Miodrag Zukovic

Chaos in Non-ideal Mechanical System with Clearance

In this paper a non-ideal mechanical system with clearance is considered. The mechanical model of the system is an oscillator connected with an unbalanced motor. Due to the existence of clearance the connecting force between motor and the fixed part of the system is discontinuous but linear. The mathematical model of the system is represented by two coupled second-order differential equations. The transient and steady-state motion and also the stability of the system are analyzed. The Sommerfeld effect is detected. For certain values of the system parameters the motion is chaotic. This is caused by the period doubling bifurcation. The existence of chaos is proved with maximal Lyapunov exponent. A new chaos control method based on the known energy analysis is introduced and the chaotic motion is transformed into a periodic one.

Chaotic Responses in a Stable Duffing System of Non-ideal Type

In this paper the dynamics of a non-linear system with non-ideal excitation are studied. An unbalanced motor with a strong non-linear structure is considered. The excitation is of non-ideal type. The model is described with a system of two coupled strong non-linear differential equations. The steady state motions and their stability is studied applying the asymptotic methods. The existence of the Sommerfeld effect in such non-linear non-idealy excited system is proved. For certain values of system parameters chaotic motion appears. The chaos is realized through period doubling bifurcation. The results of numerical simulation are plotted and the Lyapunov exponents are calculated. The Pyragas method for control of chaotic motion is applied. The parameter values for transforming the chaos into periodical motion are obtained.

Non-ideal mechanical system with an oscillator with rational nonlinearity

In this paper the generalized form of a non-ideal system which contains a pure nonlinear oscillator and a non-ideal energy source is studied. In the non-ideal oscillator-motor system there is an interaction between the motions of the oscillator and those of the motor, as the motor has an influence on the oscillator and vice versa. The mathematical model of the system is represented with two coupled nonlinear differential equations. The averaging method for solving these differential equations is based on the application of the Ateb function, which is the exact solution of the pure nonlinear oscillator. Using the obtained approximate solution, the resonant motion of the system is considered. Significant attention is paid to the steady-state motion and to the Sommerfeld effect. The influence of the order of nonlinearity on the dynamics of the nonideal system is evident. In the paper the procedure for determination of the parameters for suppression of the Sommerfeld effect of the non-ideal system is also given.

Mixed-mode dynamics of certain bistable oscillators: behavioural mapping, approximations for motion and links with van der Pol oscillators

This study is concerned with a new generalized mathematical model for single degree-of-freedom bistable oscillators with harmonic excitation of low-frequency, linear viscous damping and a restoring force that contains a negative linear term and a positive nonlinear term which is a power-form function of the generalized coordinate. Comprehensive numerical mapping of the range of bifurcatory behaviour shows that such non-autonomous systems can experience mixed-mode oscillations, including bursting oscillations (fast flow oscillations around the outer curves of a slow flow), and relaxation oscillations like a classical (autonomous) van der Pol oscillator. After studying the global system dynamics the focus of the investigations is on cubic oscillators of this type. Approximate techniques are presented to quantify their response, i.e. to determine approximations for both the slow and fast flows. In addition, a clear analogy between the behaviour of two archetypical oscillators—the non-autonomous bistable oscillator operating at low frequency and the strongly damped autonomous van der Pol oscillator—is established for the first time.

Two Degree-of-Freedom Oscillator Coupled to a Non-ideal Source

In this chapter the two degree-of-freedom structure excited with a non-ideal source is considered. The model corresponds to real energy harvester system (Felix et al. 2009), centrifugal vibration machine (Dantas and Balthazar 2006), tuned liquid column damper mounted on a structural frame (Felix et al. 2005a), portal frame (Felix et al. 2013) and portal frame foundation type shear building (Felix et al. 2005b), rotor-structure system which moves in-plane (Quinn 1997), etc.

On the oscillation death phenomenon in a double pendulum system with autoparametric interaction

This study is concerned with autoparametric interaction in a four degree of freedom damped mechanical system consisting of two identical pendula fitted onto a horizontal massive rod which can oscillate vertically and rotationally. One pendulum is harmonically excited. The equations of motion indicate that autoparametric interaction is possible by means of typical external and internal resonance conditions involving the system natural frequencies and excitation frequency. An intriguing phenomenon is demonstrated when the unforced pendulum is decoupled and no energy goes into it, as a result of which it stops oscillating. Numerical simulations are carried out to determine when and why this phenomenon occurs for a different excitation magnitude as well as for zero and non-zero initial conditions of the unforced pendulum.

Characterisation of tree vibrations based on the model of orthogonal oscillations

This study presents quantitative and qualitative insights into the analysis of data obtained by tracking the motion of reflective markers arranged along the trunk of a pole-like potted tree, which was recorded by a state-of-the-art infrared motion-tracking system. The experimental results showed in-plane damped trajectories of the markers with lateral displacements, i.e. out-of-plane vibrations of the tree under consideration. To explain such response and to determine the corresponding oscillatory characteristics, a completely new and original utilisation of the recorded in-plane damped trajectories is presented. The quantitative insight gained is based on the mechanical model that consists of two orthogonal springs and dampers placed in the plane where the motion takes place, and it is then directed towards the determination of the characteristics of the related orthogonal oscillations: two natural frequencies, the position of the principal axes to which they correspond, and two damping ratios. The qualitative insight gained involves analysing the shape and narrowness of the trajectory to assess how close-valued two natural frequencies are, and how small the overall damping is. The quantitative and qualitative methodologies presented herein are seen as beneficial for arboriculture, forestry and botany, but given the fact that orthogonal oscillations appears in many natural and engineering systems, they are also expected to be useful for specialists in other fields of science and engineering as well.

Instead Conclusions: Emergent Problems in Nowadays and Future Investigation

Nowadays the majority of engineering systems have, at least, one electromechanical sub-system in their composition. These systems fall into three groups: the conventional electromechanical systems , the micro electromechanical systems and the nano electromechanical systems . Note that micro and nano electromechanical system technologies are still in their infancies, with global research and development actively under way. Often many practical electromechanical devices are discussed in the context of simple lumped mechanical masses, electric and magnetic circuits.

Linear Oscillator and a Non-ideal Energy Source

In the non-ideal oscillator-motor system there is an interaction between the motions of the oscillator and of the motor: the motor has an influence on the oscillator and vice versa the motion of the oscillator affects the motion of the motor.

Non-ideal Energy Harvester with Piezoelectric Coupling

Advances in silicon electronics and MEMS technology reduced significantly the power consumption of devices such as wireless sensors, portable and wearable electronics. A large number of the locations where those devices are used are either remote or inaccessible. Most of these low-power devices rely heavily on electromechanical batteries as a source of power. However, batteries have a limited life span and number of recharging cycles. They are also constantly in need for recharging or replacement. For application such as wireless sensing and remote monitoring, battery replacement or recharging can be expensive, challenging or impossible in some cases. Another serious problem with batteries is the fact that they contain hazardous chemical materials that are harmful to the environment if not recycled.