Chaotic oscillation of a multi-scale hybrid nano-composites reinforced disk under harmonic excitation via GDQM

In the presented computational approach, a mathematical derivation is made to develop a nonlinear dynamic model for the nonlinear frequency and chaotic responses of the multi-scale hybrid Nano-composites reinforced disk (MHCD) embedded in a viscoelastic media and subject to a harmonic load. Using Hamilton's principle and Von Karman nonlinear theory, the nonlinear governing equation is derived. For developing an accurate solution approach, generalized differential quadrature method (GDQM) and perturbation approach (PA) are finally employed. Various geometrically parameters are taken into account to investigate the chaotic motion of the viscoelastic disk subject to harmonic excitation. The golden results of this paper is that the chaotic motion and nonlinear frequency of the disk is hardly dependent on the value of the outer to inner radius ratio (R-o/R-i) and viscoelastic parameters and it means that by increasing the value of R-o/R-i parameter and taking into account the viscoelastic foundation, the motion of the system tend to show the chaotic motion. Moreover, at the lower value of the R-o/R-i parameter, quasi-harmonic and chaotic responses can be seen for the conditions with and without considering the effect of viscoelastic foundation and at the higher value of the parameter, the chaosity of the system decreases.