Vibration of a Cantilever Beam With Prescribed End Motion

Abstract

Abstract A cantilever beam, vibrating as a result of prescribed motion of its end, is studied with particular regard to the force required to maintain such motion. The end motions in the four basic problems solved are, respectively, uniform acceleration; uniform acceleration, uniform velocity; uniform acceleration, uniform velocity, uniform deceleration, rest; and sinusoidal pulse, rest. Figs. 5, 6, 7, and 8, respectively, of the paper show the end-force variation for each of the problems considered. The method of analysis indicates that the end force on the beam may be obtained in each instance by super-position of certain basic components. The results show how the parameters of the prescribed motion determine the magnitude of the fluctuations and the direction of the corresponding end force.