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Introduction To Perturbation Techniques

The current study examines the hybrid Rayleigh–Van der Pol–Duffing oscillator (HRVD) with a cubic–quintic nonlinear term and an external excited force. The Poincare–Lindstedt technique is adapted t...

https://journals.sagepub.com/doi/pdf/10.1177/14613484211026407

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller:

Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity

Nonlinear dynamics near resonances of a rotor-active magnetic bearings system with 16-pole legs and time varying stiffness

Time-delayed control to suppress the nonlinear vibrations of a horizontally suspended Jeffcott-rotor system

A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinearities under multi-parametric excitations is studied and solved. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system with multi-parametric excitations and time-varying stiffness near the simultaneous primary and internal resonance. The stability of the steady state solution for that resonance is determined and studied using Runge-Kutta method of fourth order. It is shown that the system exhibits many typical non-linear behaviors including multiple-valued solutions, jump phenomenon, hardening and softening non-linearities and chaos in the second mode of the system. The effects of the different parameters on the steady state solutions are investigated and discussed also. A comparison to published work is reported.

Nonlinear behavior of a rotor-AMB system under multi-parametric excitations

Vibration of structures is often an undesirable phenomena and should be avoided or controlled. There are two techniques to control the vibration of a system, that is, active and passive control techniques. In this paper, a negative feedback velocity is applied to a dynamical system, which is represented by two coupled second order nonlinear differential equations having both quadratic and cubic nonlinearties. The system describes the vibration of an aircraft tail. The system is subjected to multi-external excitation forces. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations and obtain approximate solutions up to third order of accuracy. The stability of the system is investigated applying frequency response equations. The effects of the different parameters are studied numerically. Various resonance cases are investigated. A comparison is made with the available published work.

Active control of an aircraft tail subject to harmonic excitation

Vibration reduction in a 2DOF twin-tail system to parametric excitations

A rotor-active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinear under tuned, and external excitation is studied. The method of multiple scales is applied to analyze the response of two modes of a rotor-AMB system near the simultaneous combined and sub-harmonic resonance. The stability of the steady-state solution for that resonance is determined and studied applying Rung–Kutta fourth order method. It is shown that the system exhibits many typical nonlinear behaviors, including multiple-valued solutions, jump phenomenon, hardening and softening nonlinear and chaos in the second mode of the system. The effects of the different parameters on the steady-state solutions are investigated and discussed.

H. S. Bauomy

Papers

Nonlinear behavior of a rotor-AMB system under multi-parametric excitations

Active control of an aircraft tail subject to harmonic excitation

Vibration reduction in a 2DOF twin-tail system to parametric excitations

Stability analysis of a rotor-AMB system with time varying stiffness

Nonlinear study of a rotor–AMB system under simultaneous primary-internal resonance