Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

Abstract

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

A Refined Simple First-Order Shear Deformation Theory for Static Bending and Free Vibration Analysis of Advanced Composite Plates

“…A nonlinear analysis of FGM plates subjected to transverse loads in the thermal environment was investigated by Shen et al [38,39] using the TSDT. Yang et al [40] studied the buckling, free vibration and dynamic stability of laminated FGM plates using the HSDT. Yang and his co-authors [40] studied the free vibration, buckling behavior, and dynamic stability of laminated FGM plates using the HSDT.…”

Parametric Instability of Functionally Graded Timoshenko Beams with an Open Edge Crack

“…(17) is a Mathieu-Hill type equation describing the dynamic stability behavior of the laminated plate under a time-dependent periodic in-plane force. The Bolotin method [16] is employed to locate the points on the boundaries of unstable regions. Since previous studies showed that the principle unstable regions (PURs) associated with the period are usually larger than those associated with and are of greater practical importance, this paper considers the solutions with the period only.…”

“…Since previous studies showed that the principle unstable regions (PURs) associated with the period are usually larger than those associated with and are of greater practical importance, this paper considers the solutions with the period only. The standard process which is available in many references such as Ref [16] is omitted here due to page limit. Results show that the PURs of cracked FGM beams are significantly influenced by crack depth, material property gradient and beam slenderness ratio while the effect of the crack location is seen to be insignificant.…”

New Shape Function for the Bending Analysis of Functionally Graded Plate

“…The most frequently used HSDT theory is the third-order shear deformation theory (TSDT) developed for composite laminates [26,27], which takes into consideration the effects of shear strains by satisfying the condition of keeping the upper and lower surface of the laminates free of stresses. Later, that theory was used in the analysis of FGM plates [28,29] for solving buckling problems [30,31], free vibrations and dynamic stability [32,33]. In addition to TSDT, there are HSDT theories based on the shape functions which represent a special group of HSDT theories introduced in order to eliminate the need for correctional factors [34,35].…”