Analysis and Design Optimization of Axially Moving Structures with Stability Constraint under Wind Excitations

Abstract

This paper presents the stability problem of equilibrium configuration of axially moving strings with small sag-to-span ratios under wind excitations. The Galerkin approach is adopted for reduction of the string as a 4-degree-of-freedom system. The flutter instability is investigated based on the Routh-Hurwitz criterion after linearization at the equilibrium configuration of the string. Closed form conditions are presented for loss of stability and generation of limit cycles via the single and double Hopf bifurcations. To improve the operation stability the design optimization is performed to maximize the critical wind speed that may further lead to the flutter instability. Using the Relative Differential Method, the tensile rigidity and the transport speed are optimized considering the Hopf bifurcation constraints of the equilibrium. With the optimal design, the critical wind speed is maximized and the chance for the flutter instability toward the limit cycle response is reduced to the largest extent.