1:2 and 1:3 internal resonance active absorber for non-linear vibrating system

Sayed, M.; Kamel, M.

doi:10.1016/j.apm.2011.05.057

Cited by 65 publications

(40 citation statements)

References 21 publications

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“…The re-sults showed that saturation control of steady state vibrations was efficient, and in good agreement with the theory. The authors extended these results in Saved et al [5] where an active vibration absorber to eliminate the vibration of a nonlinear system was analysed in the presence of 1:2 and 1:3 internal resonance. In addition, the plant was subjected to external and parametric excitations.…”

Section: Introductionmentioning

confidence: 74%

“…The nonlinear dynamical equations of the system -obtained via VehicleSim-will be analysed by studying an equivalent spring pendulum system that has two coupled degrees of freedom whose dynamical characteristics can resemble those of the coupled flap/lag motions. The aim therefore is to identify particular terms in the nonlinear equations of motion that can shed on light energy exchange being this something that should be considered as proposed by Saved et al [5] and Tekin et al [7]. The nonlinear equations obtained represent an advantage with respect to the work presented in Chen [2] and Tekin et al [7], as it finds analogies with nonlinear systems, allowing to predict some behaviour on the system under study.…”

Section: Introductionmentioning

confidence: 99%

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Helicopter flap/lag energy exchange study

Castillo-Rivera

Tomás-Rodrı́guez

2017

Nonlinear Dyn

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract This paper presents a study on the energy exchange taking place on articulated helicopter main rotor blades. The blades are hinged and the flap/lag modes are highly coupled. These dynamical couplings existing between the two degrees of freedom are clearly identifiable as the nonlinear terms that appear in the equations of motion, are key to understand the energy exchange process. The work here conducted is carried out using VehicleSim, a multibody software specialized in modelling mechanical systems composed by rigid bodies. A spring pendulum system is also studied in order to examine its nonlinear behaviour, and to establish existing analogies with the rotor blade nonlinear dynamics. The nonlinear couplings of both systems are compared to each other, and commensurability condition is analysed by means of Short Time Fourier Transform (STFT) methods as well as the flap and lag amplitudes spectrum. Simulations are carried out and the obtained results show clear analogies in the energy exchange process taking place in both systems. The stability of these modes is also studied using Poincare' map method. Permanent repository link

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Section: Introductionmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Helicopter flap/lag energy exchange study

Castillo-Rivera

Tomás-Rodrı́guez

2017

Nonlinear Dyn

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“…They used two simple active control laws based on the linear negative velocity and acceleration feedback Sayed and Hamed [27] obtained the analytical and numerical solutions of coupled nonlinear differential equations describing the motion of pitch roll under parametric and harmonic excitations using multiple scale method. Sayed and Kamel [28,29] investigated the effects of different controllers on the vibrating system and the saturation control to reduce vibrations due to rotor blade flapping motion. The method of multiple scales is used to obtain the analytical solution of the coupled second order differential equation.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Mousa

Sayed

Eldesoky

et al. 2014

Int. J. Dynam. Control

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The aim of this paper is to investigate the stability of a simply supported laminated composite piezoelectric rectangular plate under combined excitations. Analysis of the amplitude and phase modulation equations with the associated nonlinear interaction coefficients, as provided by the multiple scale analyses of various 1:1 internal resonance conditions and primary resonance case, where ω 2 ∼ = ω 1 and 3 ∼ = ω 1 is considered. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to the second-order approximation. All possible resonance cases at this approximation order are extracted. The stable/unstable periodic solutions are determined and are presented through frequency response plots. The analytical results are verified by comparing them with those of numerical integration of the modal equations. The influence of different parameters on the dynamic behavior of the composite laminated piezoelectric rectangular plate is studied. Variation of the some parameters leads to multivalued amplitudes and hence to jump phenomena. A comparison with the available published work is reported.

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“…The method of multiple scale perturbation technique is applied to solve the non-linear differential equations and obtain approximate solutions up to and including the second-order approximations. Sayed and Kamel [25,26] investigated the effects of different controllers on the vibrating system and the saturation control of a linear absorber to reduce vibrations due to rotor blade flapping motion. Amer and Sayed [27], studied the response of one-degree-of freedom, non-linear system under multi-parametric and external excitation forces simulating the vibration of the cantilever beam.…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Analysis of Vibrations of Non-Linear System Subjected to Multi-Excitation Forces via a Non-Linear Absorber

El-Ghareeb¹,

Hamed²,

Elkader³

2012

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The dynamic response of mechanical and civil structures subjected to high-amplitude vibration is often dangerous and undesirable. Sometimes controlled vibration is desirable as in the machinery used in the formation of rigid hard material as Ceramics and diamond. This process is done via the passive control methods. The main purpose of this paper is to how reduction of vibration of nonlinear system subjected to multi-excitation forces via a nonlinear absorber. The nonlinear differential equations describing the model, which describe ultrasonic cutting machine are solved by using perturbation method. The effects of different parameter on the response of the system are studied. The stability of the numerical solution is investigated by using frequency response equations and phase-plane method. The simulation results are achieved using Matlab and Maple programs. A comparison is made with the available published work.

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1:2 and 1:3 internal resonance active absorber for non-linear vibrating system

Cited by 65 publications

References 21 publications

Helicopter flap/lag energy exchange study

Helicopter flap/lag energy exchange study

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Non-Linear Analysis of Vibrations of Non-Linear System Subjected to Multi-Excitation Forces via a Non-Linear Absorber

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