On the eigenfrequencies of a cantilevered beam with a tip mass and in-span support

Gürgöze M., Özgür K., Erol H.

Computers and Structures, vol.56, no.1, pp.85-92, 1995 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 1
  • Publication Date: 1995
  • Doi Number: 10.1016/0045-7949(94)00541-a
  • Journal Name: Computers and Structures
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.85-92
  • Istanbul Technical University Affiliated: Yes


The present study addresses essentially to the investigation of the bending eigenfrequencies of a cantilevered Bernoulli-Euler beam with a tip mass which has an in-span support. First, an exact frequency equation is established via a boundary value formulation and then an approximate frequency equation is derived using the Lagrange's multipliers method. For a design engineer who is interested in a quick but accurate determination of the fundamental eigenfrequency of the system, an approximate formula is also established by using the Dunkerley's procedure. Finally, a formula for the sensitivity of the eigenfrequencies with respect to small changes in the location of the in-span support is derived. Numerical results on a digital computer justify the usefulness of the obtained analytical results. © 1995.