Vinicius Piccirillo

On nonlinear dynamics of a parametrically excited pendulum using both active control and passive rotational (MR) damper

This paper presents two control strategies for a parametrically excited pendulum with chaotic behavior. One of them considers active control obtained by nonlinear saturation control (NSC) and the other a passive rotational magnetorheological (MR) damper. Firstly, the active control problem was formulated in order to design the external torque for the pendulum, considering the NSC. Numerical simulations were carried out in order to show the effectiveness of this method for the active control of the pendulum oscillation. The ability of the control of the proposed NSC in suppression of the chaotic behavior, considering the proposed parameters, was tested by a sensitivity analysis to parametric uncertainties. In the case of the passive rotational MR damper, firstly the influence of the introduction of the MR in a pendulum was performed considering the 0-1 test. Different electric currents are applied to suppress the chaotic behavior of the system. The numerical results showed that the simple introduction of a passive rotational MR damper without electric current did not change the chaotic behavior of the system. However, it is possible to keep the pendulum oscillating with periodic behavior using the rotational MR damper with energizing discontinuity.

Characterizing the nonlinear behavior of a pseudoelastic oscillator via the wavelet transform

The nonlinear dynamics of a shape memory oscillator (SMO) subjected to an ideal or nonideal excitation is studied. The restoring force of the oscillator is provided by a shape memory device (SMD), described by a thermomechanical model capable of reproducing the hysteretic behavior via the evolution of a suitable internal variable. Due to nonlinearities in the model, the SMO can exhibit periodic or non-periodic behaviors. The effects of the external sources on the response of SMO are studied through the scalogram analysis of continuous wavelet transform by using a new measure, called the Scale index (Benitez R, Bolos VJ and Ramirez ME. A wavelet-based tool for studying non-periodicity. Comput Math Appl 2010; 60: 634–641). Numerical results show that the Scale index can successfully detect the behavior of the system when the signal is periodic or nonperiodic, and distinguish between them in a way consistent with the indications provided by the alternative 0-1 test.

Application of a Shape Memory Absorber in Vibration Suppression

The dynamic response of structures subjected to high-amplitude vibration is often dangerous and undesirable. Dynamic vibration absorbers (DVA) have received special attention in recent years due to vibration attenuation offered by them. Thus, the present study analyzes the nonlinear dynamics of a system with a dynamic vibration absorber (DVA) using a shape memory material (SMM) whose characteristics are highly dependent upon temperature. The restoring force of the oscillator is provided by a shape-memory device (SMD) described by a thermomechanical model capable to describe the hysteretic behavior via the evolution of a suitable internal variable. Numerical simulations show the effectiveness of using the SMM in reducing oscillations of a harmonic oscillator.

Influence of Smart Material on the Dynamical Response of Mechanical Oscillator

The dynamical response of systems with shape memory alloy (SMA) or magnetorheological damper (MRD) presents a different behavior due to their nonlinear characteristics. Both systems have a nonlinear behavior due to adaptive dissipation related to their hysteretic behavior. This property is very attractive in engineering field. This paper investigates the nonlinear dynamical behavior of an SMA or MRD oscillator system. The LuGre mathematical model is used to represent the MRD behavior. On the other hand, the SMA model is based on a thermomechanical consistent model with four state variables.

Using Saturation Phenomenon to Improve Energy Harvesting in a Portal Frame Platform with Passive Control by a Pendulum

A new model of energy harvester based on a simple portal frame structure subjected to saturation phenomenon is presented. Energy is collected via a piezoelectric device whose nonlinearities are considered in the mathematical model. The system is a bistable Duffing oscillator presenting chaotic behaviour. Optimization of power harvesting and stabilization of chaotic motions to a given periodic orbit is obtained analysing the average power output and bifurcation diagrams. Control sensitivity to parametric errors in the damping and stiffness parameters of the portal frame is studied. The proposed passive control technique uses a simple pendulum tuned to the vibrations of the structure to improve energy harvesting. The results show that with the implementation of this control strategy it is possible to eliminate the need for active of semi-active control, usually more complex. The control also provides a way to regulate the energy captured to a desired operating frequency.

Proposal of a Nonlinear Piezoelectric Coupling Term to Energy Harvesting Interactions

Nowadays, new technologies have triggered the needs of new energy sources, smaller and more efficient, so the research about energy harvesting has increased substantially. Several researchers have developed the conversion of wasted mechanical energy to electrical energy using piezoelectric materials as a transducer. This chapter proposes a mathematical model for the constitutive equation of a piezoelectric transducer. Experimental results involving piezoelectric elements were considered. The proposed mathematical model allows a considerably better description. The results are closer to those obtained in a real system, reducing inaccuracy of predictive behaviour of the piezoelectric energy harvesting system. In this work, the numerical simulations show a significant difference between results obtained with the proposed model and other models available in literature.

On Optimal Control of a Nonlinear Robotic Mechanism Using the Saturation Phenomenon

In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified for a wide range of parameters. Controlling of the chaotic behaviour of the system were implemented using two control techniques, the nonlinear saturation control (NSC) and the optimal linear feedback control (OLFC). The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The NSC is based in the second order differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.