Comments on a nonlinear and nonideal electromechanical damping vibration absorber, Sommerfeld effect and energy transfer

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)

Using of a snap-through truss absorber in the attenuation of the sommerfeld effect

This work, considers a vibrating system, which consists of a snap-through truss absorber (STTA) coupled to an oscillator, under excitation of an DC motor, with an eccentricity and limited power, characterizing a non-ideal oscillator (NIO). It is aimed to use the absorber STTA, to establish the conditions, that we have the maxim attenuation of the jumpphenomenon (Sommerfeld Effect). Here, weare interestedin determining the conditions of the vibrating system, in which there arereduced amplitudes of the oscillator, when it passes through the region of resonance.

Nonlinear Interactions in a Piezoceramic Bar Transducer Powered by a Vacuum Tube Generated by a Nonideal Source

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper The mathematical model of the system is represented by coupled non-linear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation. [DOI: 10.1115/1.3124783]

On a Nonideal (MRD) Damper-Electro-mechanical Absorber Dynamics

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

A Short Note on Transverse Vibrations of a Shaft Carrying Two (or One) Disk Excited by a Nonideal Motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

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.

An overview on non-ideal vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.

Escape in a nonideal electro-mechanical system

In this work a particular system is investigated consisting of a pendalum whose point of support is vibrated along a horizontal guide by a two bar linkage driven from a DC motor, considered as a limited power source. This system is nonideal since the oscillatory motion of the pendulum influences the speed of the motor and vice-versa, reflecting in a more complicated dynamical process. This work comprises the investigation of the phenomena that appear when the frequency of the pendulum draws near a secondary resonance region, due to the existing nonlinear interactions in the system. Also in this domain due to the power limitation of the motor, the frequency of the pendulum can be captured at resonance modifying completely the final response of the system. This behavior is known as Sommerfield effect and it will be studied here for a nonlinear system.

A nonlinear and non-ideal wind generator supporting structure

We present a simple mathematical model of a wind turbine supporting tower. Here, the wind excitation is considered to be a non-ideal power source. In such a consideration, there is interaction between the energy supply and the motion of the supporting structure. If power is not enough, the rotation of the generator may get stuck at a resonance frequency of the structure. This is a manifestation of the so-called Sommerfeld Effect. In this model, at first, only two degrees of freedom are considered, the horizontal motion of the upper tip of the tower, in the transverse direction to the wind, and the generator rotation. Next, we add another degree of freedom, the motion of a free rolling mass inside a chamber. Its impact with the walls of the chamber provides control of both the amplitude of the tower vibration and the width of the band of frequencies in which the Sommerfeld effect occur. Some numerical simulations are performed using the equations of motion of the models obtained via a Lagrangian approach.

On the existence and stability of periodic orbits in non ideal problems: General results

In this work, motivated by non-ideal mechanical systems, we investigate the following O.D.E. ẋ = f (x) + εg (x, t) + ε2g (x, t, ε), where x ∈ Ω ⊂ ℝn, g, g are T periodic functions of t and there is a 0 ∈ Ω such that f (a 0) = 0 and f′ (a0) is a nilpotent matrix. When n = 3 and f (x) = (0, q (x 3) , 0) we get results on existence and stability of periodic orbits. We apply these results in a non ideal mechanical system: the Centrifugal Vibrator. We make a stability analysis of this dynamical system and get a characterization of the Sommerfeld Effect as a bifurcation of periodic orbits. © 2007 Birkhäuser Verlag, Basel.