On the eigenfrequencies of longitudinally vibrating rods carrying a tip mass and spring-mass in-span

Gurgoze M.

JOURNAL OF SOUND AND VIBRATION, vol.216, no.2, pp.295-308, 1998 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 216 Issue: 2
  • Publication Date: 1998
  • Doi Number: 10.1006/jsvi.1998.1696
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.295-308
  • Istanbul Technical University Affiliated: No


The present paper is concerned with the determination of the frequency equation and sensitivity of the eigenfrequencies of a fixed-free longitudinally vibrating rod carrying a tip mass to which a spring-mass system is attached in-span. First, the exact frequency equation is established, and then an approximate formula is given for the fundamental frequency, based on Dunkerley's procedure. Moreover, using the normal mode method, a second approximate but very accurate frequency equation is established with the help of which a sensitivity formula is derived later. Frequency equations of some simpler systems are also obtained from the general expressions by using limiting processes. These novel equations can be very useful for a design engineer who is interested in the eigencharacteristics of similar systems, and their sensitivity. (C) 1998 Academic Press.