Chaotic dynamic analysis of viscoelastic shallow spherical shells

This paper investigates the dynamic behaviour of a shallow, viscoelastic, spherical shell under a harmonic excitation. The time evolutions of the response of the corresponding nonlinear dynamical system are described by the phase portraits and the bifurcation of the parameter dependent system is studied numerically so as to identify qualitative changes in the phase portrait. The viscoelastic shell, having more than one equilibrium configuration for some problem parameters, shows periodic and/or randomlike chaotic oscillations under the given excitation according to the dimensions of the attracting set. The occurrence and nature of the chaotic attractors are verified by evaluating Lyapunov exponents.