Abstract
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.
Highlights
Recent major progress has been made in Micro-Electro-Mechanical Systems (MEMS) technology, which has led to the development of various sensors and actuators on the one hand, and a vast reduction in the size and power consumption of Complementary Metal-Oxide-Semiconductor (CMOS)
The results indicate that, at relatively small excitation amplitudes, the system response involves a typical Duffing resonance, which is a common behavior of cantilever beams under large lateral vibrations due to the presence of curvature and inertia nonlinearities
As the excitation amplitude is increased, a supercritical Hopf bifurcation occurs on the high-energy branch of the response curve and stable limit cycles are created around the unstable nodes in a narrow frequency band
Summary
Recent major progress has been made in Micro-Electro-Mechanical Systems (MEMS) technology, which has led to the development of various sensors and actuators on the one hand, and a vast reduction in the size and power consumption of Complementary Metal-Oxide-Semiconductor (CMOS). These properties arise from the structure and not the composition of the material itself, and have led to the evolution of a new generation of micro-scale devices [40,41] The application of these types of materials in energy harvesting from electromagnetic Radio Frequency (RF) waves has been investigated by many researchers in this area [42,43]. The nonlinear behavior of a piezoelectric harvester composed of a cantilevered unimorph beam with an excitation the activation of a electromagnetic superharmonic resonance, ineffective used in attached through tip magnet under an force at they bothremain primaryand when second-order environments in which the second harmonic of the excitation electromechanically dominates. First-mode resonance frequency, the governing equations are solved by implementing the perturbation
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