On regular and irregular vibrations of a non-ideal system with two degrees of freedom. 1:1 resonance

Tsuchida, M.; Guilherme, Karen de Lolo; Balthazar, José Manoel; Silva, Geraldo Nunes; Cheshankov, B. I.

doi:10.1016/s0022-460x(02)01128-8

Cited by 20 publications

(7 citation statements)

References 1 publication

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“…In case of limitation of the power of the energy source, in result of strong interaction between dynamic system and engine, Somerfield effect, requiring the increase in power from the energy source (Kononenko, 1980;Alifov and Frolov, 1985), is manifested, a linear two mass system has regular vibration motion within 1 : 1 resonance passing, and the maximum amplitude increases only during passing the resonance (Tsuchida et al, 2003). Vibration in a linear with two degrees of freedom mass system with a drive and non-ideal source and nonlinear rotation moment, is regular before resonance, and irregular during and after 1 : 1 resonance passing (Tsuchida et al, 2003). In a non-ideal system with two degrees of freedom, consisting of a dumped nonlinear oscillator, connected with rotation part, manifestation of Hopf bifurcation is a common property of non-ideal problems, related to hopping phenomenon Balthazar, 2003, 2004).…”

Section: Introductionmentioning

confidence: 99%

The nonlinear vibrations of orthogonal mechanism of vibrating table in view of friction

2018

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Abstract. In dynamics of the orthogonal mechanism of vibrating table main attention is paid to the effect of friction on vibrational process when it is interacting with non-ideal energy source. As a result of analysis of numerical solutions of nonlinear equation of motion, it is established that in general, for the period of rotation, both sliding friction and rotational friction increase the difference between the maximum and minimum angular velocity values of the driving link (engine shaft) when its average value is constant; both increase the coefficient of non-uniformity of rotation. When there is a cargo of significant mass in the working link, the effect of sliding friction impacts more on the amplitude and frequency of the angular velocity oscillations of the driving link (engine shaft) and on the frequency of the coordinate changes, as well as on the frequencies and maximum and minimum values of the projections of the velocity and acceleration of the hinge linking the work platform to coupler. Similarly, the larger of the load mass, the stronger the effect of rotational friction on the amplitude and frequency of angular velocity oscillations of the driving link (engine shaft).

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Section: Introductionmentioning

confidence: 99%

The nonlinear vibrations of orthogonal mechanism of vibrating table in view of friction

2018

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“…In particular, the book [3], entirely devoted to the Sommerfeld effect in linear and nonlinear systems, should be mentioned here. Regular and chaotic vibrations of a non-ideal system with two degrees of freedom operating near internal resonances 1:1 and 1:2 were investigated in [4] and [5], respectively. All springs and dampers were assumed there as linear elements, and the system was coupled linearly.…”

Section: Introductionmentioning

confidence: 99%

Decomposition of governing equations in the analysis of resonant response of a nonlinear and non-ideal vibrating system

2015

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The dynamic response of a nonlinear system with three degrees of freedom in resonance that is loaded, inter alia, with a non-ideal excitation is investigated. A direct current motor (DC motor) with an eccentrically mounted rotor serves as a non-ideal source of energy. The general coordinate corresponding to the rotor dynamics steadily increases as a result of rotational motion. The decomposition of the equations of motion proposed in the paper allows us to separate the vibration of rotor from its rotations. The presented approach can be used to separate the vibration from rotations in many other mechanical and mechatronic systems. The behaviour of the considered non-ideal system near two simultaneously occurring resonances is examined using the Krylov-Bogolyubov averaging method. The stability analysis of the resonant response is also carried out.Grażyna Sypniewska-Kamińska, Ph.D, research fields: engineering mechanics, nonlinear dynamics.

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“…The effect of the gravitational force is neglected. The oscillator is driven by a motor that has an unbalance and has the motor torque, which is a linear function of angular velocity, as suggested by, among others, Dantas and Balthazar (2003), Tsuchida et al (2003Tsuchida et al ( ), (2005, Souza et al (2005a,b), Castao et al (2010). The motor property is (see Felix et al, 2009b)…”

Section: Introductionmentioning

confidence: 99%

Non-ideal mechanical system with an oscillator with rational nonlinearity

Cvetićanin

Zukovic

2013

Journal of Vibration and Control

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In this paper the generalized form of a non-ideal system which contains a pure nonlinear oscillator and a non-ideal energy source is studied. In the non-ideal oscillator-motor system there is an interaction between the motions of the oscillator and those of the motor, as the motor has an influence on the oscillator and vice versa. The mathematical model of the system is represented with two coupled nonlinear differential equations. The averaging method for solving these differential equations is based on the application of the Ateb function, which is the exact solution of the pure nonlinear oscillator. Using the obtained approximate solution, the resonant motion of the system is considered. Significant attention is paid to the steady-state motion and to the Sommerfeld effect. The influence of the order of nonlinearity on the dynamics of the nonideal system is evident. In the paper the procedure for determination of the parameters for suppression of the Sommerfeld effect of the non-ideal system is also given.

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On regular and irregular vibrations of a non-ideal system with two degrees of freedom. 1:1 resonance

Cited by 20 publications

References 1 publication

The nonlinear vibrations of orthogonal mechanism of vibrating table in view of friction

The nonlinear vibrations of orthogonal mechanism of vibrating table in view of friction

Decomposition of governing equations in the analysis of resonant response of a nonlinear and non-ideal vibrating system

Non-ideal mechanical system with an oscillator with rational nonlinearity

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