Acoustic non-reciprocity, referring to the phenomenon of path-dependent propagation, has diverse applications in mechanical devices. This paper presents a numerical study on a periodic triangle-shape structure that breaks reciprocity in a passive manner over a broad range of frequency and energy. The proposed structure contains strong nonlinearity and geometric asymmetry, which contributes to a direction-dependent dispersion relationship. When the signal frequency falls in the band pass in one direction, and band gap in the other, a unidirectional wave propagation results. The system achieves giant non-reciprocity with minimal distortion in the frequency content of the signal.

Harvesting of acoustoelastic wave energy in thin plates and other structures is a promising new research direction for scavenging energy to power small sensors and devices. In particular, metamaterial-inspired harvesting concepts have shown strong potential for enhancing harvesting of acoustoelastic wave energy. In support of continued development of these metamaterial-based concepts, this paper presents a fully-coupled T -matrix formulation for assessing scattering of incident wave energy from a piezoelectric patch attached to a thin plate. The T -matrix serves as an input-output relationship between incident and reflected waves, and is developed herein for a piezoelectric patch connected to an external circuit. The utility of the T -matrix is evident in problems with multiple piezoelectric harvesters, where it can be used with other T -matrices (such as those previously formulated for rigid, void, and elastic inclusions) in a multiple scattering context. This has the potential for many uses in predicting the dynamic response of smart and active structures, but may be particularly useful in accurately assessing metamaterial-based energy harvesting enhancement strategies. Following development of the requisite T -matrix, harvesting in an example Gradient-Index (GRIN) metamaterial structure is predicted using the multiple scattering approach.

This paper introduces an analytical framework for predicting wave energy harvested by a circular piezoelectric layer from a harmonic point source excitation. The explored acoustic system analyzes a circular piezoelectric disk attached to an infinite host domain. An harmonic point source is located away from the piezoelectric disk on the infinite host layer. The analysis approach decomposes the system into two subdomains, the piezoelectric disk and an infinite plate, which are then separately analyzed. In contrast to traditional analysis methods for such systems (a sandwich of layers with different dimensions), this technique uses internal interaction forces between the different subdomains to find a close-form solution for the vibration of propagating waves over the entire field. In addition, the voltage generated by the harvester is calculated by using coupled electromechanical equations. The analysis is validated by comparing response quantities and frequency response functions at different points on the piezoelectric circular layer and host layers to those predicted using COMSOL simulations, which document good agreement. Analysis of this system is an important stepping stone to the next goal, which is optimization of energy captured from the propagating wave by designing boundary walls (reflector) on the host layer which focus the energy of the wave onto the piezoelectric domain. This focused energy can then be transferred to the electrical power by via a piezoelectric layer through an electrical circuit.

This work proposes a clearance-type electromechanical nonlinear energy sink (NES) to increase the electrical energy harvested from non-stationary mechanical waves, such as those encountered during impact and intermittent events. The key idea is to trap energy in the NES such that it can be harvested over a time period longer than that afforded by the passing disturbance itself. This leads to an asymmetrical, piece-wise nonlinear device whose functionality and analysis lie at the intersection of several current research topics, including wave-based energy harvesting, non-reciprocal wave propagation, nonlinear energy sinks (NES’s), and hybrid dynamical systems. The nonlinear energy sink concept explored uses a clearance-type nonlinearity, and resulting impact, to pass the energy of the propagating wave from a primary subdomain to a secondary subdomain where a significant portion of it is subsequently trapped and harvested. Moreover, unlike traditionally-studied single-DOF NESs, both subdomains of the NES (i.e., on either side of the clearance) contain displaceable degrees of freedom, significantly increasing the complexity of analytical solution approaches as compared to systems where one side is constrained by a known (or zero) displacement. Computational and analytical techniques are employed to optimize the energy sink and explore qualitative behavior (to include bifurcations). The analysis includes insight from Poincaré sections and bifurcation diagrams, with and without harvesters. Bifurcation diagrams and trends therein provide insight into the number and state of impact events at the NES as excitation amplitude increases. However, analytic formulations are found which quantify the relationship between the impact amplitude and the energy produced, parameterized by system properties such as the harvester effective resistance, the clearance gap, and the domain mass and stiffness. Importantly, a linear relationship between the input energy amplitude and the number of NES impacts has been observed and captured by an approximate, closed-form Poincaré map. In addition to this linear relationship, a closed-form Poincaré map is derived which maps one NES impact location to the next, greatly simplifying the analysis while providing an important tool for follow-on bifurcation studies. The results may justify further exploration in which complex structures (e.g., plates and/or three-dimensional structures) incorporate one or more of the clearance-type NESs to enhance non-stationary electroacoustic wave energy harvesting.

Harvesting of acoustoelastic wave energy in thin plates and other structures has recently gained attention from the energy harvesting community. To enhance the wave power generated, researchers have investigated metamaterial-inspired concepts to include funnels, mirrors, and defect-based resonators introduced in the metamaterial’s bandgap. Many of these concepts have been demonstrated experimentally using arrangements of cylindrical stubs mounted on the surface of a thin plate, where such stubs scatter plane and cylindrical waves in such a way as to focus mechanical energy. To support these studies, the authors have recently introduced an experimentally-verified analytical framework for investigating the coupled electromechanical response of a single circular piezoelectric harvester adhered to an infinite plate and excited by a distant harmonic point source. This paper extends these ideas to consider a similar physical system with the addition of multiple cylindrical inclusions. These additions require development of an electromechanically-coupled, multiple scattering formulation of significantly increased complexity. The formulation also includes an electrical circuit model for generating electrical current from incident waves interacting with the piezoelectric domain. Following development, the formulation is applied to the determination of optimal arrangements of scatterers which maximize the electrical power generated. Specifically, an optimization study is carried-out in which twenty-five scatterers are first placed in a semi-elliptical arrangement with the aim of focusing wave energy from one elliptical focus (i.e., source location) onto the other. It is known from past studies that additional side lobes are generated due to truncation of the ellipse, and thus not all of the energy can be focused at single point, as desired. To improve upon this situation, an optimization study is performed in which the aspect ratio of the ellipse is varied, with the goal of optimizing the power harvested from the focal point. Results from the optimization studies show conclusively that the side lobes can in fact be minimized, and that harvested power can be significantly improved.