Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses Articles uri icon

publication date

  • October 2017

issue

  • 5

volume

  • 139

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.