Nonlinear dynamic response of a functionally graded plate with a through-width surface crack

Abstract

A nonlinear vibration analysis of a simply supported functionally graded rectangular plate with a through-width surface crack is presented in this paper. The plate is subjected to a transverse excitation force. Material properties are graded in the thickness direction according to exponential distributions. The cracked plate is treated as an assembly of two subplates connected by a rotational spring at the cracked section whose stiffness is calculated through stress intensity factor. Based on Reddy's third-order shear deformation plate theory, the nonlinear governing equations of motion for the FGM plate are derived by using the Hamilton's principle. The deflection of each subplate is assumed to be a combination of the first two mode shape functions with unknown constants to be determined from boundary and compatibility conditions. The Galerkin's method is then utilized to convert the governing equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms under the external excitation, which is numerically solved to obtain the nonlinear responses of cracked FGM rectangular plates. The influences of material property gradient, crack depth, crack location and plate thickness ratio on the vibration frequencies and transient response of the surface-racked FGM plate are discussed in detail through a parametric study.

Vibration analysis of cracked FGM plates using higher-order shear deformation theory and extended isogeometric approach

“…Huang et al [32] used the Ritz method and the Reddy's third-order shear deformation theory (TSDT) to obtain the free vibration solution of FGM thick plates with side cracks. Yang et al [33] studied the nonlinear dynamic response of the cracked FGM plates based on TSDT using the Galerkin method. Recently, Huang et al [34] employed three-dimensional elasticity theory to study the free vibration of cracked rectangular FGM plates.…”

The bifurcation analysis on the circular functionally graded plate with combination resonances

“…It is very difficult to discuss the bifurcation behavior of (21) in full detail. Considering (20) and letting α 1 = α 2 = α 4 = 0, α 3 = k 1 , α 5 = k 2 , we only analyze the engineering unfolding as follows:…”

“…Here, they considered the resonant case is 1:1 internal resonance and principal parametric resonance. Recently, Yang et al [20] carried out an analysis of the nonlinear vibration of a simply supported functionally graded rectangular plate with a through-width surface crack.…”

Transient Response Analysis for a Circular Sandwich Plate with an FGM Central Disk

“…The parts under high temperatures have higher content of ceramics than metals and vice versa. Mechanical properties of this material always show a smooth and continuous change from one surface to the other by varying the volume fraction of constituent materials [3][4][5][6]. FGM structures often have the ability to withstand high temperatures while keep structural integrity, but they are easy to be sensitive to large temperature gradients or mechanical loads.…”