Reyolando M. L. R. F. Brasil

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.

On Saturation Control of a Non-Ideal Vibrating Portal Frame Foundation Type Shear-Building

In this paper, we examine the nonlinear control method based on the saturation phenomenon and of systems coupled with quadratic nonlinear ties applied to a shear-building portal plane frame foundation that supports an unbalanced direct current with limited power supply (non-ideal system). We analyze the equations of motion by using the method of averaging and numerical simulation. The interaction of the non-ideal structure with the saturation controller may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. Special attention is focused on passage through resonance when the non-ideal excitation frequency is near the portal frame natural frequency and when the non-ideal system frequency is approximately twice the controller frequency (two-to-one internal resonance).

Some comments on the numerical simulation of self-synchronization of four non-ideal exciters

In this paper, self-synchronization of four non-ideal exciters is examined via numerical simulation. The mathematical model consists of four unbalanced direct current motors with limited power supply mounted on a flexible structural frame support.

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.

Experimental study of the wind forces on rectangular latticed communication towers with antennas

Abstract With todays expanding communication systems, a large number of lattice towers to support cellular antennas are being constructed in Brazil. Due to the lightweight of these structures, wind forces are the primary concern in the design. An experimental investigation on the subject was carried out at the Boundary Layer Wind Tunnel Laboratory, University of Western Ontario (UWO), Canada. Three section models were designed and constructed based on existing latticed towers built in Brazil. The wind incidence angle; the tower solidity; the shielding effect; the influence of the wind turbulence on the drag coefficient were analyzed. Measurements were made of the mean and RMS drag and crosswind forces. The results were compared with some existing codes and standards including the Canadian (NBCC, 1995), American (ASCE 7-95, 1995), Australian/New Zealand (AS/NZS 1170.2-2002), Australian (AS 3995-1994), British (BS8100, 1986), Eurocode 1 (European Committee for Standardization, 1995) and Brazilian (NBR 6123, 1988). It is a common approach to consider the wind forces on antennas independent of the lattice tower, without considering the effects of their presence on the computation of the wind forces. The question arises whether this is a good approach or not. These effects can be described by introducing an interference factor. This factor depends, among other things, on the tower solidity. Two models with different solidity were tested for wind incidence angle of 0 degrees and antenna dishes simulated with disks made of Styrofoam attached to the windward face. The results were compared with ESDU.

Analysis of Regular and Irregular Dynamics of a Non Ideal Gear Rattling Problem

This paper presents a study on the dynamics of the rattling problem in gearboxes under non-ideal excitation. The subject has being analyzed by a number of authors such as Karagiannis and Pfeiffer (1991), for the ideal excitation case. An interesting model of the same problem by Moon (1992) has been recently used by Souza and Caldas (1999) to detect chaotic behavior. We consider two spur gears with different diameters and gaps between the teeth. Suppose the motion of one gear to be given while the motion of the other is governed by its dynamics. In the ideal case, the driving wheel is supposed to undergo a sinusoidal motion with given constant amplitude and frequency. In this paper, we consider the motion to be a function of the system response and a limited energy source is adopted. Thus an extra degree of freedom is introduced in the problem. The equations of motion are obtained via a Lagrangian approach with some assumed characteristic torque curves. Next, extensive numerical integration is used to detect some interesting geometrical aspects of regular and irregular motions of the system response.

Effect of static loading on the nonlinear vibrations of a three-time redundant portal frame: Analytical and numerical studies

An analytical study of the nonlinear vibrations in a three-time redundant portal frame is presented herewith, considering the effect of the axial forces caused by the static loading upon the first anti-symmetrical mode (sway) and the first symmetrical mode natural frequencies. It is seen that the axial forces may play an important role in tuning the sway mode and the first symmetrical mode into a 1:2 internal resonance. Harmonic support excitations resonant with the first symmetrical mode are then introduced and the amplitudes of nonlinear steady states are computed based upon a multiple scales solution. Comparisons with numerical analyses using a finite-element program developed by the authors show good qualitative agreement.

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 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.

On Lugre Friction Model to Mitigate Nonideal Vibrations

UNESP Rio Claro, Inst Geociencias & Ciencias Exatas, Dept Estat Matemat Aplicada & Comp, BR-13500230 Sao Paulo, Brazil