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Image of Vibration Testing and System Dynamics
ISSN: 2475-4811 (print)
ISSN: 2475-482X (online)
Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn

Generalized Formulation for Free Vibration of Elastic Solids with Static Loads and Application to Rotating Tapered Cantilever Beam Vibration

Journal of Vibration Testing and System Dynamics 5(2) (2021) 149--168 | DOI:10.5890/JVTSD.2021.06.004

Renfan Luo

Finmere, Rugby, Warwickshire, UK

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Abstract

By solving the three one-dimensional (1D) nonlinear dynamic differential equations analytically, it has been proved that unless the nonlinear terms are in first order, a nonlinear dynamic system never has a vibration natural frequency. For an elastic solid with nonlinear deformation and with static loads including a rotational angular velocity, a virtual small factor has been introduced to ensure a small deformation, a generalized formulation to predict vibration frequencies has been developed. Tapered rotating cantilever beams have been used to validate the formulation against FE analysis, and the analytical and FE results are in a good agreement.

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