Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

By S. Kitipornchai, Jie Yang, Kim-Meow Liew. 2004

176 citations recorded by the source corpus.

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed.

Subfields: Aerospace Engineering, Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/786119eeb1fb3970580b597e076171b1bba647a1

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In Aerospace Engineering

In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Nonlinear vibrations of FGM rectangular plates in thermal environments (2011, unknown): “[19].”
Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory (2010, background): “They also examined the nonlinear free vibrations of FGM plates with various geometrical imperfections [24].”
Stress, vibration and buckling analyses of FGM plates—A state-of-the-art review (2015, methodology): “[241,242] used the similar methodology to study the effect of initial imperfection on the nonlinear vibration and random free vibration of laminated FGM plates in thermal environments.”
Free vibration analysis of multi-directional functionally graded circular and annular plates (2012, methodology): “[22] used a combination of differential quadrature method, Galerkin technique, and an iteration process to solve the nonlinear vibration of laminated FGM plates with geometric imperfections.”
Nonlinear free vibration of shear deformable sandwich beam with a functionally graded porous core (2016, methodology): “[34] applied a semi-analytical method to the nonlinear vibration analysis of imperfect shear deformable laminated rectangular plates with Reddy’s higher-order shear deformation plate theory, and obtained the vibration frequencies under different boundary conditions.”