Investigation of nonlinear dynamic response of engineering ropeway with a moving pendulum model

Engineering ropeway has the characteristics of convenient transportation, low cost and strong environmental adaptability, which is widely used in production and life. However, strong nonlinear vibration behavior will occur due to complex coupled vibration during operation, which threatens the safety of the whole system. This kind of nonlinear vibration behavior is difficult to express in the form of analytical solution. For the comprehensive consideration of safety and efficiency in the operation of engineering ropeway, it is necessary not only to express the nonlinear vibration dynamic response of engineering ropeway quickly, but also to clarify the influence of ropeway parameters on the nonlinear vibration response. In this paper, a typical form of ropeway  bridge crane is selected for constructing a moving pendulum model, and the corresponding nonlinear vibration equation is derived by Lagrange method. By using McLaughlin series expansion and orthogonal Chebyshev polynomials, the differential equation with both sinusoidal and cosine nonlinearities is reduced to polynomial equations. The analytical approximate solution of nonlinear vibration equation of engineering ropeway is obtained by combining Newton linearization with harmonic balance method. The results show that the analytical approximation solutions are highly consistent with the exact solutions obtained by the shooting method. The influences of parameters such as rope length, hanging weight and amplitude, on the nonlinear vibration response are analyzed. It is found that the length and amplitude of the rope are positively correlated with the period, while the hanging weight is the opposite. The present results have certain guiding significance for engineering ropeway design, optimization, and application.