Gaussian and non-Gaussian stochastic response of slender continua with time-varying length deployed in tall structures

This paper presents a study to predict the probabilistic characteristics of lateral dynamic motions of a long heavy cable moving at speed within a tall host structure. The cable is subjected to a base-motion (kinematic) excitation due to a low frequency sway of the structure. The development of the deterministic equations of motion and of the stochastic models describing the lateral dynamic behavior of the cable is presented. Due to the time-varying length of the cable the system exhibits nonstationary dynamic characteristics and its response is governed by nonstationary ordinary differential equations. Two stochastic models of motion of the structure are considered. In the first model the excitation is represented as a narrow-band Gaussian process mean-square equivalent to a harmonic process. The second model involves a non-Gaussian process in the form of a random train of pulses, idealizing the action of strong wind gusts. The differential equations to determine the mean values and the second-order joint statistical moments of the response are formulated and solved numerically. A parametric study is conducted to demonstrate the influence of speed of the cable on the deterministic and stochastic characteristics of the response.