Abstract
An analytical solution is proposed to investigate the time-dependent characteristics of two-layer functionally graded plates with a viscoelastic interlayer. The elastic modulus in each graded layer varies through the thickness following an arbitrary function, and its mechanical properties are described based on the Kirchhoff theory. The Maxwell-Wiechert model is applied to simulate the viscoelastic adhesive interlayer with the neglect of memory effect. The energy equation of the system is expressed by the deformation components, which are expanded as the double trigonometric series. By virtue of variational method, the solutions of stress and deformation are determined efficiently. The comparison study indicates that the present solution matches the finite element solution well; however, the finite element method is highly time-consuming because of the fine mesh in the geometric shape and the time step. Finally, the influences of the geometry and material on the time-dependent behavior of the structure are discussed in detail.
Highlights
Graded (FG) materials composed of two or more constituent phases are being extensively researched due to their continuous property along a particular orientation and are widely applied in weight sensitive areas, such as sensors and actuators, metallic porous and shape memory alloy structure [1,2,3] etc
The adjacent layers in layered Functionally graded (FG) plate are commonly connected by the flexible interlayer made of polymer adhesive with smaller modulus than that of FG layer, which inevitably leads to the slips in the interlayer [7,8,9]
Joseph and Mohanty [14] designed a finite element (FE) model relied on the first-order shear deformation theory for the analysis of the free vibration of a beam with FG constraining layer and viscoelastic core
Summary
Graded (FG) materials composed of two or more constituent phases are being extensively researched due to their continuous property along a particular orientation and are widely applied in weight sensitive areas, such as sensors and actuators, metallic porous and shape memory alloy structure [1,2,3] etc. The polymer material naturally possesses the viscoelastic property; the mechanical behavior of the layered FG plate is timedependent and can be greatly influenced by the interlayer [10,11,12]. The investigation of such a problem becomes essential and deserves in-depth studies. By the use of Fourier series and Rayleigh-Ritz method, a unified accurate solution based on the first-order shear deformation theory was provided by Yang et al [15] to study the vibration and damping of a FG sandwich plate with a soft or hard core. The effects of the geometry and material on the time-dependent behaviour of the structure are discussed in detail
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