Nonlinear Dynamic Stability of Cylindrical Reticulated Shells with Initial Damage

Abstract

As large-span structures, reticulated shells are widely used in large-scale public building and act as emergency shelters in the event of sudden disasters. However, spatial reticulated shells are dynamic-sensitive structures; the effect of the initial structural damage on dynamic stability should be considered. In this study, a new nonlinear dynamic model of cylindrical reticulated shells with initial damage is proposed to investigate the effect of initial damage accurately. Firstly, the damage constitutive relations of the building steels are built based on the irreversible thermodynamic theory; furthermore, its fundamental equations are obtained using simulated shell methods. Then, the nonlinear vibration differential equations with damage are obtained and studied with support. Meanwhile, the nonlinear natural vibration frequency with initial damage is derivatized. After that, a bifurcation problem with initial damage is studied by using Flouquet Index, and the dynamic stability state at the equilibrium point is analyzed in depth. It is found that the local dynamic stability of the system is determined via its initial condition, geometric parameters, and initial damage. Moreover, the initial damage dominates over other influence factors due to its strong randomness and uncertainty for the same structure. The damage accumulation results in the transition of the equilibrium point. In addition, the nonlinear natural vibration frequency decreases to zero with the accumulation of the damage reaching 0.618; the local stability of cylindrical reticulated shells fails and they even lose whole stability. This study provides a theoretical foundation for the future investigation of whole stability with initial damage.

Keywords

• initial damage
• cylindrical reticulated shell
• bifurcation
• nonlinear stability
• nonlinear natural vibration frequency