Dynamic response of an overhead crane system

A simply supported uniform Euler-Bernoulli beam carrying a crane (carriage and payload) is modelled. The crane carriage is modelled as a particle as is the payload which is assumed to be suspended from the carriage on a massless rigid rod and is restricted to motion in the plane defined by the beam axis and the gravity vector. The two coupled integro-differential equations of motion are derived using Hamilton's principle and operational calculus is used to determine the vibration of the beam which is, in turn, used to obtain the dynamics of the suspended payload. The natural frequencies of vibration of the beam-crane system for a stationary crane are investigated and the explicit frequency equation is derived for that set of cases. Numerical examples are presented which cover a range of carriage speeds, carriage masses, pendulum lengths and payload masses. It is observed that the location and the value of the maximum beam deflection for a given set of carriage and payload masses is dependent upon the carriage speed. At very fast carriage speeds, the maximum beam deflection occurs close to the end of the beam where the carriage stops as a result of inertial effects and at very slow speeds occurs near the middle of the beam because the system reduces to a quasi-static situation. (C) 1998 Academic Press Limited.