Free vibration of exponential functionally graded rectangular plates in thermal environment with general boundary conditions

摘要

In this article, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of Classical or Kirchhoff's plate theory are investigated. The eigenfrequency equation is obtained by the use of Rayleigh-Ritz method. Displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of FG plate are supposed to vary along thickness direction of the constituents according to exponential law. The objective is to study the effects of constituent volume fractions and aspect ratios on the natural frequencies. New results for frequency parameters are incorporated under various sets of boundary conditions after performing a test of convergence. Comparison with the results from the existing literature is provided for validation in special cases. Mode shapes for clamped FG rectangular plates with respect to aspect ratios and constituent volume fractions are also reported. The present study also involves the power-law variation of temperature dependent material properties for the convergence and validation of the results for FG plate in thermal environment. As such, new results for exponential FG plate under the consideration of thermal conditions are incorporated after checking the convergence of frequencies.