Beneficial nonlinear dynamic regimes for energy harvesting

The mechanical properties exhibited by bistable shells have raised considerable research interests over more than three decades. Two stable equilibrium positions easily attainable by composite structures with large deformations and little energy have found numerous engineering applications. Aerospace, bionics, passive vibration isolation, energy harvesting are the main fields of application so far explored. Examples of recent significant applications are: aircraft morphing wings; shape morphing microrobot in medicine; shape morphing structure in civil engineering. By dynamically activating the transition between the equilibrium positions a variety of dynamic regimes of the bistable composite shells can be triggered enabling advantageous operating conditions. 

The nonlinear dynamics of a bistable laminate with two remarkably different stable geometric configurations was considered by the authors in Brunetti et al. [1]. The considered bistable composite shells are obtained by inducing a prestress on initially curved stress-free configurations. Therefore, the asymmetry of the clamped stable states is controlled by the curvature of the shell’s stress-free configuration. It is shown that the relevant difference between the shell’s stable shapes triggers a level of kinetic energy extracted usually not achievable with the symmetric stable shapes [2].

The nonlinear dynamic behavior of the shell was studied through an extensive experimental campaign. To demonstrate the global picture of the dynamics of the shell, two maps were constructed which allow to identify, for each pair of amplitude and frequency values, the number and type of possible motions. Starting from these maps, the efficiency of the different motions with respect to the energy harvesting capacity was then evaluated. To this aim, a new index based on RMS values of shell strains and harvested electrical power was proposed. The index gave evidence that the periodic in-well vibrations around the 𝐶 configuration and reversible snap-through motion provide the highest values of recovered energy. Further developments will address the energy harvesting opportunities offered by cantilever shells characterized by clamped and free edges with opposite curvatures [3].

Systems that convert available energy from the environment (e.g., kinetic, wind, solar, thermal, chemical) into electrical energy can be used as direct power sources or to charge storage devices such as batteries and supercapacitors. At small scale, these harvesting systems may eventually replace on-board batteries that require periodic replacement, a particularly attractive alternative for devices that are inaccessible. Low power applications such as wireless smart sensors represent a growing market, particularly in the health sciences and in monitoring the state of critical infrastructure. Power consumption of these devices generally ranges from tens of micro- to hundreds of milli-W. Since vibration is pervasive in the environment, kinetic energy generators are an attractive alternative for powering autonomous, small-scale systems, and several recent studies have focused on this alternative. Activities such as walking on a pedestrian bridge and a train wheel traversing a track represent examples of pulse-like excitations applied to flexible structures, capable of producing vibrations suitable for energy harvesting.

A vibration-based electromagnetic bistable energy harvesting system (BNEH) coupled to a directly excited, weakly damped linear primary system (LO) is studied in [4]. The coupled equations governing the dynamics of the two-degree-of-freedom system are used to compute two energy harvesting measures: energy harvesting efficiency and total harvested energy. Mass ratio and damping in the coupling, which is provided by both the mechanical inherent damping of the BNEH and the electromechanical coupling, are found to be the key parameters governing the energy harvesting performance. Under a single impulse, by decreasing the energy level, three different mechanisms are exploited to attain a fast energy capture and harvesting: periodic cross-well oscillations, a regime of aperiodic cross- and in-well oscillations, and fully in-well oscillations. By comparing the energy harvesting capabilities of the system with and without the negative linear coupling stiffness, a significant enhancement in terms of both energy harvesting efficiency and total energy harvested due to the addition of the bistability is observed. For the considered set of parameters, the nonlinear device is found to be able to absorb and harvest above 40 mJ at the highest energy level, 90% of which is harvested in the first 0.4 s, whereas energy of the order of mJ can still be harvested at very low input energy regimes. Energy harvesting capability greater than 400 mJ per applied impulse is achievable for high-energy inputs and for optimal impulse periods.

In order to validate the numerical predictions presented in [4], an experimental investigation of an electromagnetic energy harvester coupled through a bistable, essentially nonlinear element to a weakly damped primary linear oscillator (LO) is reported in [5]. The combined electromagnetic harvester and bistable coupling element represent the so called BNEH. The LO is directly subjected to low energy impulsive excitations. The coupling is represented by a prebuckled clamped-clamped beam constrained to exhibit transverse motion in the direction of its weak bending axis, resulting in a stiffness characteristic at its connection to the harvester containing both negative linear and cubic terms. A computational model representing the experimental apparatus is developed, and the performance of the system is studied experimentally and computationally under both isolated and repeated impulses. A model is also developed for the monostable counterpart, and comparisons are made demonstrating the superior performance of the bistable configuration.

[1]  Brunetti M., Kloda L., Romeo F., Warminski J., Multistable cantilever shells: Analytical prediction, numerical simulation and experimental validation, Composites Science and Technology, 165, pp 397-410, 2018.

[2] Brunetti M., Mitura A., Romeo F., Warminski J., Nonlinear dynamics of bistable composite cantilever shells: An experimental and modelling study, Journal of Sound and Vibrations, https://doi.org/10.1016/j.jsv.2022.116779, 2022.

[3] Mitura A., Brunetti M., Kloda L., Romeo F., Warminski J., Experimental nonlinear dynamic regimes for energy harvesting from cantilever bistable shells, Mechanical Systems and and Signal Processing, 206, https://doi.org/10.1016/j.ymssp.2023.110890, 2024.

[4] Chiacchiari S., Romeo F., Mc Farland M., Bergman L., Vakakis A.I., Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment, Int. J. of Nonlinear Mechanics, 94, 84-97, 2017.

[5] Chiacchiari S., Romeo F., Mc Farland M., Bergman L., Vakakis A.I., Vibration energy harvesting from impulsive excitations via a bistable nonlinear attachment – Experimental Study, Mechanical Systems and Signal Processing, in press.