On the free vibration characteristics of multiscale hybrid conical panels utilizing Chebyshev-Ritz route

This study investigates the vibrational behavior of three-phase polymer-glass fiber (FG)-carbon nanotubes (CNT) nanocomposites conical panels. Effects of the wavy shape of CNTs and the viscoelastic nature of the polymer matrix are considered. First and foremost, the equivalent material properties are estimated in the context of a three-step hierarchical approach. Then, the governing equations are attained by combining the first-order shear deformation theory (FSDT) and Hamilton's principle. Furthermore, the Ritz method is employed to extract the frequency responses with the help of Chebyshev polynomials for both simply supported and clamped ends panels. For the parametrical studies, the effect of different geometrical constraints, for instance, the effects of relaxation time and the effect of considering different waviness coefficients for the CNT, are reported. The findings of this paper reveal the significant effect of the viscoelastic properties of the polymer matrix on the estimation of the dimensionless frequency. For instance, under simply supported boundary conditions and a relaxation parameter of 60 s, the frequency of the structure reduces by approximately 23% after 100 s.