ON THE EIGENFREQUENCIES OF A CANTILEVER BEAM WITH ATTACHED TIP MASS AND A SPRING-MASS SYSTEM

This paper deals with the derivation of the frequency equation of a sp ecial combined dynamic system. It consists of a clamped-free Bernoulli -Euler beam with a tip mass where a spring-mass system is attached to it. The derivation of the frequency equation is essentially carried ou t by means of the Lagrange multipliers method. Frequency equations of some simpler systems are also obtained from the general expression by using limiting processes. These equations are then numerically solved for various combinations of physical parameters. The comparison with t he results from the solution of the corresponding Bernoulli-Euler freq uency equations shows that the frequency equations established are ver y accurate. (C) 1996 Academic Press Limited