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research-article

Exact Eigensolutions for a Family of Non-Uniform Rods with End Point Masses

[+] Author and Article Information
Lourdes Rubio

Associate Professor Department of Mechanical Engineering University Carlos III of Madrid Madrid, Spain
lrubio@ing.uc3m.es

José Fernández-Sáez

Professor Department of Continuum Mechanics and Structural Analysis University Carlos III of Madrid Madrid, Spain
ppfer@ing.uc3m.es

Antonino Morassi

Professor Polytechnic Department of Engineering and Architecture University of Udine Udine, Italy
antonino.morassi@uniud.it

1Corresponding author.

ASME doi:10.1115/1.4036467 History: Received December 22, 2016; Revised March 15, 2017

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.

Copyright (c) 2017 by ASME
Topics: Rods , Vibration , Cantilevers
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