Vibrations of Multiscale Hybrid Thick Plates with Viscoelastic Polymer Matrix

The purpose of this research is to study the free vibration response of composite plates made up of three-phase polymer–glass fiber (FG)–carbon nanotubes (CNTs). Polymer matrix has an important property, i.e. the elastic modulus and Poisson’s ratio decrease over time. In this study, the waviness of the CNTs is also taken into consideration. A three-step hierarchical approach is adopted to estimate the elastic properties of the composite media. The governing equations are derived by quasi-3D plate theory and Hamilton’s principle. The adopted quasi-3D model takes into account the nonuniform shear and normal strain distribution and also satisfies the condition of traction-free on top and bottom surfaces. The natural frequencies of this composite are found using the Navier solution method for simply supported boundary conditions. This work investigates how the dimensionless frequency is affected by time, plate geometry, fiber mass fraction, and CNT mass fraction, all of which have a substantial impact. For example, it is highlighted that for a specific plate, after 60s, the frequency drops by about 14% if one takes the time parameter into account. In addition, increasing the mass fraction of CNTs or FGs results in higher frequencies.