Shock and Vibration

Shock and Vibration / 2007 / Article

Open Access

Volume 14 |Article ID 146801 | https://doi.org/10.1155/2007/146801

Hongzhi Zhong, Minmao Liao, "Higher-Order Nonlinear Vibration Analysis of Timoshenko Beams by the Spline-Based Differential Quadrature Method", Shock and Vibration, vol. 14, Article ID 146801, 10 pages, 2007. https://doi.org/10.1155/2007/146801

Higher-Order Nonlinear Vibration Analysis of Timoshenko Beams by the Spline-Based Differential Quadrature Method

Received18 Jan 2006
Revised18 Aug 2006

Abstract

Higher-order nonlinear vibrations of Timoshenko beams with immovable ends are studied. The nonlinear effects of axial deformation, bending curvature and transverse shear strains are considered. The nonlinear governing differential equations are solved using a spline-based differential quadrature method (SDQM), which is constructed based on quartic B-splines. Ratios of the nonlinear to the linear frequencies are extracted and their variations with the ratio of amplitude to radius of gyration are examined. In contrast to the well-recognized finding for the nonlinear fundamental frequency of beams, some higher-order nonlinear frequencies decrease with the increase of ratio of amplitude to radius of gyration.

Copyright © 2007 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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