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

Acta Mechanica Sinica 2018年第5期34卷 970-982页

作者： S.Ali Ghasabi Mohammadreza Arbabtafti Majid Shahgholi Mechanical Engineering Faculty Shahid Rajaee Teacher Training UniversityTehranIran

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

关键词： Strain gradient theory micro-rotating shaft Stability Nonlinear oscillation Bifurcation Multiple scales method

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