Large deflection model for nonlinear flexural vibration analysis of a highly flexible rotor-bearing system

摘要

Highlights?A notable nonlinear mathematical representation has been developed to depict a highly flexible rotating-shaft with a rigid disk arising from large elastic deformation.?Natural frequencies have been determined from the resultant closed-form expressions for different layout of the rotor-bearing system.?Influence of rotary inertia on the critical speeds has been reported.?A clear representation of linear and nonlinear critical speed has been depicted through Campbell diagram and Fourier Spectrum.?Poincare maps also have illustrated for qualitatively demonstrating the nature of transient behavior of the system with and without damping.Graphical abstract1. Nonlinear free vibration for a highly flexiblerotor- bearing systemalong two transverse directions has been illustrated as compared to the rotating shaft only.2. The effect of nonlinearity and rotary inertia to obtain the natural frequencies has been depicted and FFT has been enlisted tosubstantiatethe outcomes presented in Campbell diagram.3. The nature of transient behavioral patterns has been demonstrated qualitatively through Time history,FFT and Poincare’s sectionsupon changing the control parameters.Display OmittedAbstractInvestigation of critical speeds and nonlinear free vibration analysis of a highly flexible rotor system have been studied. The rotary inertia and gyroscopic effect combined with inextensible geometric condition for pinned-guided shaft element have been taken into account to develop the governing equation of motion. The closed-form mathematical expressions have been derived for determining both linear and nonlinear natural frequencies and their behavioral patterns have been simultaneously demonstrated through time histories, FFTs and Poincare’s maps upon changing the control parameters. The nonlinear natural frequencies have been found to be higher by about 4–6% as compared to the findings obtained via linear analysis. For lower spin speed of the shaft, both linear and nonlinear forward natural frequencies have been found to be dominant. The influence of rotary inertia on natural frequencies by considering Euler and Rayleigh beam elements, separately has been reported. The system response has been observed to be either periodic or quasi-periodic depending on the spin speed. Outcomes which were not ex