Free and forced vibration analysis of rectangular/circular/annular plates made of carbon fiber-carbon nanotube-polymer hybrid composites

A multiscale finite element method is adopted in this paper to study the vibrational characteristics of polymer matrix composite plates reinforced with the combination of carbon fibers (CFs) and carbon nanotubes (CNTs). The effects of nanoscale and microscale are coupled through a two-step procedure. In the first step, random dispersion of CNTs into the polymer matrix is modelled using a three-phase representative volume element (RVE). In the selected RVE, the influence of the interphase formed because of non-bonded interactions between the polymer matrix and CNTs is taken into account. In the second step, the distribution of CFs into the composite is modelled, and the elastic properties of CF-CNT-polymer matrix hybrid composite are calculated for various values of volume fractions of reinforcement phases. Then, the free and forced vibration behaviors of composite plates are analyzed. It is considered that the plates have rectangular, circular, and annular shapes and are under clamped/simply supported edge conditions. The effects of CNT/CF reinforcement on the elastic modulus and density of composite and on the free/forced vibration response of the considered structures are investigated. It is shown that the vibrational behavior of plates is significantly affected by the hybrid reinforcement with CNT and CF.