Higher-order nonlinear vibration analysis of Timoshenko beams by the spline-based differential quadrature method

Article type: Research Article

Authors: Zhong, Hongzhi | Liao, Minmao

Affiliations: Department of Civil Engineering, Tsinghua University, Beijing 100084, P.R. China

Note: [] Corresponding author. Tel.: +86 10 62781891; Fax: +86 10 62771132; E-mail: hzz@tsinghua.edu.cn

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.

Keywords: Timoshenko beam, nonlinear vibration, spline-based differential quadrature

Journal: Shock and Vibration, vol. 14, no. 6, pp. 407-416, 2007