Vibration of a Flexible Manipulator Carrying Offset Payloads

Resonance is an important consideration in the design and performance of manipulators. A simple model of a manipulator consists of a beam carrying heavy bodies. Publications are available on the vibration of beams carrying thin disk at each end and up to two disks in-span. The problem has not been tackled taking the axial width of the disks into account. In this paper the vibration of an Euler-Bernoulli stepped beam carrying an axially wide rigid body at each end and one at the step is investigated. The centre of mass of the body is assumed to be on the beam axis but within or outside its width. The frequency equations are expressed as 4^th order determinants equated to zero for 64 combinations of the ‘general’, degenerate and classical boundary conditions at the ends. Tables of the first three frequency parameters are presented for example sets of 15 system parameters. Some of the models considered in this paper are valid models of manipulators, space structures and the like. Designers often use numerical methods like finite element formulation to obtain natural frequencies. The tables presented in this paper may be used to judge the frequencies obtained by numerical methods.