Panagiotis Alevras

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.

NUMERICAL INVESTIGATION OF THE PARAMETRIC PENDULUM UNDER FILTERED RANDOM PHASE EXCITATION

The parametrically excited pendulum is a highly nonlinear system which has been thoroughly studied regarding the responses stability and the fundamental types of motion that could be established. The rotating potential of a pendulum having its suspension point ver- tically excited was numerically identified and the appropriate excitation characteristics were presented. In this paper, the excitation is modeled using the random phase modulation and the rotational motion is sought. The resulting stochastic system is analyzed by using a nu- merical Path Integration (PI) method solving the Chapman-Kolmogorov equation to construct parameter space plots. The Probability Density Function (PDF) is computed and the rotational regions are identified as well as the effect of noise intensity onto them. Previous studies have shown that for small values of noise intensity the stochastic response resembles the deterministic one. However numerical simulations showed that with increasing noise intensity the regions of rotational motion become narrower. In order to improve the systems response a linear single- degree-of-freedom (SDOF) system is intercepted to filter the noisy excitation, forming a base excited SDOF system acting on the pendulum suspension point. The interaction between the moving pendulum mass and the SDOF filter is investigated with the goal being for the former to establish rotational motion.

Energy harvesting from torsional vibrations using a nonlinear oscillator

Harvesting ambient energy in a variety of systems and applications is a relatively recent trend, often referred to as Energy Harvesting. This can be typically achieved by harvesting energy (that would otherwise get wasted) through a physical process aiming to convert energy amounts to useful electrical energy. The harvested energy can be thermal, solar, wind, wave or kinetic energy, with the last class mainly referring to harvesting energy from vibrating components or structures. More often these oscillations are error states from the systems’ ideal function and through harvesting this potentially wasted energy could be reclaimed and become useful. Regardless of the generally low power output of the devices designed to harvest energy from vibrations, their use remains an attractive concept, which is mostly attributed to the growing use of modern electronic devices that exploit the low power requirements of semi-conductors. Energy Harvesting applications are often met in situations where a network of essential electronic devices, such as sensors in Structural Health Monitoring or bio-implantable devices, becomes hardly accessible. Harvesting ambient vibrations to power up these devices offers the option to utilize wireless sensors rendering these systems autonomous. Typical cases of systems, where ambient vibrations are ubiquitous are met in automotive and aerospace applications. Besides their potentially adverse impact, the energy carried by vibrating parts could be harvested, such that wireless sensors are powered. In this paper, a concept for harvesting torsional vibrations is proposed, based on a concept that employs magnetic levitation to establish a nonlinear Energy Harvester. Experience has shown that linear harvesters require resonant response to operate, often leading to low performance of the device when the excitation frequency deviates from resonance conditions. This is why harvesters with essential nonlinearity are preferred, since they are able to demonstrate high response levels over wider frequency regions. Herein, the conducted study aims to demonstrate the functionality of this concept for torsional systems. A mathematical model of the coupled nonlinear electromechanical system is established, seeking preliminary estimates of the harvested power. The compelling attribute of this system lies in the dependency of its linear natural frequency on the excitation frequency, which is found to cause multiple response peaks in the corresponding frequency spectra. Moreover, the selection of the static equilibrium of the levitating magnet is found to greatly influence the system’s response.

Energy Response Probability Density Function of a Rotating Parametric Pendulum

The rich dynamic response of a parametric pendulum to a harmonic excitation acting on its pivot point has been shown to include among others rotational trajectories. On this foundation, the potential of developing a wave energy converter (WEC) has been suggested exploiting the bobbing motion of waves as the necessary excitation for the pendulum to establish rotary motion. Quite often in the study of dynamical systems, the random nature of environmental inputs cannot be ignored rendering deterministic analyses inadequate. Thereafter, stochastic analysis of these systems has to be employed. Considering a pendulum structure floating on ocean waves, the need for a stochastic frame is raised due to the strong randomness dictating the motion of waves. In this paper, the probability density function of the energy transferred to the pendulum is calculated using a path integration (PI) algorithm. Subsequently, this information is utilized to evaluate the probability of the pendulum to lay in a rotational regime.