Non-linear vibrations of suspension bridges with external excitation

Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined.     

Experimental analysis of a stochastic model for estimating wind-borne compact debris trajectory in turbulent winds

The impact of flying debris against building envelopes during high winds is a major source of structural damage. For example, damage produced by Hurricanes Katrina and Ike in the United States on the facades of tall buildings, located in urban areas, has been documented. It is therefore of relevance to analyze the vulnerability of tall buildings to debris-induced non-structural damage in the general context of performance-based wind engineering. In order to analyze the random trajectory of debris in highly turbulent winds, a numerical model combined with a probability-based algorithm was recently proposed by the authors (Moghim and Caracoglia, 2013). This model investigates the trajectory of “compact debris”, defined as point-mass objects of negligible mass moments of inertia and for which the aerodynamics is predominantly controlled by the drag force. The model replicates both the inherent randomness in debris properties and the effect of wind shear and atmospheric turbulence to estimate debris trajectory and the likelihood of impact against vertical building facades in a probabilistic setting.This paper describes the comparison between numerical model results and wind tunnel experiments. Tests were carried out in the Northeastern University׳s small scale wind tunnel in both smooth flow and grid-generated turbulent flow. The motion of spheres and cubes, simulating compact debris objects, was investigated in two dimensions (2D) on a vertical plane.The 2D motion of compact objects of various sizes was captured by a high-speed digital camera at different flow speeds. Experimental results showed to be consistent with numerical simulations. They also confirmed that not only mean flow speed but also turbulence features can have a non-negligible effect on the trajectory of compact objects.