Vibration of a Flexible Hanging Chain with a Mass on the End in a Nonstationary Regime of the Motion Mechanism in Hoisting Machines

The article is focused on the vibrations of a heavy chain with a mass on the end when the hoisting machines are in a nonstationary regime of motion, assuming that motor or brake torque is a linear function of the speed of the motion mechanism. An approach based on the application of approximate analytical solution of the system of differential equations of motion has been presented. The solution was obtained by two iterations based on the Fourier and small parameter methods, the representation of the motion of any point of the chain, and the intensity of the inertial perturbation forces by Eigenfunction series of the free vibration task. Our analytical results have been illustrated with a numerical example on the basis of the technical characteristics of the crane trolley and a visual Fortran computer program has been created.