Investigation of the mechanical properties on the large amplitude free vibrations of the functionally graded material sandwich plates

Abstract

In this paper, the geometrically nonlinear formulation based on von Karman’s assumptions is employed to study the large amplitude free vibrations of functionally graded materials sandwich plates. The functionally graded material sandwich plate is made up of two layers of power-law functionally graded material face sheet and one layer of ceramic homogeneous core. A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange’s equations. Employing the harmonic balance method, the equations of motion are converted from time domain to frequency domain and then solved iteratively using the linearized updated mode method. Results for linear and nonlinear frequency parameters of the simply supported functionally graded material sandwich plates are computed and compared with the published values, and an excellent agreement was found. The influence of the mechanical properties of the functionally graded material, thickness ratio of FGM layers, and volume fraction exponent on the backbone curves and on the nonlinear frequency parameters are investigated. The effects of the material properties of two different types of ceramics on the large amplitude vibration behaviors of the functionally graded material sandwich plates is also presented and discussed for the first time.

Factors Affecting the Stability of Functionally Graded Sandwiched Beams

“…A hierarchical finite element is employed to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia. The equations of motion for the nonlinear vibration of the functionally graded material sandwich plates are obtained using Lagrange"s equations [16]. The study of effect of the system parameters on free vibration behavior of FGO and FGSW beams forms an important aspect of investigation [17].…”

In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

“…Joseph and Mohanty [36] investigated the buckling and free vibration of a sandwich plate with viscoelastic core and FG material constraining lamina under high temperature environment by using the first-order shear deformation theory and considering both the longitudinal and transverse deformation of the core. Belalia [37] investigated the large amplitude free vibrations of FG sandwich plates by using the geometrically nonlinear formulation based on von Karman’s assumptions. A hierarchical finite element was employed in his study to define the model, taking into account the effects of the transverse shear deformation and the rotatory inertia.…”

Natural frequency, damping and forced responses of sandwich plates with viscoelastic core and graphene nanoplatelets reinforced face sheets

“…Feng et al (2017) developed theoretical formulations to study the nonlinear free vibration of a multilayer polymer nanocomposite beam reinforced by GPLs. Belalia (2019) investigated the free vibrations of the geometrically nonlinear functionally graded sandwich plates with ceramic core by von Karman’s assumptions. Hellal et al (2019) examined the hygro-thermal environmenal effects on dynamic and buckling of functionally graded sandwich plates resting on elastic foundations, and Joseph and Mohanty (2019) employed the finite element method to study the free vibration of a three-layered sandwich plate with the viscoelastic core layer and functionally graded material constraining layer.…”