Transversal vibration of chain ropeway system having support boundary conditions with polygonal action

Abstract

The purpose of this paper is to characterize the modal parameters and transverse vibrations of a monochain ropeway system for hilly orchards. The moving chain is modeled with uniform distribution and concentrated inertial loads. In order to study the dynamical behavior of the moving chain, Hamilton's principle is applied to obtain the homogenous differential equation of transverse vibration. With the boundary conditions subjected to the polygonal action caused by chain-support engagement, the coupling effect of concentrated load, variable tension, and time-dependent speed on transverse vibration is investigated. The contribution of residue of singularity to total vibrations in phase space is numerically analyzed by using the Laplace transform method. The influence of the boundary condition considering the polygonal action is investigated in terms of excitation frequency and amplitude coupled with transport speed. The transverse vibrations are calculated numerically and measured experimentally. The numerical results are in agreement with the experimental data, which suggest that the amplitude and frequency of vibration are proportional to the value of propagation speed. The analytical solution to the moving chain problem provides a feasible reference for its stability analysis and wind-induced vibration control.