Rotating potential of a stochastic parametric pendulum

The parametric pendulum is a fruitful dynamical system manifesting some of the most interesting phenomena of nonlinear dynamics, well-known to exhibit rather complex motion including period doubling, fold and pitchfork bifurcations, let alone the global bifurcations leading to chaotic or rotational motion. In this thesis, the potential of establishing rotational motion is studied considering the bobbing motion of ocean waves as the source of excitation of a oating pendulum. The challenge within this investigation lies on the fact that waves are random, as well as their observed low frequency, characteristics which pose a broader signi cance within the study of vibrating systems. Thus, a generic study is conducted with the parametric pendulum being excited by a narrow-band stochastic process and particularly, the random phase modulation is utilized. In order to explore the dynamics of the stochastic system, Markov-chain Monte-Calro simulations are performed to acquire a view on the in uence of randomness onto the parameter regions leading to rotational response. Furthermore, the Probability Density Function of the response is calculated, applying a numerical iterative scheme to solve the total probability law, exploiting the Chapman-Kolmogorov equation inherent to Markov processes. A special case of the studied structure undergoing impacts is considered to account for extreme weather conditions and nally, a novel design is investigated experimentally, aiming to set the ground for future development

A historical and critical analysis of the Australian law applicable to the payment of dividends

Historically, dividends be paid only out of profits. In 2010, the law was changed to allow payment of dividends if a company has a net asset position and the rights of creditors and shareholders are not harmed. This study examines the laws of dividends historically, internationally, currently and going forward

Vibration energy harvester for variable speed rotor applications using passively self-tuned beams

A vibration energy harvester is proposed for rotating systems based on transverse vibrations of an assembly of thin beams and electromagnetic interaction of a carried magnet with a coil of wire. The harvester is designed in a way such that centrifugal forces are utilized to tune the system’s natural frequency to the expected frequency of torsional vibrations. In fact, a novel combination of a tuning mass positioned at the beam’s support and an applied preload are introduced to establish a tuning mechanism that is capable of maintaining resonance along a wide frequency range. The device’s tuning can cover relatively high rotor speeds, overcoming previous limitations on the size and the physics of tuning via axial loads. Moreover, exact expressions of the beams’ mode shapes are taken into account to improve the accuracy of the proposed tuning mechanism. Numerical simulations of the device’s response are carried out for case studies corresponding to different frequency orders. It is shown that the system can maintain a flat power output across a wide range of operating speeds, effectively leading to purely broadband energy harvesting

Vibration energy harvester for variable speed rotor applications using passively self-tuned beams

A vibration energy harvester is proposed for rotating systems based on transverse vibrations of an assembly of thin beams and electromagnetic interaction of a carried magnet with a coil of wire. The harvester is designed in a way such that centrifugal forces are utilized to tune the system’s natural frequency to the expected frequency of torsional vibrations. In fact, a novel combination of a tuning mass positioned at the beam’s support and an applied preload are introduced to establish a tuning mechanism that is capable of maintaining resonance along a wide frequency range. The device’s tuning can cover relatively high rotor speeds, overcoming previous limitations on the size and the physics of tuning via axial loads. Moreover, exact expressions of the beams’ mode shapes are taken into account to improve the accuracy of the proposed tuning mechanism. Numerical simulations of the device’s response are carried out for case studies corresponding to different frequency orders. It is shown that the system can maintain a flat power output across a wide range of operating speeds, effectively leading to purely broadband energy harvesting

GPU computing for accelerating the numerical Path Integration approach

The paper discusses a novel approach of accelerating the numerical Path Integration method, used for generating a stationary joint response probability density function of a dynamic system subjected to a random excitation, by the GPU computing. The paper proposes the parallelization of nested loops technique and demonstrates the advantages of GPU computing. Two, three and four dimensional in space problems are investigated as a part of the pilot project and the achieved maximum accelerations are reported. Three degree-of-freedom system (6D) is approached by the Path Integration technique for the first time. The application of the proposed GPU methodology for problems of stochastic dynamics and reliability are discussed

Broadband energy harvesting from parametric vibrations of a class of nonlinear Mathieu systems

The nonlinear dynamics of Mathieu equation with the inclusion of a cubic stiffness component is considered for broadband vibration energy harvesting. Results of numerical integration are compared with the corresponding solution of a regular Duffing oscillator, which is widely used to model nonlinear energy harvesting. Use of Duffing oscillators has shown direct correspondence between the effective frequency range of the associated hysteretic phenomenon and the value of the nonlinearity coefficient. Due to that, a broadband energy harvester requires strong nonlinearity, especially for high frequencies of interest. This letter demonstrates that the effectiveness of parametrically-excited systems is not constrained by the same requirement. Based on this, it is suggested that parametrically-excited systems can be a robust means of broadband vibration harvesting

Torsional vibration energy harvesting through transverse vibrations of a passively tuned beam

The paper highlights the potential of harvesting vibration energy from mechanical systems in the form of electrical power to activate remote electronic devices. The principal idea is based upon the resonant response of a lightweight oscillator subjected to applied external excitation, coupled with an electrodynamic transducer (e.g. piezoelectric material, inductive coils). As far as the mechanical system is concerned, the aim is to maximize the harvested energy when an attachment vibrates with relatively high amplitudes. This means that the system natural frequency should be close to the expected dominant frequency of the applied (host) vibrations. However, in practice the dominant vibration frequency varies either within a limited range due to system uncertainties or across a large band due to the fundamental operation of the host structure, such as in rotational power transmission systems with speed variations. Recently, the introduction of nonlinearities has been proposed in order to compensate for small-scale frequency shifts. Nevertheless, in most cases one cannot fully bypass the necessary tuning effects, attributed to linear stiffness components in system dynamics. In this paper, a rotational vibration energy harvester is outlined, based upon a beam attachment, coupled with an electromagnetic transducer. The stiffening effect due to centrifugal action is utilized in order to passively tune the attachment to the dominant frequency of the rotational host structure. A reduced order model of the harvester is presented and its power extraction potential is assessed

Parametric resonance of a nonlinear energy harvester for torsional vibrations

Torsional vibrations occur commonly in power transmission systems and components. Often these vibrations are subject to transient frequency response, which are nevertheless dominated by fixed multiples of the main shaft speed (such as engine order vibrations). In this paper, a lightweight electromagnetic oscillator is proposed as an energy harvester from these torsional vibrations. A nonlinear spring is applied to tune the response of the oscillator to parametric excitations. Numerical analysis is carried out to predict output power of the harvester over a wide range of frequencies. The dynamics of the system offers the potential of increasing the effective operation band of the harvester, employing parametric resonance

Nonlinear energy harvesting from base excitation in automotive applications

Energy harvesting is an emerging technological field, aiming, among others, to harvest kinetic energy from mechanical oscillations and converting the same to useful electrical energy. Usually, the reclaimed energy is quite small, acquired by lightweight devices which can be positioned in confined spaces and do not significantly add to the system mass and inertia. This potential use is in line with the vehicular powertrain development principle of high output power- to-light weight ratio as this concept has progressively led to increasing vibratory energy. These devices would potentially supply a few mW of power, which can typically power automotive sensors, potentially reducing the ever-increasing vehicle wiring network. A multitude of such devices positioned strategically can recover some of the vibratory energy of a plethora of vibration phenomena. The paper outlines some of these phenomena and proposes the use of a magnetic translational harvester. A preliminary study based on an experimental set up and a devised non-linear model show good potential across a range of frequencies, typical of engine order vibration at engine idling condition. However, the potential exists for both the optimisation of the demonstrated observer and increased energy recovery for suitable location(s) in the powertrain system

Conceptual Design of a Floating Modular Energy Island for Energy Independency: A Case Study in Crete

This paper aims to investigate the development of a floating artificial sustainable energy island at a conceptual design level that would enhance the energy independence of islands focusing on a case study on the island of Crete. This paper provides a baseline assessment showing the immense potential of wind and solar energy in and around Crete integrating the third significant renewable energy source (RES) of ocean waves into the energy island. The selection of the best location for the floating offshore platforms that compose the energy island is addressed through exploiting the great potential of the above-mentioned RES, taking into consideration criteria with regard to several significant human activities. To this end, the concept of an innovative floating modular energy island (FMEI) that integrates different renewable energy resources is proposed; in addition, a case study that focuses on the energy independency of a big island illustrates the concept referring to the substitution of the local thermal power plants that are currently in operation in Crete with sustainable energy power. Although focused on the renewable energy resources around Crete, the work of this paper provides a basis for a systematic offshore renewable energy assessment as it proposes a new methodology that could be used anywhere around the globe