authors
- RUBIO RUIZ DE AGUIRRE, MARIA LOURDES
- FERNANDEZ SAEZ, JOSE
- MORASSI, ANTONINO
Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses
Articles
Overview
published in
publication date
- October 2017
issue
- 5
volume
- 139
Digital Object Identifier (DOI)
International Standard Serial Number (ISSN)
- 1048-9002
Electronic International Standard Serial Number (EISSN)
- 1528-8927
abstract
- In this paper, new exact closed-form solutions for free longitudinal vibration of a one-parameter countable family of cantilever rods with one end tip mass are obtained. The analysis is based on the reduction of the equation governing the longitudinal vibration to the Sturm-Liouville canonical form and on the use of double Darboux transformations. The rods for which exact eigensolutions are provided are explicitly determined in terms of an initial rod with known closed-form eigensolutions. The method can be also extended to include longitudinally vibrating rods with tip mass at both ends.