DYNAMIC-RESPONSE OF AN OVERHEAD CRANE SYSTEM

A simply supported uniform Euler-Bernoulli beam carrying a crane (carr iage and payload) is modelled. The crane carriage is modelled as a par ticle as is the payload which is assumed to be suspended from the carr iage 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 integ ro-differential equations of motion are derived using Hamilton's princ iple and operational calculus is used to determine the vibration of th e beam which is, in turn, used to obtain the dynamics of the suspended payload. The natural frequencies of vibration of the beam-crane syste m for a stationary crane are investigated and the explicit frequency e quation is derived for that set of cases. Numerical examples are prese nted 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 p ayload masses is dependent upon the carriage speed. At very fast carri age 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.