On numerical simulations of a nonlinear self-excited system with two non-ideal sources

In this work, the dynamic behavior of self-synchronization and synchronization through mechanical interactions between the nonlinear self-excited oscillating system and two non-ideal sources are examined by numerical simulations. The physical model of the system vibrating consists of a non-linear spring of Duffing type and a nonlinear damping described by Rayleigh's term. This system is additional forced by two unbalanced identical direct current motors with limited power (non-ideal excitations). The present work mathematically implements the parametric excitation described by two periodically changing stiffness of Mathieu type that are switched on/off. Copyright © 2005 by ASME.

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.

An investigation of a two-stage nonlinear vibration isolation system

This paper investigates the most desirable configuration of a two-stage nonlinear vibration isolation system, in which the isolators contain hardening geometric stiffness nonlinearity and linear viscous damping. The force transmissibility of the system is used as the measure of the effectiveness of the isolation system. The hardening nonlinearity is achieved by placing horizontal springs onto the suspended and intermediate masses, which are supported by vertical springs. It is found that nonlinearity in the upper stage has very little effect and thus serves little purpose. The nonlinearity in the lower stage, however, has a profound effect, and can significantly improve the effectiveness of the isolation system. Further, it is found that it is desirable to have high damping in the upper stage and very low damping in the lower stage. © 2012 Elsevier Ltd.

Nonlinear control system applied to atomic force microscope including parametric errors

The performance of the optimal linear feedback control and of the state-dependent Riccati equation control techniques applied to control and to suppress the chaotic motion in the atomic force microscope are analyzed. In addition, the sensitivity of each control technique regarding to parametric uncertainties are considered. Simulation results show the advantages and disadvantages of each technique. © 2013 Brazilian Society for Automatics - SBA.

Influence of ideal and non-ideal excitation sources on the dynamics of a nonlinear vibro-impact system

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

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

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

Nonlinear dynamics and control strategies: On a energy harvester vibrating system with a linear form to non-ideal motor torque

In this paper, we deal with the research of a vibrating model of an energy harvester device, including the nonlinearities in the model of the piezoelectric coupling and the non-ideal excitation. We show, using numerical simulations, in the analysis of the dynamic responses, that the harvested power is influenced by non-linear vibrations of the structure. Chaotic behavior was also observed, causing of the loss of energy throughout the simulation time. Using a perturbation technique, we find an approximate analytical solution for the non-ideal system. Then, we apply both two control techniques, to keep the considered system, into a stable condition. Both the State Dependent Ricatti Equation (SDRE) control as the feedback control by changing the energy of the oscillator, were efficient in controlling of the considered non-ideal system.

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

Simulations of the Frequency Modulated Atomic Force Microscope (FM-AFM) nonlinear control system

The Frequency Modulated - Atomic Force Microscope (FM-AFM) is apowerful tool to perform surface investigation with true atomic resolution. The controlsystem of the FM-AFM must keep constant both the frequency and amplitude ofoscillation of the microcantilever during the scanning process of the sample. However,tip and sample interaction forces cause modulations in the microcantilever motion.A Phase-Locked Loop (PLL) is used as a demodulator and to generate feedback signalto the FM-AFM control system. The PLL performance is vital to the FM-AFMperformace since the image information is in the modulated microcantilever motion.Nevertheless, little attention is drawn to PLL performance in the FM-AFM literature.Here, the FM-AFM control system is simulated, comparing the performancefor di erent PLL designs.

Nonlinear ball and beam control system identification

The Ball and Beam system is a common didactical experiment in control laboratories that can be used to illustrate many different closed-loop control techniques. The plant itself is subjected to many nonlinear effects, which the most common comes from the relative motion between the ball and the beam. The modeling process normally uses the lagrangean formulation. However, many other nonlinear effects, such as non-viscous friction, beam flexibility, ball slip, actuator elasticity, collisions at the end of the beam, to name a few, are present. Besides that, the system is naturally unstable. In this work, we analyze a subset of these characteristics, in which the ball rolls with slipping and the friction force between the ball and the beam is non-viscous (Coulomb friction). Also, we consider collisions at the ends of the beam, the actuator consists of a (rubber made) belt attached at the free ends of the beam and connected to a DC motor. The model becomes, with those nonlinearities, a differential inclusion system. The elastic coefficients of the belt are experimentally identified, as well as the collision coefficients. The nonlinear behavior of the system is studied and a control strategy is proposed.

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Weed interference on maize (Zea mays) under no tillage system

A field trial was carried out in Brazil in March 2002 with the aim to evaluate the effects of different timing and extension of weedy period on maize productivity. The hybrid Pioneer 30K75 was sowed under 7 t ha(-1) mulching promoted by glyphosate spraying. The treatments were divided in two groups: In the first group, weeds were maintained since the maize sowing until different periods in the crop cycle: 0, 14, 28, 42, 56, 70, and 150 days (harvesting time). In the second group, the maize crop was kept weed free for the same periods of the first group. Weed control was done through hand hoeing. A complete randomized blocks experimental design with five replications was used for plots distribution in the field. Nonlinear regression model was used to study the effects of weedy or weedfree periods on maize productivity. Weed community included 13 families and 31 species. Asteraceae, Poaceae, and Euphorbiaceae were the most abundant families. Results showed that under no tillage condition with 7 t ha-1 mulching at sowing time, the maize crop could cohabit with weed community for 54 days without any yield lost. on the other hand, if the crop was kept weed free for 27 days, the weed interference was not enable to reduce maize production. According to these results one weed control measure between 27 and 54 days after crop emergence could be enough to avoid any reduction in maize productivity.

Global dynamics of the Rikitake system

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)