• Smart Structures and Systems
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• v.15 no.6
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• pp.1521-1542
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• 2015

The use of shape memory alloys (SMAs) in dynamical systems has an increasing importance in engineering especially due to their capacity to provide vibration reductions. In this regard, experimental tests are essential in order to show all potentialities of this kind of systems. In this work, SMA springs are incorporated in a dynamical system that consists of a one degree of freedom oscillator connected to a linear spring and a mass, which is also connected to the SMA spring. Two types of springs are investigated defining two distinct systems: a pseudoelastic and a shape memory system. The characterisation of the springs is evaluated by considering differential calorimetry scanning tests and also force-displacement tests at different temperatures. Free and forced vibration experiments are made in order to investigate the dynamical behaviour of the systems. For both systems, it is observed the capability of changing the equilibrium position due to phase transformations leading to hysteretic behaviour, or due to temperature changes which also induce phase transformations and therefore, change in stiffness. Both situations are investigated by promoting temperature changes and also pre-tension of the springs. This article shows several experimental tests that allow one to obtain a general comprehension of the dynamical behaviour of SMA systems. Results show the general thermo-mechanical behaviour of SMA dynamical systems and the obtained conclusions can be applied in distinct situations as in rotor-bearing systems.

• Coupled systems mechanics
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• v.4 no.3
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• pp.251-262
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• 2015

The current paper aims at investigating the nonlinear dynamical behaviour of an electrically actuated microcantilever. The microcantilever is excited by a combination of AC and DC voltages. The nonlinear equation of motion of the microcantilever is obtained by means of force and moment balances. A high-dimensional Galerkin scheme is then applied to reduce the equation of motion to a discrete model. A numerical technique, based on the pseudo-arclength continuation method, is used to solve the discretized model. The electrostatic deflection of the microcantilever and static pull-in instabilities, due to the DC voltage, are analyzed by plotting the so-called DC voltage-deflection curves. At the simultaneous presence of the DC and AC voltages, the nonlinear dynamical behaviour of the microcantilever is analyzed by plotting frequency-response and force-response curves.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.231-242
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• 2004

The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied: constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like ‘Coloured noise’.

• East Asian mathematical journal
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• v.27 no.5
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• pp.521-525
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• 2011

We use a weaker version of the celebrated Newton-Kantorovich theorem [3] reported by us in [1] to find solutions of discrete dynamical systems involving operators with chaotic behavior. Our results are obtained by extending the application of the shadowing lemma [4], and are given under the same computational cost as before [4]-[6].

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.721-741
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• 2011

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.753-757
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• 1994

In control system design, whether the various subsystems are in discrete time or continuous time, the state space is usually regarded as a continuum. However, when the system is implemented, some subsystems may have a state space which is a subset of finite computer arithmetic. This is an important concern if a subsystem has chaotic behaviour, because it is theoretically possible for rich and varied motions in a continuum to collapse to trivial and degenerate behaviour in a finite and discrete state space [5]. This paper discusses new ways to describe these effects and reports on computer experiments which document and illustrate such collapsing behaviour.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.465-498
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• 2011

Concrete structures are generally cracked in flexural tension at working loads. Concrete beams with asymmetric section details and crack patterns exhibit different flexural rigidity depending upon the sense of the applied flexural moment. In this paper, three different models, having the same natural period, of such SDOF bilinear dynamical systems have been proposed. The Model-I and Model-II have constant damping coefficient, but the latter is characterized by two stiffness coefficients depending upon the sense of vibration amplitude. The Model-III, additionally, has two damping coefficients as well. In this paper, the dynamical response of Model-III to sinusoidal loading has been investigated and compared with that of Model-II studied earlier. It has been found that Model-III exhibits regular and irregular sub-harmonics, jump phenomena and strong sensitivity to initial conditions, forcing frequency, system period as well as the sense of peak sinusoidal force. The constant sustained load has been found to affect the natural period of the dynamical system. The predictions of Model-I have been compared with those of the approximate linear model adopted in present practice. The behaviour exhibited by different models of the SDOF cracked elastic concrete structures under working loads and the theoretical and practical implications of the approach followed have been critically evaluated.

• Wind and Structures
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• v.8 no.5
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• pp.373-388
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• 2005

Quasi-steady approaches have been often adopted to model wind forces on moving cylinders in cross-flow and to study instability conditions of rigid cylinders supported by visco-elastic devices. Recently, much attention has been devoted to the experimental study of inclined and/or yawed circular cylinders detecting dynamical phenomena such as galloping-like instability, but, at the present state-of-the-art, no mathematical model is able to recognize or predict satisfactorily this behaviour. The present paper presents a generalization of the quasi-steady approach for the definition of the flow-induced forces on yawed and inclined circular cylinders. The proposed model is able to replicate experimental behaviour and to predict the galloping instability observed during a series of recent wind-tunnel tests.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.613-621
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• 2001

In this paper we show that if a dynamical system $\phi$ has bishadowing and cyclically bishadowing properties on the chain recurrent set CR($\phi$) then all nearby continuous perturbations of $\phi$ behave chaotically on a neighborhood of each chain component of $\phi$ wheneer it has a fixed point. This is a generalization of the results obtained by Diamond et al.([3]).

• Proceedings of the IEEK Conference
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• 2000.11d
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• pp.81-84
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• 2000

Cellular automata are discrete dynamical systems whose behaviour is completely specified in terms of a local relation. If cellular automata convergence to fixed points, then it can be used to image processing. From the generalized Potts automata point of view, we propose in this paper a cellular automata technique for reducing image noise. To minimize blurring effect, an algorithm based on neighborhood median computation is Preferred. Experimental results are reported.