Coupled flapwise-chordwise-axial-torsional dynamic responses of rotating pre-twisted and inclined cantilever beams subject to the base excitation

• Published in: Applied mathematics and mechanics Vol. 40; no. 8; pp. 1053 - 1082
• Main Authors: Zeng, Jin, Ma, Hui, Yu, Kun, Xu, Zhitao, Wen, Bangchun
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.08.2019; Springer Nature B.V; School of Mechanical Engineering and Automation, Northeastern University,Shenyang 110819, China%School of Mechanical Engineering and Automation, Northeastern University,Shenyang 110819, China; Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang 110819, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Cantilever beams; Classical Mechanics; Excitation; Finite element method; Fluid- and Aerodynamics; Hamilton's principle; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Rotation; Torsion; Torsional vibration; modal characteristic; flapwise-chordwise-axial-torsional; 65L15; 74S05; rotating Timoshenko beam; vibration response; 7; base excitation; O347.6; V214.3; 70J35
• DOI: 10.1007/s10483-019-2506-6
• ISSN: 0253-4827

A rotating pre-twisted and inclined cantilever beam model (RPICBM) with the flapwise-chordwise-axial-torsional coupling is established with the Hamilton principle and the finite element (FE) method. The effectiveness of the model is verified via comparisons with the literatures and the FE models in ANSYS. The effects of the setting and pre-twisted angles on the dynamic responses of the RPICBM are analyzed. The results show that: (i) the increase in the setting or pre-twisted angle results in the increases in the first-order flapwise and torsional frequencies while the decrease in the first-order chordwise frequency under rotating conditions; (ii) a positive/negative setting angle leads to a positive/negative constant component, while a positive/negative pre-twisted angle leads to a negative/positive constant component; (iii) when the rotation speed is non-zero, the pre-twisted angle or non-zero setting angle will result in the coupled flapwise-chordwise-axial-torsional vibration of the RPICBM under axial base excitation.