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

Hongzhi Zhong | Zendy; Minmao Liao | Zendy

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

Author(s) -

Hongzhi Zhong,

Minmao Liao

Publication year - 2006

Publication title -

shock and vibration

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.418

H-Index - 45

eISSN - 1875-9203

pISSN - 1070-9622

DOI - 10.1155/2007/146801

Subject(s) - nonlinear system , vibration , mathematical analysis , quadrature (astronomy) , mathematics , quartic function , curvature , spline (mechanical) , amplitude , transverse plane , gyration , geometry , physics , structural engineering , engineering , optics , acoustics , quantum mechanics , pure mathematics

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

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