The dramatic reduction in power consumption of current integrated circuits has evoked great research interests in harvesting ambient energy, such as vibrations, as a potential power supply for electronic devices to avoid battery replacement. Currently, most vibration-based energy harvesters are designed as linear resonators to achieve optimal performance by matching their resonance frequencies with the ambient excitation frequencies a priori. However, a slight shift of the excitation frequency will cause a dramatic reduction in performance. Unfortunately, in the vast majority of practical cases, the ambient vibrations are frequency-varying or totally random with energy distributed over a wide frequency spectrum. Hence, developing techniques to increase the bandwidth of vibration-based energy harvesters has become the next important problem in energy harvesting. This paper reviews the advances made in the past few years on this issue. The broadband vibration-based energy harvesting solutions, covering resonance tuning, 2 multimodal energy harvesting, frequency up-conversion and techniques exploiting nonlinear oscillations, are summarized in detail with regard to their merits and applicability in different circumstances.

Energy-harvesting device with mechanical frequency-up conversion mechanism for increased power efficiency and wideband operation Applied Physics Letters 96, 111906 (2010); 10.1063/1.3360219 Low-frequency and wideband vibration energy harvester with flexible frame and interdigital structure AIP Advances 5, 047151 (2015); We present a non-resonant, frequency up-converted electromagnetic energy harvester that generates significant power from human-body-induced vibration, e.g., hand-shaking. Upon excitation, a freely movable non-magnetic ball within a cylinder periodically hits two magnets suspended on two helical compression springs located at either ends of the cylinder, allowing those to vibrate with higher frequencies. The device parameters have been designed based on the characteristics of human hand-shaking vibration. A prototype has been developed and tested both by vibration exciter (for non-resonance test) and by manual hand-shaking. The fabricated device generated 110 lW average power with 15.4 lW cm À3 average power density, while the energy harvester was mounted on a smart phone and was hand-shaken, indicating its ability in powering portable hand-held smart devices from low frequency (<5 Hz) vibrations.

Last decade has seen growing research interest in vibration energy harvesting using piezoelectric materials. When developing piezoelectric energy harvesting systems, it is advantageous to establish certain analytical or numerical model to predict the system performance. In the last few years, researchers from mechanical engineering established distributed models for energy harvester but simplified the energy harvesting circuit in the analytical derivation. While, researchers from electrical engineering concerned the modeling of practical energy harvesting circuit but tended to simplify the structural and mechanical conditions. The challenges for accurate modeling of such electromechanical coupling systems remain when complicated mechanical conditions and practical energy harvesting circuit are considered in system design. In this article, the aforementioned problem is addressed by employing an equivalent circuit model, which bridges structural modeling and electrical simulation. First, the parameters in the equivalent circuit model are identified from theoretical analysis and finite element analysis for simple and complex structures, respectively. Subsequently, the equivalent circuit model considering multiple modes of the system is established and simulated in the SPICE software. Two validation examples are given to verify the accuracy of the proposed method, and one further example illustrates its capability of dealing with complicated structures and non-linear circuits.

This letter presents a comparative study of different tip cross-sections for small scale wind energy harvesting based on galloping phenomenon. A prototype device is fabricated with a piezoelectric cantilever and a tip body with various cross-section profiles (square, rectangle, triangle, and D-shape) and tested in a wind tunnel. Experimental results demonstrate the superiority of the square-sectioned tip for the low cut-in wind speed of 2.5 m/s and the high peak power of 8.4 mW. An analytical model is established and verified by the experimental results. It is recommended that the square section should be used for small wind galloping energy harvesters.

The classical limit of quantum mechanics is usually discussed in terms of Ehrenfest*s theorem, which states that, -for a sufficiently narrow wave packet, the mean position in the quantum state will follow a classical trajectory. We show, however, that that criterion is neither necessary nor sufficient to identify the classical regime. Generally speaking, the classical limit of a quantum state is not a single classical orbit, but an ensemble of orbits. The failure of the mean position in the quantum state to follow a classical orbit often merely reflects the fact that the centroid of a classical ensemble need not follow a classical orbit. A quantum state may behave essentially classically, even when Ehrenfest's theorem does not apply, if it yields agreement with the results calculated from the Liouville equation for a classical ensemble. We illustrate this fact with examples that include both regular and chaotic classical motions.PACS number(s): 03.65.Bz, 03.6S. Sq, 05.45. +b