Optimization of an Impact-Based Frequency Up-Converted Piezoelectric Vibration Energy Harvester for Wearable Devices.

This work presents a novel development of the impact-based mechanism for piezoelectric vibration energy harvesters. More precisely, the effect of an impacting mass on a cantilever piezoelectric transducer is studied both in terms of the tip mass value attached to the cantilever and impact position to find an optimal condition for power extraction. At first, the study is carried out by means of parametric analyses at varying tip mass and impact position on a unimorph MEMS cantilever, and a suitable physical interpretation of the associated electromechanical response is given. The effect of multiple impacts is also considered. From the analysis, it emerges that the most effective configuration, in terms of power output, is an impact at the cantilever tip without a tip mass. By changing the value of the tip mass, a sub-optimal impact position along the beam axis can also be identified. Moreover, the effect of a tip mass is deleterious on the power performance, contrary to the well-known case of a resonant energy harvester. A mesoscale prototype with a bimorph transducer is fabricated and tested to validate the computational models. The comparison shows a good agreement between numerical models and the experiments. The proposed approach is promising in the field of consumer electronics, such as wearable devices, in which the impact-based device moves at the frequencies of human movement and is much lower than those of microsystems.

Piezoelectric Energy Harvesting from Low-Frequency Vibrations Based on Magnetic Plucking and Indirect Impacts.

This work proposes a mono-axial piezoelectric energy harvester based on the innovative combination of magnetic plucking and indirect impacts, e.g., impacts happening on the package of the harvester. The harvester exploits a permanent magnet placed on a non-magnetic mass, free to move within a predefined bounded region located in front of a piezoelectric bimorph cantilever equipped with a magnet as the tip mass. When the harvester is subjected to a low-frequency external acceleration, the moving mass induces an abrupt deflection and release of the cantilever by means of magnetic coupling, followed by impacts of the same mass against the harvester package. The combined effect of magnetic plucking and indirect impacts induces a frequency up-conversion. A prototype has been designed, fabricated, fastened to the wrist of a person by means of a wristband, and experimentally tested for different motion levels. By setting the magnets in a repulsive configuration, after 50 s of consecutive impacts induced by shaking, an energy of 253.41 µJ has been stored: this value is seven times higher compared to the case of harvester subjected to indirect impacts only, i.e., without magnetic coupling. This confirms that the combination of magnetic plucking and indirect impacts triggers the effective scavenging of electrical energy even from low-frequency non-periodical mechanical movements, such as human motion, while preserving the reliability of piezoelectric components.

Wearable Ball-Impact Piezoelectric Multi-Converters for Low-Frequency Energy Harvesting from Human Motion.

Multi-converter piezoelectric harvesters based on mono-axial and bi-axial configurations are proposed. The harvesters exploit two and four piezoelectric converters (PCs) and adopt an impinging spherical steel ball to harvest electrical energy from human motion. When the harvester undergoes a shake, a tilt, or a combination of the two, the ball hits one PC, inducing an impact-based frequency-up conversion. Prototypes of the harvesters have been designed, fabricated, fastened to the wrist of a person by means of a wristband and watchband, and experimentally tested for different motion levels. The PCs of the harvesters have been fed to passive diode-based voltage-doubler rectifiers connected in parallel to a storage capacitor, Cs = 220 nF. By employing the mono-axial harvester, after 8.5 s of consecutive impacts induced by rotations of the wrist, a voltage vcs(t) of 40.2 V across the capacitor was obtained, which corresponded to a stored energy of 178 µJ. By employing the bi-axial harvester, the peak instantaneous power provided by the PCs to an optimal resistive load was 1.58 mW, with an average power of 9.65 µW over 0.7 s. The proposed harvesters are suitable to scavenge electrical energy from low-frequency nonperiodical mechanical movements, such as human motion.

An Autoencoder-Based Deep Learning Approach for Load Identification in Structural Dynamics.

In civil engineering, different machine learning algorithms have been adopted to process the huge amount of data continuously acquired through sensor networks and solve inverse problems. Challenging issues linked to structural health monitoring or load identification are currently related to big data, consisting of structural vibration recordings shaped as a multivariate time series. Any algorithm should therefore allow an effective dimensionality reduction, retaining the informative content of data and inferring correlations within and across the time series. Within this framework, we propose a time series AutoEncoder (AE) employing inception modules and residual learning for the encoding and the decoding parts, and an extremely reduced latent representation specifically tailored to tackle load identification tasks. We discuss the choice of the dimensionality of this latent representation, considering the sources of variability in the recordings and the inverse-forward nature of the AE. To help setting the aforementioned dimensionality, the false nearest neighbor heuristics is also exploited. The reported numerical results, related to shear buildings excited by dynamic loadings, highlight the signal reconstruction capacity of the proposed AE, and the capability to accomplish the load identification task.

PMUTs Arrays for Structural Health Monitoring of Bolted-Joints.

Micro-electro-mechanical systems (MEMS) have enabled new techniques for the miniaturization of sensors suitable for Structural Health Monitoring (SHM) applications. In this study, MEMS-based sensors, specifically Piezoelectric Micromachined Ultrasonic Transducers (PMUT), are used to evaluate and monitor the pre-tensioning of a bolted joint structural system. For bolted joints to function properly, it is essential to maintain a suitable level of pre-tensioning. In this work, an array of PMUTs attached to the head and to the end of a bolt, serve as transmitter and receiver, respectively, in a pitch-catch Ultrasonic Testing (UT) scenario. The primary objective is to detect the Change in Time of Flight (CTOF) of the acoustic wave generated by the PMUT array and propagating along the bolt's axis between a non-loaded bolt and a bolt in service. To model the pre-tensioning of bolted joints and the transmission of the acoustic wave to and from a group of PMUTs through the bolt, a set of numerical models is created. The CTOF is found to be linearly related to the amount of pre-tensioning. The numerical model is validated through comparisons with the results of a preliminary experimental campaign.

An Experimental and Numerical Study on Glass Frit Wafer-to-Wafer Bonding.

A thermo-mechanical wafer-to-wafer bonding process is studied through experiments on the glass frit material and thermo-mechanical numerical simulations to evaluate the effect of the residual stresses on the wafer warpage. To experimentally characterize the material, confocal laser profilometry and scanning electron microscopy for surface observation, energy dispersive X-ray spectroscopy for microstructural investigation, and nanoindentation and die shear tests for the evaluation of mechanical properties are used. An average effective Young's modulus of 86.5 ± 9.5 GPa, a Poisson's ratio of 0.19 ± 0.02, and a hardness of 5.26 ± 0.8 GPa were measured through nanoindentation for the glass frit material. The lowest nominal shear strength ranged 1.13 ÷ 1.58 MPa in the strain rate interval to 0.33 ÷ 4.99 × 10-3 s-1. To validate the thermo-mechanical model, numerical results are compared with experimental measurements of the out-of-plane displacements at the wafer surface (i.e., warpage), showing acceptable agreement.

Reinforcement learning optimisation for graded metamaterial design using a physical-based constraint on the state representation and action space.

The energy harvesting capability of a graded metamaterial is maximised via reinforcement learning (RL) under realistic excitations at the microscale. The metamaterial consists of a waveguide with a set of beam-like resonators of variable length, with piezoelectric patches, attached to it. The piezo-mechanical system is modelled through equivalent lumped parameters determined via a general impedance analysis. Realistic conditions are mimicked by considering either magnetic loading or random excitations, the latter scenario requiring the enhancement of the harvesting capability for a class of forcing terms with similar but different frequency content. The RL-based optimisation is empowered by using the physical understanding of wave propagation in a such local resonance system to constrain the state representation and the action space. The procedure outcomes are compared against grading rules optimised through genetic algorithms. While genetic algorithms are more effective in the deterministic setting featuring the application of magnetic loading, the proposed RL-based proves superior in the inherently stochastic setting of the random excitation scenario.

Physically-based reduced order modelling of a uni-axial polysilicon MEMS accelerometer.

In this paper, the mechanical response of a commercial off-the-shelf, uni-axial polysilicon MEMS accelerometer subject to drops is numerically investigated. To speed up the calculations, a simplified physically-based (beams and plate), two degrees of freedom model of the movable parts of the sensor is adopted. The capability and the accuracy of the model are assessed against three-dimensional finite element simulations, and against outcomes of experiments on instrumented samples. It is shown that the reduced order model provides accurate outcomes as for the system dynamics. To also get rather accurate results in terms of stress fields within regions that are prone to fail upon high-g shocks, a correction factor is proposed by accounting for the local stress amplification induced by re-entrant corners.

Efficient Modeling and Simulation of PMUT Arrays in Various Ambients.

This paper presents a numerical reduced-order modeling (ROM) approach for complex multi-layered arrays of piezoelectric micromachined ultrasonic transducers (PMUTs). The numerical modeling technique adopted to generate an array of PMUTs consisting of a considerable number of transducers allows for a large reduction in computational cost without reducing accuracy. The modeling idea is based on coupling shell elements applied to the PMUT structural layers with 3D-solid elements applied to the piezoelectric layer. A set of eigenfrequency and frequency domain analyses are presented considering a single ROM of a PMUT performing in different ambients and the performing central frequencies are obtained for every considered scenario. A unique arrangement of 228 PMUTs is presented and tested for its ability to transmit and receive acoustic waves. The operating frequency band of the array and the level of interference and cross-talk among different PMUTs in the near field are estimated. Finally, the results from a preliminary experimental test performed to analyze the acoustic abilities of an 8 × 8 array of PMUTs are presented. A corresponding numerical model is created and the obtained results matched the experimental data, leading to a validation of the modeling technique proposed in this work.

Two-scale simulation of drop-induced failure of polysilicon MEMS sensors.

In this paper, an industrially-oriented two-scale approach is provided to model the drop-induced brittle failure of polysilicon MEMS sensors. The two length-scales here investigated are the package (macroscopic) and the sensor (mesoscopic) ones. Issues related to the polysilicon morphology at the micro-scale are disregarded; an upscaled homogenized constitutive law, able to describe the brittle cracking of silicon, is instead adopted at the meso-scale. The two-scale approach is validated against full three-scale Monte-Carlo simulations, which allow for stochastic effects linked to the microstructural properties of polysilicon. Focusing on inertial MEMS sensors exposed to drops, it is shown that the offered approach matches well the experimentally observed failure mechanisms.

A New Approach for the Control and Reduction of Warpage and Residual Stresses in Bonded Wafer.

A geometrical modification on silicon wafers before the bonding process, aimed to decrease (1) the residual stress caused by glass frit bonding, is proposed. Finite element modeling showed that (2) by introducing this modification, the wafer out-of-plane deflection was decreased by 34%. Moreover, (3) fabricated wafers with the proposed geometrical feature demonstrated an improvement for the (4) warpage with respect to the plain wafers. A benefit for curvature variation and overall shape of the (5) bonded wafers was also observed.

On the Effects of Package on the PMUTs Performances-Multiphysics Model and Frequency Analyses.

This paper deals with a multiphysics numerical modelling via finite element method (FEM) of an air-coupled array piezoelectric micromachined ultrasonic transducers (PMUTs). The proposed numerical model is fully 3D with the following features: the presence of the fabrication induced residual stresses, which determine a geometrically non-linear initial deformed configuration of the diaphragms and a remarkable shift of the fundamental frequency; the multiple coupling between different physics, namely electro-mechanical-coupling for the piezo-electric model, acoustic-structure interaction at the acoustic-structure interface and pressure acoustics in the surrounding air. The model takes into account the complete set of PMUTs belonging to the silicon die in a 4 x 4 array configuration and the protective package, as well. The results have been validated by experimental data, in terms of initial static pre-deflected configuration of the diaphragms and frequency response function of the PMUT. The numerical procedure was applied, to analyze different package configurations of the device, to study the influence of the holes on the acoustic transmission in terms of SPL and propagation pattern and consequently extract a set of design guidelines.

A design strategy to match the band gap of periodic and aperiodic metamaterials.

The focus of this paper is on elastic metamaterials characterised by the presence of wide sub-wavelength band gap. In most cases, such mechanical property is strictly connected to the periodic repetition of the unit cell. Nonetheless, the strict periodicity requirement could represent a drawback. In this paper, we present a design strategy for aperiodic elastic metamaterials in order to achieve the same performances as for the periodic counterparts. This is done by exploiting the concept of separation of modes for different building blocks, arranged in aperiodic fashion. A theoretical explanation is provided, as well as numerical simulations; the concept is validated by means of a set of experimental tests on prototypes that are realized via additive manufacturing.

Modeling Impact-induced Failure of Polysilicon MEMS: A Multi-scale Approach.

Failure of packaged polysilicon micro-electro-mechanical systems (MEMS) subjected to impacts involves phenomena occurring at several length-scales. In this paper we present a multi-scale finite element approach to properly allow for: (i) the propagation of stress waves inside the package; (ii) the dynamics of the whole MEMS; (iii) the spreading of micro-cracking in the failing part(s) of the sensor. Through Monte Carlo simulations, some effects of polysilicon micro-structure on the failure mode are elucidated.

3-D Design and Simulation of a Piezoelectric Micropump.

The objective of this paper is to carefully study the performances of a new piezoelectric micropump that could be used, e.g., for drug delivery or micro-cooling systems. The proposed micropump is characterized by silicon diaphragms, with a piezoelectric actuation at a 60 V input voltage, and by two passive valves for flow input and output. By means of a 3-D Finite Element (FE) model, the fluid dynamic response during different stages of the working cycle is investigated, together with the fluid-structure interaction. The maximum predicted outflow is 1.62 µL min - 1 , obtained at 10 Hz working frequency. The computational model enables the optimization of geometrical features, with the goal to improve the pumping efficiency: The outflow is increased until 2.5 µL min - 1 .

Low frequency 3D ultra-wide vibration attenuation via elastic metamaterial.

The design of innovative metamaterials with robust and reliable performances is attracting increasing interest in the scientific community because of their unique properties and for their unexplored potential. In particular, dynamical properties of periodic structures are widely studied specifically for their bandgap opening characteristic, which enables the design of structures with unprecedented dynamical behaviour. In the present work an ultra-wide three-dimensional bandgap is presented, with extremely low frequency range of operation. Numerical simulations and analytical models are proposed to prove the claimed properties, together with experiments carried out on a prototype built by means of additive manufacturing.

3D auxetic single material periodic structure with ultra-wide tunable bandgap.

The design and the combination of innovative metamaterials are attracting increasing interest in the scientific community because of their unique properties that go beyond the ones of natural materials. In particular, auxetic materials and phononic crystals are widely studied for their negative Poisson's ratio and their bandgap opening properties, respectively. In this work, auxeticity and phononic crystals bandgap properties are properly combined to obtain a single phase periodic structure with a tridimensional wide tunable bandgap. When an external tensile load is applied to the structure, the auxetic unit cells change their configurations by exploiting the negative Poisson's ratio and this results in the tuning, either hardening or softening, of the frequencies of the modes limiting the 3D bandgap. Moreover, the expansion of the unit cell in all the directions, due to the auxeticity property, guarantees a fully 3D bandgap tunability of the proposed structure. Numerical simulations and analytical models are proposed to prove the claimed properties. The first experimental evidence of the tunability of a wide 3D bandgap is then shown thanks to the fabrication of a prototype by means of additive manufacturing.

Multi-scale Analysis of MEMS Sensors Subject to Drop Impacts.

The effect of accidental drops on MEMS sensors are examined within the frame-work of a multi-scale finite element approach. With specific reference to a polysilicon MEMSaccelerometer supported by a naked die, the analysis is decoupled into macro-scale (at dielength-scale) and meso-scale (at MEMS length-scale) simulations, accounting for the verysmall inertial contribution of the sensor to the overall dynamics of the device. Macro-scaleanalyses are adopted to get insights into the link between shock waves caused by the impactagainst a target surface and propagating inside the die, and the displacement/acceleration his-tories at the MEMS anchor points. Meso-scale analyses are adopted to detect the most stresseddetails of the sensor and to assess whether the impact can lead to possible localized failures.Numerical results show that the acceleration at sensor anchors cannot be considered an ob-jective indicator for drop severity. Instead, accurate analyses at sensor level are necessary toestablish how MEMS can fail because of drops.

Self-induced parametric amplification arising from nonlinear elastic coupling in a micromechanical resonating disk gyroscope.

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator, and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied, and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.