Frequency Characteristics of Multiscale Hybrid Nanocomposite Annular Plate Based on a Halpin–Tsai Homogenization Model with the Aid of GDQM

Abstract

In this article, we study the vibration performance of multiscale hybrid nanocomposite (MHC) annular plates (MHCAP) resting on Winkler–Pasternak substrates exposed to nonlinear temperature gradients. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macroscale, respectively. The annular plate is modeled based on higher-order shear deformation theory (HSDT). We present a modified Halpin–Tsai model to predict the effective properties of the MHCAP. Hamilton’s principle was employed to establish the governing equations of motion, which is finally solved by the generalized differential quadrature method (GDQM). In order to validate the approach, numerical results were compared with available results from the literature. Subsequently, a comprehensive parameter study was carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, outer temperature, volume fraction and orientation angle of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio, and inner radius to thickness ratio on the response of the plate. The results show that applying a sinusoidal temperature rise and locating more CNTs in the vicinity of the bottom surface yielded the highest natural frequency.

A solution for free vibration of rotating hybrid multiscale nanocomposite conical shell

“…However, Tornabene et al 21 used Eshelby–Mori–Tanaka scheme to consider agglomeration of the nanoparticles in the matrix of the three phase hybrid CNT nanocomposite and investigated the frequency response of annular plate, cylindrical and conical shell using GDQ method. Safarpour et al 22 carried out similar investigation on annular plate and concluded that by including more CNTs at the bottom surface of the annular plate results more stiffness in the structures. Gholami et al 23 studied the nonlinear frequency response of hybrid CNT nanocomposite rectangular plate by employing time periodic discretization rule and the pseudo-arc length continuation methodology.…”

Wave Dispersion Behaviors of Multi-Scale CNT/Glass Fiber/Polymer Nanocomposite Laminated Plates

“…Moreover, Ebrahimi and Dabbagh [13] investigated the natural frequency response of MSH nanocomposite beams in a thermal environment on the basis of a higher-order shear deformation theory (HSDT). The thermal effect on the MSH annular plates was solved by Safarpour et al [14] using the generalized differential quadrature method (GDQM). In addition, the vibration characteristics and nonlinear frequency of the MSH disks and plates embedded in a viscoelastic media were investigated [15,16].…”