Wyniki wyszukiwania - BazTech

1

SDRE applied to position and vibration control of a robot manipulator with a flexible link

Lima J. J., Tusset A. M., Janzen F. C., Piccirillo V., Nascimento C. B., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1067--1078

EN

This paper presents position and vibration control of a flexible robot composed of two rigid and one flexible links. Position is controlled by the current applied to the DC motor armature. To control vibrations of the flexible structure, Shape Memory Alloys (SMA) are used. Due to phase transformations, the SMA can change its stiffness through temperature variation, considering and taking advantage of this characteristic the vibration control is done. Control is achieved via the State Dependent Ricatti Equations (SDRE) technique, which uses suboptimal control and system local stability search. The simulation results show the feasibility of the proposed control for the considered system.

2

Homotopy analysis of a forced nonlinear beam model with quadratic and cubic nonlinearities

Shahlaei-Far S., Nabarrete A., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 4

1219--1230

EN

This study investigates forced nonlinear vibrations of a simply supported Euler-Bernoulli beam on a nonlinear elastic foundation with quadratic and cubic nonlinearities. Applying the homotopy analysis method (HAM) to the spatially discretized governing equation, we derive novel analytical solutions and discuss their convergence to present nonlinear frequency responses with varying contributions of the nonlinearity coefficients. A comparison with numerical solutions is conducted and nonlinear time responses and phase planes are compared to the results from linear beam theory. The study demonstrates that apart from nonlinear problems of free vibrations, HAM is equally capable of solving strongly nonlinear problems of forced vibrations.

3

A nonlinear electromechanical pendulum arm with a nonlinear energy sink control (NES) approach

Alişverişçi G. F., Bayıroluǧlu H., Felix J. L. P., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2016

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Vol. 54 nr 3

975--986

EN

This paper considers the nonlinear dynamics of an electromechanical device with a pendulum arm and a Nonlinear Energy Sink (NES) put on the point of the pendulum suspension. It is shown that the (NES) is capable of absorbing energy from the system. The numerical results are shown in a bifurcation diagram, phase plane, Poincar´e map and Lyapunov exponents.

4

On suppression of chaotic motions of a portal frame structure under non-ideal loading using a magneto-rheological damper

Tusset A. M., Piccirillo V., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 3

653--664

EN

We consider chaotic motions of a portal frame structure under non-ideal loading. To suppress this chaotic behavior, a controlling scheme is implemented. The control strategy involves application of two control signals and nonlinear feedforward control to maintain a desired periodic orbit, and state feedback control to bring the system trajectory into the desired periodic orbit. Additionally, the control strategy includes an active magneto-rheological damper to actuate the system. The control force of the damper is a function of the voltage applied in the coil of the damper that is based on the force given by the controller.

5

TM-AFM nonlinear motion control with robustness analysis to parametric errors in the control signal determination

Balthazar J. M., Tusset A. M., Bueno Á. M.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 1

93--106

EN

Nonlinear motion of the microcantilever probe in the Atomic Force Microscope (AFM) has been extensively studied considering mainly the van der Waals forces. Since the behavior of the microcantilever is vital to quality of generated images, the study of control strategies that force the probe to avoid undesired behavior such as chaotic motion, is also of significant importance. A number of published works has shown that the microcantilever is subject to chaotic motion for a certain combination of parameters. For such a parameter combination, the control system must suppress the chaotic motion. Here, an study of the AFM mathematical model is presented, aiming to find a region of operation of the AFM where the motion is chaotic. In order to suppress the chaotic motion, a periodic orbit of the system is obtained, and the controller forces the system to that periodic orbit. Two control strategies are used, namely: The State Dependent Riccati Equation (SDRE) and the Optimal Linear Feedback Control (OLFC). Both control strategies consider the complete nonlinearities of the system, and the OLFC guarantees the global stability. The numerical simulations carried out showed the efficiency of the control methods as well as the sensitivity of each control strategy to parametric errors. Without the parametric errors, both control strategies were effective in maintaining the system into the desired orbit. On the other hand, in the presence of parametric errors, the SDRE technique was more robust than the OLFC.

6

Dynamical jump attenuation in a non-ideal system through a magnetorheological damper

Piccirillo V., Tusset A. M., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 3

595--604

EN

This paper is concerned with the Sommerfeld effect (Jump phenomena) attenuation in an non-ideal mechanical oscillator connected with an unbalanced motor excitation with a limited power supply (non-ideal system) using a magnetorheological damper (MRD). The dynamical response of systems with MRD presents different behavior due to their nonlinear characteristic. MRD nonlinear response is associated with adaptive dissipation related to their hysteretic behavior. The Bouc-Wen mathematical model is used to represent the MRD behavior. Numerical simulations show different aspects about the Sommerfeld effect, illustrating the influence of the different electric current applied in the MRD to control the force developed by this damper.

7

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

Moraes F. H., Pontes B. R. (jr), Silveira M., Balthazar J. M., Brasil R. M. L. R. F.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 3

763--774

EN

The objective of the present work is to analyze the dynamics of a vibro-impact system consisting of two blocks of different mass coupled by a spring with two stages. Two different types of excitation sources for the system are used in the analysis: the first is an ideal excitation in form of a harmonic force, and the second is a non-ideal excitation in form of a DC electric motor with limited power supply which has an unbalanced rotor. The control parameter for both situations is the excitation frequency of the system. The analysis includes time histories of displacements and velocities, phase portraits and diagrams of the displacement and frequency, used to show the Sommerfeld effect. For certain values of the parameters of the system, the motion is chaotic. The mathematical model of the system is used to obtain an insight to the global dynamics of the vibro-impact system. The model with a non-ideal excitation is more realistic, complete and complex than the model with the ideal excitation.

8

On the analytical solution for the slewing flexible beam-like system: analysis of the linear part of the perturbed problem

Fenili A., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 1

51-68

EN

The dynamical system investigated in this work is a nonlinear flexible beam-like structure in slewing motion. Non-dimensional and perturbed governing equations of motion are presented. The analytical solution for the linear part of these perturbed equations for ideal and for non-ideal cases are obtained. This solution is necessary for the investigation of the complete weak nonlinear problem where all nonlinearities are small perturbations around a linear known solution. This investigation shall help the analyst in the modelling of dynamical systems with structure-actuator interactions.

PL

Układem dynamicznym badanym w pracy jest podzespół zawierający podatną belkę poruszającą się ruchem obrotowym w płaszczyźnie poziomej. Zaprezentowano bezwymiarowe i perturbowane równania ruchu. Rozwiązania analityczne części zlinearyzowanej tych równań uzyskano dla przypadku idealnego i nieidealnego. Taka postać rozwiązania jest niezbędna do analizy zupełnego i słabo nieliniowego problemu, w którym nieliniowości stanowią niewielkie perturbacje wokół rozwiązania liniowego. Prezentowane wyniki badań mogą okazać się pomocą dla analityków zajmujących się modelowaniem układów dynamicznych uwzględniających interakcje zachodzące pomiędzy daną konstrukcją bazową, a zamocowanymi na niej aktywnymi elementami wykonawczymi (aktuatorami).

9

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

Piccirillo V., Balthazar J. M., Pontes B. R. Jr., Felix J. L. P.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 3

597-620

EN

In this paper, we present nonlinear dynamic behaviour of a system which consists of a mass connected to a rigid support by a shape memory alloy (SMA) element and a damper. In order to disturb the system, a DC motor with limited power supply is connected to the mass, causing an interaction between the vibrating structure and the energy source. The SMA element is characterised using a one-dimensional phenomenological constitutive model, based on the classical Devonshire theory. We analyse the non-ideal system in form of two coupled nonlinear differential equations. Some interesting nonlinear phenomena as the Sommerfeld effect and nonlinear resonance including periodic, chaotic and hyperchaotic regime are presented.

PL

W pracy przedstawiono opis dynamiki nieliniowego układu złożonego z masy połączonej ze sztywnym podłożem za pośrednictwem elementu z pamięcią kształtu i tłu- mikiem. W celu realizacji wymuszenia w układzie zastosowano silnik prądu stałego z ograniczonym poborem mocy, który pobudza do ruchu masę, tworząc w ten sposób sprzężenie mechaniczne pomiędzy układem drgającym a źródłem energii. Element z pamięcią kształtu opisano za pomocą jednowymiarowego modelu fenomenologicznego opartego na teorii Devenshire’a. Przeanalizowano rozważany nieidealny układ opisany dwoma sprzężonymi nieliniowymi równaniami ruchu. Zaobserwowano i opisano interesujące zjawiska nieliniowe w postaci efektu Sommerfelda i nieliniowego rezonansu w zakresie drgań okresowych, chaotycznych i hiperchaotycznych.

10

Control and chaos for vibro-impact and non-ideal oscillators

de Souza S. L. T., Caldas I. L., Viana R. L., Balthazar J. M.

Journal of Theoretical and Applied Mechanics

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2008

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Vol. 46 nr 3

641-664

EN

In the paper, we discuss dynamics of two kinds of mechanical systems. Initially, we consider vibro-impact systems which have many implemen- tations in applied mechanics, ranging from drilling machinery and metal cutting processes to gear boxes. Moreover, from the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phe- nomena, particularly chaotic motion. In this paper, we review recent works on the dynamics of vibro-impact systems, focusing on chaotic mo- tion and its control. The considered systems are a gear-rattling model and a smart damper to suppress chaotic motion. Furthermore, we inve- stigate systems with non-ideal energy source, represented by a limited power supply. As an example of a non-ideal system, we analyse chaotic dynamics of the damped Duffing oscillator coupled to a rotor. Then, we show how to use a tuned liquid damper to control the attractors of this non-ideal oscillator.

PL

W pracy przedyskutowano zagadnienie dynamiki mechanizmów dwóch rodzajów. Najpierw rozważono układ drgający z uderzeniami, który znajduje liczne aplikacje praktyczne w mechanice stosowanej, począwszy od urządzeń wiertniczych przez procesy cięcia metalu do skrzyń biegów włącznie. Z punktu widzenia dynamiki maszyn układy wibro-uderzeniowe wykazują bogactwo interesujących zjawisk, wliczając w to chaos. W pracy zaprezentowano przegląd ostatnich prac dotyczących dynamiki układów wibro-uderzeniowych, w których zajęto się problemem chaosu i możliwości jego sterowania. Przeanalizowano układy mechaniczne na przykładzie modelu kół zębatych z systemem ”inteligentnego” tłumika do eliminacji ruchu chaotycznego. Zajęto się, po drugie, mechanizmami z nieidealnym źródłem energii odwzorowanym poprzez układ ograniczonego poboru mocy. Jako przykład zbadano dynamikę chaotyczną tłumionego oscylatora Duffinga połączonego z wirnikiem. Pokazano sposób zastosowania płynnego tłumika do sterowania formą atraktorów obserwowanych w nieidealnym oscylatorze.