Static and Dynamic Analysis of a Bistable Frequency Up-Converter Piezoelectric Energy Harvester.

Using energy harvesting to convert ambient vibrations efficiently to electrical energy has become a worthy concept in recent years. Nevertheless, the low frequencies of the ambient vibrations cannot be effectively converted to power using traditional harvesters. Therefore, a frequency up-conversion harvester is presented to convert the low-frequency vibrations to high-frequency vibrations utilizing magnetic coupling. The presented harvester consists of a low-frequency beam (LFB) and a high-frequency beam (HFB) with identical tip magnets facing each other at the same polarity. The HFB, fully covered by a piezoelectric strip, is utilized for voltage generation. The dynamic behavior of the system and the corresponding generated voltage signal has been investigated by modeling the system as a two-degrees-of-freedom (2DOF) lumped-parameter model. A threshold distance of 15 mm that divides the system into a monostable regime with a weak magnetic coupling and a bistable regime with a strong magnetic coupling was revealed in the static analysis of the system. Hardening and softening behaviors were reported at the low frequency range for the mono and bistable regimes, respectively. In addition, a combined nonlinear hardening and softening behavior was captured for low frequencies at the threshold distance. Furthermore, a 100% increment was achieved in the generated voltage at the threshold compared to the monostable regime, and the maximum generated voltage was found to be in the bistable regime. The simulated results were validated experimentally. Moreover, the effect of the external resistance was investigated, and a 2 MΩ resistance was found to be optimal for maximizing the generated power. It was found that frequency up-converting based on magnetic nonlinearity can effectively scavenge energy from low-frequency external vibrations.

Voltage and Deflection Amplification via Double Resonance Excitation in a Cantilever Microstructure.

Cantilever electrostatically-actuated resonators show great promise in sensing and actuating applications. However, the electrostatic actuation suffers from high-voltage actuation requirements and high noise low-amplitude signal-outputs which limit its applications. Here, we introduce a mixed-frequency signal for a cantilever-based resonator that triggers its mechanical and electrical resonances simultaneously, to overcome these limitations. A single linear RLC circuit cannot completely capture the response of the resonator under double resonance excitation. Therefore, we develop a coupled mechanical and electrical mathematical linearized model at different operation frequencies and validate this model experimentally. The double-resonance excitation results in a 21 times amplification of the voltage across the resonator and 31 times amplitude amplification over classical excitation schemes. This intensive experimental study showed a great potential of double resonance excitation providing a high amplitude amplification and maintaining the linearity of the system when the parasitic capacitance is maintained low.

Tunable Resonators for Nonlinear Modal Interactions.

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

In-Plane MEMS Shallow Arch Beam for Mechanical Memory.

We demonstrate a memory device based on the nonlinear dynamics of an in-plane microelectromechanical systems (MEMS) clamped⁻clamped beam resonator, which is deliberately fabricated as a shallow arch. The arch beam is made of silicon, and is electrostatically actuated. The concept relies on the inherent quadratic nonlinearity originating from the arch curvature, which results in a softening behavior that creates hysteresis and co-existing states of motion. Since it is independent of the electrostatic force, this nonlinearity gives more flexibility in the operating conditions and allows for lower actuation voltages. Experimental results are generated through electrical characterization setup. Results are shown demonstrating the switching between the two vibrational states with the change of the direct current (DC) bias voltage, thereby proving the memory concept.

Multifrequency excitation of a clamped-clamped microbeam: Analytical and experimental investigation.

Using partial electrodes and a multifrequency electrical source, we present a large-bandwidth, large-amplitude clamped-clamped microbeam resonator excited near the higher order modes of vibration. We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation. The first-frequency source is swept around the first three modes of vibration, whereas the second source frequency remains fixed. New additive and subtractive resonances are demonstrated. We illustrated that by properly tuning the frequency and amplitude of the excitation force, the frequency bandwidth of the resonator is controlled. The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom. Using the Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device. A good agreement between the theoretical and experimental data are reported.

Theoretical prediction of experimental jump and pull-in dynamics in a MEMS sensor.

The present research study deals with an electrically actuated MEMS device. An experimental investigation is performed, via frequency sweeps in a neighbourhood of the first natural frequency. Resonant behavior is explored, with special attention devoted to jump and pull-in dynamics. A theoretical single degree-of-freedom spring-mass model is derived. Classical numerical simulations are observed to properly predict the main nonlinear features. Nevertheless, some discrepancies arise, which are particularly visible in the resonant branch. They mainly concern the practical range of existence of each attractor and the final outcome after its disappearance. These differences are likely due to disturbances, which are unavoidable in practice, but have not been included in the model. To take disturbances into account, in addition to the classical local investigations, we consider the global dynamics and explore the robustness of the obtained results by performing a dynamical integrity analysis. Our aim is that of developing an applicable confident estimate of the system response. Integrity profiles and integrity charts are built to detect the parameter range where reliability is practically strong and where it becomes weak. Integrity curves exactly follow the experimental data. They inform about the practical range of actuality. We discuss the combined use of integrity charts in the engineering design. Although we refer to a particular case-study, the approach is very general.