A fully consistent linearized model for vibration analysis of rotating beams in the framework of geometrically exact theory
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- 作者：Davide Invernizzi davide.invernizzi@polimi.it" class="auth_mail" title="E-mail the corresponding author ; Lorenzo Dozio ; lorenzo.dozio@polimi.it" class="auth_mail" title="E-mail the corresponding author
- 关键词：Rotating beam ; Geometrically exact beam theory ; Free vibration ; Geometric stiffening ; Consistent linearization
- 刊名：Journal of Sound and Vibration
- 出版年：2016
- 出版时间：26 May 2016
- 年：2016
- 卷：370
- 期：Complete
- 页码：351-371
- 全文大小：753 K
文摘
The equations of motions governing the free vibrations of prismatic slender beams rotating in a plane at constant angular velocity are derived according to a geometrically exact approach. Compared to other modeling methods, additional stiffening terms induced by pre-stress are found in the dynamic equations after fully consistent linearization about the deformed equilibrium configuration. These terms include axial, bending and torsional stiffening effects which arise when second-order generalized strains are retained. It is shown that their contribution becomes relevant at moderate to high angular speeds, where high means that the equilibrium state is subject to strains close to the limit where a physically linear constitutive law still applies. In particular, the importance of the axial stiffening is specifically investigated. The natural frequencies as a function of the angular velocity and other system parameters are computed and compared with benchmark cases available in the literature. Finally, the error on the modal characteristics of the rotating beam is evaluated when the linearization is carried out about the undeformed configuration.