Numerical Studies of a Nonlinear Flexible Rotating System Under Harmonic Ground Motion
01 Jan 2015-pp 1677-1687
TL;DR: In this paper, the Euler-Bernoulli beam theorem has been adopted in order to derive the partial differential equation governing the dynamics characteristics of the rotating system using extended Hamilton's principle.
Abstract: The nonlinear behavior of a rotating system with large elastic deformation subjected to harmonically varying ground disturbance has been investigated numerically. The Euler-Bernoulli beam theorem has been adopted in order to derive the partial differential equation governing the dynamics characteristics of the rotating system using extended Hamilton’s principle. Method of multiple scales has been selected in approximately finding the nonlinear dynamic characteristics of the system for possible resonance conditions. The effect of nonlinearities and other variations in the values of different parameters like amplitude of external excitation, position of disk along the span, and mass of the disk on the system performance has been investigated. The outcome from the present work will furnish a proper guidance to the designers in the vicinity of the limitation and safe range of operational speed of rotor shaft under the variation of other control parameters.
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TL;DR: In this article, the vibration and stability analysis of an unbalanced rotor mounted on high-static-low-dynamic-stiffness supports is presented. And the stiffness of the supports is modeled as symmetric of cubic order.
22 citations
References
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Book•
01 Jan 1981
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Abstract: Algebraic Equations. Integrals. The Duffing Equation. The Linear Damped Oscillator. Self-Excited Oscillators. Systems with Quadratic and Cubic Nonlinearities. General Weakly Nonlinear Systems. Forced Oscillations of the Duffing Equation. Multifrequency Excitations. The Mathieu Equation. Boundary-Layer Problems. Linear Equations with Variable Coefficients. Differential Equations with a Large Parameter. Solvability Conditions. Appendices. Bibliography. Index.
3,020 citations
"Numerical Studies of a Nonlinear Fl..." refers methods in this paper
...The Perturbation methods are a collection of techniques which can be used to simplify and solve a wide range of mathematical problems, involving small or large parameters [6–8]....
[...]
Book•
01 Jan 1995
TL;DR: Perturbation Methods Dynamical Systems and Equilibrium Solutions Dynamic Solutions Tools to Characterize Different Motions Two-to-One Internal Resonance Combination Internal Resonances Three-toone Internal ResonANCE Combination internal Resonances Systems with Quadratic and Cubic Nonlinearities Gyroscopic Systems Systems with More than One internal Resonance Random Excitations
Abstract: Perturbation Methods Dynamical Systems and Equilibrium Solutions Dynamic Solutions Tools to Characterize Different Motions Two-to-One Internal Resonances Combination Internal Resonances Three-to-One Internal Resonances Combination Internal Resonances Systems with Quadratic and Cubic Nonlinearities Gyroscopic Systems Systems with More than One Internal Resonance Random Excitations
1,030 citations
"Numerical Studies of a Nonlinear Fl..." refers methods in this paper
...The Perturbation methods are a collection of techniques which can be used to simplify and solve a wide range of mathematical problems, involving small or large parameters [6–8]....
[...]
TL;DR: In this paper, the dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally, focusing on behavior in bending near the critical speeds of rotation.
Abstract: The dynamic behavior of flexible rotor systems subjected to base excitation (support movements) is investigated theoretically and experimentally. The study focuses on behavior in bending near the critical speeds of rotation. A mathematical model is developed to calculate the kinetic energy and the strain energy. The equations of motion are derived using Lagrange equations and the Rayleigh-Ritz method is used to study the basic phenomena on simple systems. Also, the method of multiple scales is applied to study stability when the system mounting is subjected to a sinusoidal rotation. An experimental setup is used to validate the presented results.
98 citations
TL;DR: In this article, the free vibrations of an in-extensional simply supported rotating shaft with nonlinear curvature and inertia are considered, and the results of perturbation method are validated with numerical simulations.
89 citations
TL;DR: In this article, a mathematical model incorporating the higher order deformations in bending is developed and analyzed to investigate the nonlinear dynamics of rotors, and the kinetic and strain energies of the rotor system are derived and the Rayleigh-Ritz method is used to discretize these energy expressions.
35 citations