Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 54 6 2022 08 23 Nonlinear Torsional Vibrations of Axially Loaded Pretwisted Beam with Primary Resonance Excitations Nonlinear Torsional Vibrations of Axially Loaded Pretwisted Beam with Primary Resonance Excitations 1271 1302 4812 10.22060/mej.2022.20718.7301 FA Seyed Ali Sina صنعتی شاهرود-مهندسی مکانیک Hassan Haddadpour Dept. of Aerospace Engineering, Sharif Univ. of Tech. Journal Article 2021 10 28 Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. In this paper, nonlinear torsional vibrations of thin walled beams will be investigated. The method of multiple scales will be implemented as a solution method and different nonlinear phenomena will be studied. The obtained results are compared with the available results in the literature which reveals an excellent agreement between different solution methodologies. The outcomes of this study show that beam nonlinear torsional dynamics and the related phenomena could influence the linear torsional dynamic of beams under axial load, e.g. rotating beams. Forced torsional vibrations of a beam with the excitation in the form of primary resonance of the first and second modes have been investigated. It has been demonstrated that in the case of the beam with two ends clamped boundary conditions, three-to-one internal resonance will appear. The primary resonance of the first and second modes has been solved in two sets of boundary conditions, torsionally clamped-fixed and torsionally fixed-fixed. Nonlinear response, amplitude-phase equations, fixed points, and their stability have been studied. Frequently used thin walled beams have low torsional stiffness and their torsional deformations may be of such magnitudes that it is not adequate to treat the angles of cross section rotation as small. In this paper, nonlinear torsional vibrations of thin walled beams will be investigated. The method of multiple scales will be implemented as a solution method and different nonlinear phenomena will be studied. The obtained results are compared with the available results in the literature which reveals an excellent agreement between different solution methodologies. The outcomes of this study show that beam nonlinear torsional dynamics and the related phenomena could influence the linear torsional dynamic of beams under axial load, e.g. rotating beams. Forced torsional vibrations of a beam with the excitation in the form of primary resonance of the first and second modes have been investigated. It has been demonstrated that in the case of the beam with two ends clamped boundary conditions, three-to-one internal resonance will appear. The primary resonance of the first and second modes has been solved in two sets of boundary conditions, torsionally clamped-fixed and torsionally fixed-fixed. Nonlinear response, amplitude-phase equations, fixed points, and their stability have been studied. https://mej.aut.ac.ir/article_4812_29ec23f7ed792401df1a93b04a731625.pdf