Study on vibration suppression of single degree of freedom system with moment of inertia as a function of time

Abstract

In order to shorten the time required to lift and lower a load using a crane, we investigated the vibration of a simple pendulum, whose rope length is a function of time. We solved the free vibration of a simple pendulum, whose moment of inertia is a function of time, using the mathematical processing program Mathematica, and substituted the obtained solution into the left side of the equation of motion, which resulted in the sum of each term becoming zero, confirming that the solution is valid from the viewpoint of conservation of energy. We fixed the support point of the simple pendulum and investigated the time function of the rope length that increases or suppresses the angular displacement during lifting and lowering operations. We also investigated the effect on angular displacement when the support point moves.