On the eigenfrequencies of a cantilever beam with attached tip mass and a spring-mass system

Gurgoze M.

JOURNAL OF SOUND AND VIBRATION, vol.190, no.2, pp.149-162, 1996 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 190 Issue: 2
  • Publication Date: 1996
  • Doi Number: 10.1006/jsvi.1996.0053
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.149-162
  • Istanbul Technical University Affiliated: No


This paper deals with the derivation of the frequency equation of a special 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 out 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 the results from the solution of the corresponding Bernoulli-Euler frequency equations shows that the frequency equations established are very accurate. (C) 1996 Academic Press Limited