Frequency of Functionally Graded Plates with Three-Dimensional Asymptotic Approach
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The harmonic vibration problem of functionally graded plats is studied by means of a three-dimensional asymptotic theory formulated in terms of transfer matrix. Instead of using multiple time scales expansion, the frequency is determined in a much simpler way that renders the asymptotic method to be practically validated for finding any high-order solutions. This is illustrated by applying the refined formulation to a functionally graded rectangular plate with simply supported edges. The locally effective material properties are estimated by the Mori-Tanaka scheme. Accurate natural frequencies associated with flexural, extensional, and thickness-stretching modes are provided.
author list (cited authors)
Reddy, J. N., & Cheng, Z.