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.
Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 22, 2016; final manuscript received March 15, 2017; published online July 13, 2017. Assoc. Editor: Michael Leamy.
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Rubio, L., Fernández-Sáez, J., and Morassi, A. (July 13, 2017). "Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses." ASME. J. Vib. Acoust. October 2017; 139(5): 051018. https://doi.org/10.1115/1.4036467
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