in the vibration characteristics of structures [8]. Accurate and efficient tools will be required to predict their dynamic response for vibration control and structural design. Given the efficient and safe use of FGM, many investigations considering multiple loading conditions and environments have been published by numerous research workers using different measures. Some of the papers have been carried out to understand the vibration characteristics of Functionally Graded FG plates such as the free vibration and stress distribution of a structure made of Materials 2019, 12, 4084; doi:10.3390/ma12244084 www.mdpi.com/journal/materials
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