Dynamic modeling and coupling characteristics of rotating inclined beams with twisted-shape sections
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RESEARCH ARTICLE
Jin ZENG, Chenguang ZHAO, Hui MA, Bangchun WEN
Dynamic modeling and coupling characteristics of rotating inclined beams with twisted-shape sections
© Higher Education Press 2020
Abstract In the existing literature, most studies investigated the free vibrations of a rotating pre-twisted cantilever beam; however, few considered the effect of the elasticsupport boundary and the quantification of modal coupling degree among different vibration directions. In addition, Coriolis, spin softening, and centrifugal stiffening effects are not fully included in the derived equations of motion of a rotating beam in most literature, especially the centrifugal stiffening effect in torsional direction. Considering these deficiencies, this study established a coupled flapwise– chordwise–axial–torsional dynamic model of a rotating double-tapered, pre-twisted, and inclined Timoshenko beam with elastic supports based on the semi-analytic method. Then, the proposed model was verified with experiments and ANSYS models using Beam188 and Shell181 elements. Finally, the effects of setting and pretwisted angles on the degree of coupling among flapwise, chordwise, and torsional directions were quantified via modal strain energy ratios. Results showed that 1) the appearance of torsional vibration originates from the combined effect of flapwise–torsional and chordwise– torsional couplings dependent on the Coriolis effect, and that 2) the flapwise–chordwise coupling caused by the pure pre-twisted angle is stronger than that caused by the pure setting angle. Keywords elastic-support boundary, pre-twisted beam, semi-analytic method, modal strain energy ratio, torsional vibration
Received August 3, 2019; accepted November 25, 2019
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Jin ZENG, Chenguang ZHAO, Hui MA ( ), Bangchun WEN School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China E-mails: [email protected]; [email protected] Hui MA Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, China
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Introduction
Rotating pre-twisted beam-like structures are extensively used in machinery; aerospace industry; and power systems [1], such as fan blades [2], marine propellers [3], and wind turbines [4]. The important feature of this kind of structure is that its modal characteristics are closely related to many engineering failure problems such as flutter, stability, and fatigue failure [5,6]. Therefore, many studies have investigated its dynamic characteristics through experimental, analytical, and numerical methods [7–12]. Early studies were primarily focused on the rotating pretwisted cantilever beam. Adopting Hamilton’s principle and Newtonian method, Hodges and Dowell [13] theoretically derived the coupled flapwise–chordwise–axial– torsional equations of motion of a rotating pre-twisted Euler–Bernoulli beam and found that Hamilton’s principle was easier and more precise to handle the equations of motion than the Newtonian method due to lesser chance of inadvert
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