Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

摘要: In this paper, the stability and bifurcation analysis of symmetrical asymmetrical micro-rotating shafts are investigated when rotational speed is in vicinity critical speed. With help Hamilton’s principle, nonlinear equations motion derived based on non-classical theories such as strain gradient theory. dynamic modeling, geometric nonlinearities due to strains, gradients considered. The bifurcations steady state solution compared between classical theory theories. It observed that using a has considerable effect steady-state response system. As result, under theory, shaft becomes completely stable least damping coefficient, while highest coefficient. Under modified total eccentricity, eccentricity. Also, it shown by increasing ratio radius gyration per length scale parameter, results approach those