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

Rubio, Lourdes; Fernandez-Saez, José; Morassi, Antonino

doi:10.1115/1.4036467

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In this paper, new exact closed-form solutions for free longitudinal vibration of a oneparameter 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.

Titolo:	Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses
Autori:	Rubio Lourdes Fernandez-Saez José MORASSI, Antonino (Corresponding) mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2017
Rivista:	JOURNAL OF VIBRATION AND ACOUSTICS
Citazione:	Exact Eigensolutions for a Family of Nonuniform Rods With End Point Masses / Rubio, Lourdes; Fernandez-Saez, José; Morassi, Antonino. - In: JOURNAL OF VIBRATION AND ACOUSTICS. - ISSN 1048-9002. - STAMPA. - 139:5(2017), pp. 1-8.
Abstract:	In this paper, new exact closed-form solutions for free longitudinal vibration of a oneparameter 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.
Handle:	http://hdl.handle.net/11390/1123054
Appare nelle tipologie:	1.1 Articolo in rivista

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