ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Low-Frequency Free Vibration of Rods with Finite Strain

Journal of Applied Nonlinear Dynamics 3(1) (2014) 85--93 | DOI:10.5890/JAND.2014.03.007

A.M. Baghestani, S.J. Fariborz$^{1}$ , S.M. Mousavi$^{2}$

$^{1}$ Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Avenue, Tehran, Iran

$^{2}$ Department of Civil and Structural Engineering, Aalto University, PO box 12100, FI-00076, Finland

Abstract

The governing differential equation for the free vibration of a rod undergoing finite strain is obtained by means of Hamiltonâ€™s principle. The equation contains quadratic as well as cubic nonlinear terms. For the low-frequency analysis of rods, the two harmonics solution is considered for the equation. The Galerkin method is employed to convert the partial differential equation to a system of two nonlinear ordinary differential equations. These equations are solved utilizing generalized differential quadrature(GDQ) and continuation methods to obtain the backbone curves and also mode shapes of vibration for rods with two different kinds of boundary conditions.

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