Chaotic Vibration Analysis of Nano Composite Doubly Curved Shell Structure

Abstract

The nano composite materials have been recently developed as an advanced composite. It has good mechanical properties like stiffness, low-density, toughness and good strength to weight ratio. The nonlinear dynamics of a nano composite doubly curved shell structure are investigated in this work. The property of three-phase composite is obtained using the rule of mixing and the Halpin T Sai model. Higher order shear deformation theory (3rd order) is used to determine displacement and strain for the two-phase composite. By utilizing Von Karman geometric nonlinearity to establish the relationship between strain and displacement. The Hamilton's approach is use to obtain the governing equation of a nano composite shell structure and the shell structure is considered as simply supported. The Galerkin approach is used to discretize the partial nonlinear differential equation of motion into a single nonlinear equation in terms of dimensionless transverse displacement that resembles the Duffing equation. Solution of this duffing equation is use to study the effect of coefficient of dimensionless forcing term on the magnitude of dimensionless transverse displacement. The frequency response diagram has been plotted by using the Duffing equation and then solving the resulting governing equation to plot the amplitude of the non-dimensional displacement with respect to dimensionless excitation frequency. The time series, phase portrait and the Poincaré map are plotted.