Study on vibrant characteristic in skip's loading

Aiming at skip's loading in course of mine hoisting,the differential equation of motion for the skip with variable coal mass was built.By means of variable substitution,it is found that the differential equation of motion is a Bessel equation.Based on the equation,responses of elastic displacement,velocity,acceleration of skip and cable tension close to sheave were deduced.With different loading fluxes,the results show that amplitude of velocity and acceleration attenuate distinctly along with skip's loading,and elastic displacement and cable tension increase gradually.When theloading flux rises,amplitudes increase and frequency decline quickly,whereas,final frequency with equal load weight are almost same.