Non-oscillatory behavior and dynamic stability of a thin shell subjected to follower forces with small disturbances

Abstract

The deformation and dynamic behavior mechanism of submerged thin shell structures are in principle of a non-conservative nature as circulatory system, and the disturbance forces of various types exist in a marine environment. This paper describes a characteristic analysis on non-periodic behavior and unstable state of a thin shell subjected to follower forces with small disturbances. For that purpose, the governing equations for finite deformation and dynamic behavior of a thin shell were defined in a mono-clinically particle coordinates description. Then, the stability region chart of the disturbed equilibrium in an excitation field is calculated numerically. Moreover, the chaotic behaviors of a partial spherical shell are investigated by using the power spectra, phase plane portraits and Poincare sections. By the results of these studies, it is clarified that the dynamic behaviors of a thin shell have two scenarios, as ‘Self-organization type’ and ‘Self-assembly type’, getting to unstable state through non-periodic motion.