Aline Souza de Paula

Numerical Investigation of an Adaptive Vibration Absorber Using Shape Memory Alloys

The tuned vibration absorber (TVA) is a well-established passive vibration control device for achieving vibration reduction of a primary system subjected to external excitation. This contribution deals with the non-linear dynamics of an adaptive tuned vibration absorber (ATVA) with a shape memory alloy (SMA) element. Initially, a single-degree of freedom oscillator with an SMA element is analyzed showing the general characteristics of its dynamical response. Then, the analysis of an ATVA with an SMA element is carried out. Initially, small amplitude vibrations are considered in such a way that the SMA element does not undergo a stress-induced phase transformation. Under this assumption, the SMA influence is only caused by stiffness changes corresponding to temperature-induced phase transformation. Afterwards, the influence of the hysteretic behavior due to stress-induced phase transformation is considered. A proper constitutive description is employed in order to capture the general thermomechanical aspects of the SMAs. The hysteretic behavior introduces complex characteristics to the system dynamics but also changes the absorber response allowing vibration reduction in different frequency ranges. Numerical simulations establish comparisons of the ATVA results with those obtained from the classical TVA.

BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

A multiparameter chaos control method applied to maps

Chaos is a kind of nonlinear system response that has a dense set of unstable periodic orbits (UPOs) embedded in a chaotic attractor. The idea of the chaos control is to explore the UPO stabilization obtaining dynamical systems that may quickly react to some new situation, changing conditions and their response. The OGY (Ott-Grebogi-Yorke) method achieves system stabilization by using small perturbations promoted in the neighborhood of the desired orbit when the trajectory crosses a specific surface, such as a Poincare section. This contribution proposes a multiparameter (MP) method based on OGY approach in order to control chaotic behavior using different control parameters. As an application of the proposed multiparameter general formulation it is presented an uncoupled approach where the control parameters do not influence the system dynamics when they are not active. This method is applied to control chaos in maps using two control parameters. The two-dimensional Henon and Ikeda maps are of concern. Results show that the proposed procedure can be a good alternative for chaos control since it provides a more effective UPO stabilization than the classical single-parameter OGY approach.

Chaos control applied to cardiac rhythms represented by ECG signals

The control of irregular or chaotic heartbeats is a key issue in cardiology. In this regard, chaos control techniques represent a good alternative since they suggest treatments different from those traditionally used. This paper deals with the application of the extended time-delayed feedback control method to stabilize pathological chaotic heart rhythms. Electrocardiogram (ECG) signals are employed to represent the cardiovascular behavior. A mathematical model is employed to generate ECG signals using three modified Van der Pol oscillators connected with time delay couplings. This model provides results that qualitatively capture the general behavior of the heart. Controlled ECG signals show the ability of the strategy either to control or to suppress the chaotic heart dynamics generating less-critical behaviors.

Controlling a Shape Memory Alloy Two-Bar Truss Using Delayed Feedback Method

This work discusses the use of chaos control in smart structures. An archetypal model of a shape memory alloy (SMA) two-bar truss is treated. This system exhibits both constitutive and geometrical nonlinearities presenting a complex nonlinear dynamics response including either the snap-through or the chaotic behaviors. A constitutive model that presents a close agreement with experimental data is employed to describe the themomechanical SMA behavior. A variation of the continuous time-delayed feedback method is employed as a control strategy. This variable structure controller is applied to the stabilization of unstable periodic orbits of the SMA structure avoiding the snap-through behavior.

Nonlinear dynamics of a SMA large-scale space structure

Large-scale structures are of special interest of aerospace applications, especially the ones involving smart materials. This paper deals with an archetypal system with two degrees of freedom that resembles the use of SMA elements as vibration isolation systems on a sparse aperture satellite array. The system has SMA elements in two perpendicular directions connected to a mass. Each SMA element is connected to a base structure. Imperfections are represented by establishing a comparison between two different systems: ideal and perturbed configuration system. The perturbed configuration is characterized by a situation where all SMA elements are in a stress-free state. The thermomechanical behavior of SMA elements is described by a constitutive model with internal constrains. Numerical tests of this system are of concern showing its general dynamical behavior. Periodic and chaotic motions are investigated showing the complex behaviors of this kind of system. The effect of imperfection in system dynamics is also discussed. Keywords: shape memory alloys, smart structures, aerospace structures, nonlinear dynamics

Nonlinear dynamics of a flexible portal frame under support excitation

This paper presents a nonlinear dynamic analysis of a flexible portal frame subjected to support excitation, which is provided by an electro-dynamical shaker. The problem is reduced to a mathematical model of four degrees of freedom and the equations of motion are derived via Lagrangian formulation. The main goal of this study is to investigate the dynamic interactions between a flexible portal frame and a non-ideal support excitation. The numerical analysis shows a complex behavior of the system, which can be observed by phase spaces, Poincaŕ sections and bifurcation diagrams..

Experimental bifurcation control of a parametric pendulum

The aim of the study is to maintain the desired period-1 rotation of the parametric pendulum over a wide range of the excitation parameters. Here the Time-Delayed Feedback control method is employed to suppress those bifurcations, which lead to loss of stability of the desired rotational motion. First, the nonlinear dynamic analysis is carried out numerically for the system without control. Specifically, bifurcation diagrams and basins of attractions are computed showing co-existence of oscillatory and rotary attractors. Then numerical bifurcation diagrams are experimentally validated for a typical set of the system parameters giving undesired bifurcations. Finally, the control has been implemented and investigated both numerically and experimentally showing a good qualitative agreement.

Shape Memory Alloys

This chapter presents a general overview of shape memory alloys (SMAs). A discussion about thermomechanical behaviors is carried out establishing the most important characteristics of these alloys. Applications of SMAs in different areas of human knowledge are explained. Thermomechanical characterization is discussed considering different experimental procedures. Afterward, a brief review of constitutive models is presented. A model with assumed transformation kinetics is explored showing some numerical simulations.

Chaos Control Methods Applied to Avoid Bifurcations in Pendulum Dynamics

This paper deals with the application of chaos control methods in order to perform bifurcation control of a parametric pendulum-shaker system. The extended time-delayed feedback control method is employed to maintain stable rotational solution of the system avoiding bifurcation to chaos. The considered pendulum system is chosen due to its potential application for extracting energy from sea waves. This alternative concept of energy harvesting is based on exploiting the rotational unbounded solution of the pendulum dynamics. The bifurcation control proposed allows the system to keep the desired rotational solution over extended parameter range avoiding undesirable changes in system dynamics.