The effect of nonlinear temperature distribution on the vibrational behavior of a size‐dependent FG laminated rectangular plates undergoing prescribed overall motion

Abstract

In this article, the effect of the nonlinear temperature distribution on the free vibration analysis of size‐dependent rotating laminated rectangular FG micro‐/nanoplates are developed based on modified couple stress theory and exponential shear deformation theory. The modified couple stress theory model contains one length scale parameter to consider the small size effect. In exponential shear deformation theory, exponential functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The Eigen frequency 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. The effect of material compositions, rotation speed, hub ratio, length‐to‐thickness ratio, aspect ratio, material length scale parameter, number of layered, and temperature filed on the vibration characteristics is examined. The present theoretical results are verified by comparing with those in literature. POLYM. COMPOS., 40:766–778, 2019. © 2018 Society of Plastics Engineers

The effect of multidimensional temperature distribution on the vibrational characteristics of a size-dependent thick bi-directional functionally graded microplate

“…While the third-order plate theory takes account both normal and shear deformations without the shear correction factor, the authors could not find any research on free vibration of 2D-FG microplates using this theory. 45–48 Moreover, the assumption of multidimensional temperature distribution is required to study effect of thermal environment in 2D-FGMs. So, the innovation of this article is application of the third-order plate theory with size-dependent model for free vibration analysis of bi-directional FG microplate.…”