Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model

Abstract

An analytical answer to the natural vibration problem of a composite plate consisted of multi-scale hybrid nanocomposites, is presented here for the first time. In this paper, the constituent material of the structure is made of an epoxy matrix which is reinforced by both macro- and nano-size reinforcements, namely carbon fiber (CF) and carbon nanotube (CNT). The effective material properties like Young's modulus or density are derived utilizing a micromechanical scheme incorporated with the Halpin-Tsai model. To present a more realistic problem, the plate is placed on a two-parameter elastic substrate. Then, on the basis of an energy-based Hamiltonian approach, the equations of motion are derived using the classical theory of plates. Finally, the governing equations will be solved analytically to obtain the natural frequency of the system's oscillation. Afterward, the normalized form of the results will be presented to put emphasis on the impact of each parameter on the dimensionless frequency of nanocomposite plates. It is worth mentioning that the effects of various boundary conditions on the frequency of the plate are covered, too. To show the efficiency of presented modeling, the results of this article are compared to those of former attempts. Numerical results declare that plates fabricated from the hybrid nanocomposites can endure higher frequencies compared with those consisted of conventional composites.