ON SELF-EXCITED VIBRATION ANALYSIS FOR AXIALLY MOVING STRINGS WITH TRANSVERSE WIND EXCITATIONS

There exist axially translating string structures, e.g. string cars that operate under wind loadings in outdoor environments. The wind excitation may cause severe vibrations and jeopardize the safety of the strings. In this paper the authors investigate the nonlinear vibration of the translating strings with small sag-to-span ratios under wind excitations. The governing partial differential equation is obtained by modeling the wind excitation as a nonlinear function of the transport speed. The Galerkin approach is adopted to reduce the string to an approximate system with a few numbers of DOFs. After linearization of the system the stability of the equilibrium configuration is investigated through an eigenvalue analysis. Explicit conditions are provided for loss of stability based on the Routh-Hurwicz criterion as well as for generation of stable limit cycles via the Hopf bifurcation, both taking transport speed and wind speed as the controlling parameters. The periodic motion of the string is determined using incremental harmonic method, with stability analyses carried out by eigenvalue computation for the Floquet multipliers. Various stability conditions are presented considering the transport speed, wind speed and the viscous damping as operation parameters.