A mathematical model of fringe capacitance for a nano-based proximity sensor, which takes the presence of different resistivities into account, is developed. An analytical solution obtained for a rectangular-shape sensor with applying of Gauss, Conversation of Charge and Ohm laws into Laplace's equation 2 ( , , , ) = 0 gives the electric potential distribution by which the fringe capacitance in a 2D domain area can be calculated. The calculated capacitance evidently decreases drastically due to the fringe phenomena while object moves toward the polymeric sensor. The model also asserts that the change of capacitance is under a noticeable influence of sensor resistivity, particularly in the range of 10 3 -10 5 Ω.m, the initial capacitance varies from 0.045pF to 0.024 pF. The fabricated flexible nanocomposite sensors, Thermoplastic Polyurethane (TPU) reinforced by 1wt.% Carbon Nanotubes (CNTs) having resistivity 10P 5 P Ω.m, are capable of detecting presence of an external object in a wide range of distance and indicating remarkable correlation with the mathematical solution.Our proximity sensor fabrication is straightforward and relatively simple. An unprecedented detection range of measurement reveals promising ability of this proximity sensor in applications of motion analysis and healthcare systems.
The deliberate introduction of nonlinearities is widely used as an effective technique for the bandwidth broadening of conventional linear energy harvesting devices. This approach not only results in a more uniform behavior of the output power within a wider frequency band through bending the resonance response, but also contributes to energy harvesting from low-frequency excitations by activation of superharmonic resonances. This article investigates the nonlinear dynamics of a monostable piezoelectric harvester under a self-powered electromagnetic actuation. To this end, the governing nonlinear partial differential equations of the proposed harvester are order-reduced and solved by means of the perturbation method of multiple scales. The results indicate that, according to the excitation amplitude and load resistance, different responses can be distinguished at the primary resonance. The system behavior may involve the traditional bending of response curves, Hopf bifurcations, and instability regions. Furthermore, an order-two superharmonic resonance is observed, which is activated at lower excitations in comparison to order-three conventional resonances of the Duffing-type resonator. This secondary resonance makes it possible to extract considerable amounts of power at fractions of natural frequency, which is very beneficial in micro-electro-mechanical systems (MEMS)-based harvesters with generally high resonance frequencies. The extracted power in both primary and superharmonic resonances are analytically calculated, then verified by a numerical solution where a good agreement is observed between the results.
In this paper, coupled electromechanical behavior of a vibrational energy harvesting system composed of a unimorph piezoelectric laminated beam with a large attached tip mass is investigated. To achieve this goal, first the electromechanically coupled partial differential equations governing the lateral displacement and output voltage of the harvester are extracted through exploiting the Hamilton’s principle. Considering vibration damping due to mechanical to electrical energy conversion, a complex modal analysis is performed to extract the complex eigenfrequencies and eigenfunctions of the system. Furthermore, an exact analytical solution is presented for the system response to the harmonic base excitations, including output voltage and harvested power. To validate the analytical results, at the next step a finite element simulation is conducted through ABAQUS software. To perform a fully-coupled analysis which brings into account the effect of harvesting circuit, user subroutine User-defined Amplitude (UAMP) is utilized to calculate the voltage–current relation and impose the correct electrical charge on the electrodes in each step by monitoring the output voltage of the system at previous time increments. Results of both analytical and numerical simulations are compared for a Micro-Electro-Mechanical Systems (MEMS) harvester as a case study, where a very good agreement is observed between them.
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