Extremely large oscillation and nonlinear frequency of a multi-scale hybrid disk resting on nonlinear elastic foundation. (September 2020) - Shariati, Ali; Ghabussi, Aria; Habibi, Mostafa; Safarpour, Hamed; Safarpour, Mehran; Tounsi, Abdelouahed; Safa, Maryam
Abstract: This is a fundamental study on the nonlinear vibrations considering large amplitude in multi-sized hybrid Nano-composites (MHC) disk (MHCD) relying on nonlinear elastic media and located in an environment with gradually changed temperature feature. Carbon fibers (CF) or carbon nanotubes (CNTs) in the macro or nano sizes respectively are responsible for reinforcing the matrix. For prediction of the efficiency of the properties MHCD's modified Halpin-Tsai theory has been presented. The strain-displacement relation in multi-sized laminated disk's nonlinear dynamics through applying Von Karman nonlinear shell-theory and using third-order-shear-deformation-theory (TSDT) is determined. The energy methods called Hamilton's principle is applied for deriving the motion equations along with Boundary Conditions (BCs), which has ultimately been solved using the perturbation approach (PA) and generalized differential quadrature method (GDQM). At the final stage, the outcomes illustrate that patterns of FG, fibers' various directions, the WCNT and VF factors, top surface's applied temperature and temperature gradient have considerable impact on the MHCD's nonlinear dynamics. Another important consequence is that, the influences of the θ, WCNT and VF amounts on the disk's nonlinear vibrations may be taken into account at the larger amounts of the high deflection element and the negative axial load's impact on the structure's nonlinear dynamics is more extreme. A more general conclusion of this study is that for designing the MHCD should be more attention to the nonlinearity parameter. Highlights: Nonlinear frequency and large amplitude vibrations of multi-scale hybrid Nano-composites disk resting on elastic foundation under the temperature gradient effect is firstly investigated. The displacement-strains of nonlinear vibration of the multi-scale laminated disk is obtained via third-order shear deformation (TSDT) theory and Von Karman nonlinear shell theory. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano or macro scale, respectively. Some benchmark results related to nonlinear frequency and nonlinear dynamic response of nano-composite disk have been presented under mechanical and thermal effects.