Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure

A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

On nonlinear dynamics in a free fluid surface of a tank excited by a non-ideal power source

We investigate the nonlinear oscillations in a free surface of a fluid in a cylinder tank excited by non-ideal power source, an electric motor with limited power supply. We study the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Additionally, the dynamics of parametrically excited surface waves in the tank can reveal new characteristics of the system. The fluid-dynamic system is modeled in such way as to obtain a nonlinear differential equation system. Numerical experiments are carried out to find the regions of chaotic solutions. Simulation results are presented as phase-portrait diagrams characterizing the resonant vibrations of free fluid surface and the existence of several types of regular and chaotic attractors. We also describe the energy transfer in the interaction process between the hydrodynamic system and the electric motor. Copyright © 2011 by ASME.

Numerical and experimental investigation of a vibration system with non-ideal vibration source

An excitation force that is not influenced by the system's states is said to be an ideal energy source. In real situations, a direct and feedback coupling between the excitation source and the system must always exist. This manifestation of the law of conversation of energy is known as Sommerfeld Effect. In the case of obtaining a mathematical model for such system, additional equations are usually necessary to describe the vibration sources and their coupling with the mechanical system. In this work, a cantilever beam and a non-ideal electric DC motor that is fixed to the beam free end is analyzed. The motor has an unbalanced mass that provides excitation to the system proportional to the current applied to the motor. During the motor's coast up operation, as the excitation frequency gets closer to the beam first natural frequency and if the drive power increases further, the DC motor speed remains constant until it suddenly jumps to a much higher value (simultaneously the vibration amplitude jumps to a much lower value) upon exceeding a critical input power. It was found that the Sommerfeld effect depends on some system parameters and the motor operational procedures. These parameters are explored to avoid the resonance capture in Sommerfeld effect. Numerical simulations and experimental tests are used to help insight this dynamic behavior.

Control and chaos for vibro-impact and non-ideal oscillators

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implementations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic motion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we investigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

On the control of a non-ideal engineering system: A friction-driven oscillating system with limited power supply

In this work a switching feedback controller for stick-slip compensation of a 2-DOF mass-spring-belt system which interacts with an energy source of limited power supply (non-ideal case) is developed. The system presents an oscillatory behavior due to the stick-slip friction. As the system equilibrium for a conventional feedback controller is not the origin, a switching control law combining a state feedback term and a discontinuous term is proposed to regulate the position of the mass. The problem of tracking a desired periodic trajectory is also considered. The feedback system is robust with respect to the friction force that is assumed to be within known upper and lower bounds.

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Control and chaos for vibro-impact and non-ideal oscillators

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A note on the attenuation of the sommerfeld effect of a non-ideal system taking into account a MR damper and the complete model of a DC motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On non-ideal simple portal frame structural model: Experimental results under a non-ideal excitation

We present measurements of the non-linear oscillations of a portal frame foundation for a non-ideal motor. We consider a three-time redundant structure with two columns, clamped in their bases and a horizontal beam. An electrical unbalanced motor is mounted at mid span of the beam. Two non-linear phenomena are studied: a) mode saturation and energy transfer between modes; b) interaction between high amplitude motions of the structure and the rotation regime of a real limited power motor. The dynamic characteristics of the structure were chosen to have one-to-two internal resonance between the anti-symmetrical mode (sway motions) and the first symmetrical mode natural frequencies. As the excitation frequency reaches near resonance conditions with the 2nd natural frequency, the amplitude of this mode grows up to a certain level and then it saturates. The surplus energy pumped into the system is transferred to the sway mode, which experiences a sudden increase in its amplitude. Energy is transformed from low amplitude high frequency motion into high amplitude low frequency motion. Such a transformation is potentially dangerous.We consider the fact that real motors, such as the one used in this study, have limited power output. In this case, this energy source is said to be non-ideal, in contrast to the ideal source whose amplitude and frequency are independent of the motion of the structure. Our experimental research detected the Sommerfeld Effect: as the motor accelerates to reach near resonant conditions, a considerable part of its output energy is consumed to generate large amplitude motions of the structure and not to increase its own angular speed. For certain parameters of the system, the motor can get stuck at resonance not having enough power to reach higher rotation regimes. If some more power is available, jump phenomena may occur from near resonance to considerably higher motor speed regimes, no stable motions being possible between these two.