In-plane Nonlinear Random Vibration Of Cable System Under Non-gaussian Random Excitation

As a flexible structure with small weight and low damping,cable is sensitive to various excitations or displacement of the end support.Large vibration is prone to occur.Coupled with the randomness of the load,the cable presents a very complex nonlinear random vibration response.The nonlinear random vibration of cable has been studied extensively so far,but it appeared to be limited to Gaussian white noise excited cases.However,the random disturbances in reality are non-Gaussian excitations.There will be large errors if Gaussian excitations are replaced by non-Gaussian excitations.In this paper,the system is supposed to be excited by Poisson white noise,and the single-degree-of-freedom(SDOF)system and in-plane random vibration of cable system under Poisson white noise excitation is studied.The research contents are as follows:(1)In this paper,the iterative method of weighted residuals is developed to calculate the stationary response of SDOF nonlinear system under non-Gaussian excitation.Further,the influence of Poisson white noise excitation parameters of the system is analyzed.The research shows,the analytical solution obtained by the iterative method with weighted residuals is in good agreement with the results obtained by Monte Carlo simulation,and it can clearly describe the non-linear characteristics of various nonlinear vibration systems compared with other methods.(2)The stochastic differential equation of the in-plane vibration of cable system under Poisson white noise excitation is formulated,without regard to cable angle and the influence of the cable's gravity along the chordwise direction.In addition,only the first-order modal of the cable is analyzed.Then,taking an actual cable system as an example,the stochastic response of the cable system is analyzed by the iterative method with weighted residuals mentioned in(1).The applicability and correctness of the proposed method are examined.The results show that the numerical analytical solution obtained by the iterative method of weighted residuals agrees well with the results of Monte Carlo simulation.(3)Based on the research in(2),considering the influence of the cable angle and cable gravity along the chordwise direction of force,a more precise stochastic differential equation of the in-plane vibration of stay cable system under Poisson white noise excitation is formulated.Then,taking an actual stay cable system as an example,the approximate steady-state closed solution of the probability density function of the system is analyzed by the iterative method of weighted residuals.Finally,the effects of sag ratio,damped coefficient and pulse arrival rate on the in-plane stochastic vibration of cable are examined.The results show that the asymmetric appearance of response is becoming much obvious while the sag ratio increases;the response is then suppressed obviously as the coefficient of damping increases,but the degree of suppression decreases as the damping coefficient increases;the response of stay cable system increases rapidly with the increase of pulse arrival rate.Besides,the feasibility of the method is compared with the Monte Carlo simulation.The results show that the analytical solutions are in good agreement with Monte Carlo simulation data.Therefore,the method proposed in this paper can provide a new idea for studying the nonlinear random vibration of the cable.Furthermore,it can offer a new way for the reliability discrimination and optimization design of the cable structure.