Mathematical analysis of the well known model of a piezoelectric energy harvester is presented. The harvester is designed as a cantilever Timoshenko beam with piezoelectric layers attached to its top and bottom faces. Thin, perfectly conductive electrodes are covering the top and bottom faces of the piezoelectric layers. These electrodes are connected to a resistive load. The model is governed by a system of three partial differential equations. The first two of them are the equations of the Timoshenko beam model and the third one represents Kirchhoff’s law for the electric circuit. All equations are coupled due to the piezoelectric effect. We represent the system as a single operator evolution equation in the Hilbert state space of the system. The dynamics generator of this evolution equation is a non-selfadjoint matrix differential operator with compact resolvent. The paper has two main results. Both results are explicit asymptotic formulas for eigenvalues of this operator, i.e., the modal analysis for the electrically loaded system is performed. The first set of the asymptotic formulas has remainder terms of the order O ( 1 n ) , where n is the number of an eigenvalue. These formulas are derived for the model with variable physical parameters. The second set of the asymptotic formulas has remainder terms of the order O ( 1 n 2 ) , and is derived for a less general model with constant parameters. This second set of formulas contains extra term depending on the electromechanical parameters of the model. It is shown that the spectrum asymptotically splits into two disjoint subsets, which we call the α -branch eigenvalues and the θ -branch eigenvalues. These eigenvalues being multiplied by “i” produce the set of the vibrational modes of the system. The α -branch vibrational modes are asymptotically located on certain vertical line in the left half of the complex plane and the θ -branch is asymptotically close to the imaginary axis. By having such spectral and asymptotic results, one can derive the asymptotic representation for the mode shapes and for voltage output. Asymptotics of vibrational modes and mode shapes is instrumental in the analysis of control problems for the harvester.
more »
« less
Multiple-Scale Analysis of a Tunable Bi-Stable Piezoelectric Energy Harvester
Abstract This paper presents the theoretical modeling and multiple-scale analysis of a novel piezoelectric energy harvester composed of a metal cantilever beam, piezoelectric films, and an axial preload spring at the moveable end. The harvester experiences mono- and bi-stable regimes as the stiffness of preload spring increases. The governing equations are derived with two high-order coupling terms induced by the axial motion. The literature shows that these high-order coupling terms lead to tedious calculations in the stability analysis of solutions. This work introduces an analytical strategy and the implementation of the multiple-scale method for the harvester in either the mono- or bi-stable status. Numerical simulations are performed to verify the analytical solutions. The influence of the electrical resistance, excitation level, and the spring pre-deformation on the voltage outputs and dynamics are investigated. The spring pre-deformation has a slight influence on the energy harvesting performance of the mono-stable system, but a large effect on that of the bi-stable system.
more »
« less
- Award ID(s):
- 1935951
- NSF-PAR ID:
- 10282543
- Date Published:
- Journal Name:
- ASME Letters in Dynamic Systems and Control
- Volume:
- 1
- Issue:
- 2
- ISSN:
- 2689-6117
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Thin-walled corrugated tubes that have a bending multistability, such as the bendy straw, allow for variable orientations over the tube length. Compared to the long history of corrugated tubes in practical applications, the mechanics of the bending stability and how it is affected by the cross sections and other geometric parameters remain unknown. To explore the geometry-driven bending stabilities, we used several tools, including a reduced-order simulation package, a simplified linkage model, and physical prototypes. We found the bending stability of a circular two-unit corrugated tube is dependent on the longitudinal geometry and the stiffness of the crease lines that connect separate frusta. Thinner shells, steeper cones, and weaker creases are required to achieve bending bi-stability. We then explored how the bending stability changes as the cross section becomes elongated or distorted with concavity. We found the bending bi-stability is favored by deep and convex cross sections, while wider cross sections with a large concavity remain mono-stable. The different geometries influence the amounts of stretching and bending energy associated with bending the tube. The stretching energy has a bi-stable profile and can allow for a stable bent configuration, but it is counteracted by the bending energy which increases monotonically. The findings from this work can enable informed design of corrugated tube systems with desired bending stability behavior.more » « less
-
null (Ed.)Abstract Controlling and manipulating elastic/acoustic waves via artificially structured metamaterials, phononic crystals, and metasurfaces have gained an increasing research interest in the last decades. Unlike others, a metasurface is a single layer in the host medium with an array of subwavelength-scaled patterns introducing an abrupt phase shift in the wave propagation path. In this study, an elastic metasurface composed of an array of slender beam resonators is proposed to control the elastic wavefront of low-frequency flexural waves. The phase gradient based on Snell’s law is achieved by tailoring the thickness of thin beam resonators connecting two elastic host media. Through analytical and numerical models, the phase-modulated metasurfaces are designed and verified to accomplish three dynamic wave functions, namely, deflection, non-paraxial propagation, and focusing. An oblique incident wave is also demonstrated to show the versatility of the proposed design for focusing of wave energy incident from multiple directions. Experimentally measured focusing metasurface has nearly three times wave amplification at the designed focal point which validates the design and theoretical models. Furthermore, the focusing metasurface is exploited for low-frequency energy harvesting and the piezoelectric harvester is improved by almost nine times in terms of the harvested power output as compared to the baseline harvester on the pure plate without metasurface.more » « less
-
This paper investigates the energy production of a “meso-scale”, wind-based energy harvester that exploits the torsional aeroelastic instability of a rigid blade-airfoil, elastically supported at equidistant supports. Torsional flutter is a single mode aeroelastic instability phenomenon, in which a diverging dynamic angular rotation of a body occurs. The apparatus relies on a simple mechanism that uses flow-induced pitch motion to extract and convert airflow kinetic energy to electrical energy. The system is composed by a rigid blade-airfoil, connected to a support structure through a non-linear restoring force (torsional spring-like) mechanism that enables the rotation about a reference pivot axis. The proposed technology is designed to be efficient in the range of low and medium wind speeds (10-13 m/s), in which horizontal-axis wind turbines and other harvesters are not efficient. Deterministic pre-flutter, incipient flutter and post-critical vibrations of the apparatus have been already explored in a previous study. This work aims to further investigate the aeroelastic behavior of the “flapping foil” by examining the effect of turbulence, random experimental error and modeling simplifications of the aeroelastic forces. The analysis is conducted at incipient flutter in the frequency domain using classical unsteady force models. Monte Carlo methods are employed to solve for the probability of incipient flutter speed. Several configurations are considered to improve the efficiency of the energy harvester.more » « less
-
more » « less
Abstract Photo‐electrochemistry is the major trajectory for directly transforming solar energy into chemical compounds. The performance of a photo‐electrochemical (PEC) system is directly related to the interfacial electrical band energy landscape. Recently, piezotronics has stood out as a promising strategy for tuning interfacial energetics. It applies intrinsic or deformation‐induced ionic displacements (ferroelectric and piezoelectric polarizations) to engineer the interfacial charge distribution, and thereby the band structures of PEC electrodes. Here, contemporary research efforts of coupling piezotronics with photo‐electrochemisty are reviewed. Quantitative band diagrams of a polarization‐tuned semiconductor–electrolyte junction are first introduced, with an emphasis on the impact of interface chemistry. Experimental advances of employing piezoelectric and ferroelectric polarizations to enhance the charge separation and transportation, and surface kinetics of PEC water splitting are discussed. Finally, critical challenges of applying piezotronics in PEC systems and promising solutions are presented.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4046961
