The wind turbulence is considered as the addition of a time varying wind speed component to the mean wind component. It is shown that the structure is subjected to mu1tiharmonic external and parametric excitations due to wind turbulence in addition to the nonlinear self-excited wind forces due to the mean wind component. The effect of primary resonance due to a single component of turbulence on the galloping response is investigated in this paper using the method of multiple scales as a perturbation technique. comparisons between the analytical and numerical solutions indicate the accuracy of the analysis.
Galloping is the vibration of a structure in the perpendicular direction to the mean wind flow. It occurs due to the aerodynamic forces which are induced by small transverse motions of the structure. The aerodynamic self-excited forces act, in the direction of the transverse motion resulting in negative damping which increases the amplitude of the transverse motion until it settles down to a limit cycle. Galloping of a structure occurs above, a certain critical wind speed usually called "onset wind speed" [12,13]. Galloping usually occurs in pylons of suspension and cable stayed bridges [3,4], prismatic tall building [9,10], and overhead power transmission lines [14,15]. The prediction of galloping amplitude has relied, so far, on curve fitting of the aerodynamic transverse force function using wind tunnel experiments. Parksinson and Smith [13], studied the galloping of a square prism under steady flow using the method of Kry10v and Bogo1iubov to solve the nonlinear differential equation in the across wind direction. Novak and Davenport [9] studied the galloping of prisms in turbulent flow. They pointed out that turbulence may cause the loss of dynamic stability due to the parametric resonance.
