Andrea Cammarano

Tuning a resonant energy harvester using a generalized electrical load

A fundamental drawback of vibration-based energy harvesters is that they typically feature a resonant mass/spring mechanical system to amplify the small source vibrations; the limited bandwidth of the mechanical amplifier restricts the effectiveness of the energy harvester considerably. By extending the range of input frequencies over which a vibration energy harvester can generate useful power, e.g. through adaptive tuning, it is not only possible to open up a wider range of applications, such as those where the source frequency changes over time, but also possible to relax the requirements for precision manufacture or the need for mechanical adjustment in situ. In this paper, a vibration-based energy harvester connected to a generalized electrical load (containing both real and reactive impedance) is presented. It is demonstrated that the reactive component of the electrical load can be used to tune the harvester system to significantly increase the output power away from the resonant peak of the device. An analytical model of the system is developed, which includes non-ideal components arising from the physical implementation, and the results are confirmed by experiment. The − 3 dB (half-power) bandwidth of the prototype energy harvester is shown to be over three times greater when presented with an optimized load impedance compared to that for the same harvester presented with an optimized resistive only load.

The use of normal forms for analysing nonlinear mechanical vibrations

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recalled. It is shown how this method can be placed within the context of the general theory of normal forms provided the damping and forcing terms are treated as unfolding parameters. The approach is contrasted to the alternative theory of nonlinear normal modes (NNMs) which is argued to be problematic in the presence of damping. The efficacy of the normal form method is illustrated on a model of the vibration of a taut cable, which is geometrically nonlinear. It is shown how the method is able to accurately predict NNM shapes and their bifurcations.

Out-of-unison resonance in weakly nonlinear coupled oscillators

Resonance is an important phenomenon in vibrating systems and, in systems of nonlinear coupled oscillators, resonant interactions can occur between constituent parts of the system. In this paper, out-of-unison resonance is defined as a solution in which components of the response are 90° out-of-phase, in contrast to the in-unison responses that are normally considered. A well-known physical example of this is whirling, which can occur in a taut cable. Here, we use a normal form technique to obtain time-independent functions known as backbone curves. Considering a model of a cable, this approach is used to identify out-of-unison resonance and it is demonstrated that this corresponds to whirling. We then show how out-of-unison resonance can occur in other two degree-of-freedom nonlinear oscillators. Specifically, an in-line oscillator consisting of two masses connected by nonlinear springs—a type of system where out-of-unison resonance has not previously been identified—is shown to have specific parameter regions where out-of-unison resonance can occur. Finally, we demonstrate how the backbone curve analysis can be used to predict the responses of forced systems.

Waveguides of a Composite Plate by using the Spectral Finite Element Approach

This work presents the extension of an existing procedure for evaluating the waveguides and the dispersion curves of a laminate made up of thin orthotropic composite plates arbitrarily oriented. The adopted approach is based on one-dimensional finite-element mesh throughout the thickness. Stiffness and mass matrices available in the literature for isotropic material are reported in full expanded form for the selected problem. The aim of the work is the development of a tool for the simulation of the most common composite materials. The knowledge of the wave characteristics in a plate allows correct sizing of the numerical mesh for the frequency-dependent analysis. The development of new stiffness matrices and the analysis for different heading angles are detailed to take into account the general anisotropic nature of the composite. The procedure concerns a standard polynomial eigenvalue problem in the wavenumber variable and is focused on the evaluation of the dispersion curves for all the propagating waves within the materials. A comparison with an analytical approach is also shown in the results using the classical laminate plate theory (CLPT). However, limits of CLPT are outlined and spectral finite element method can be successfully used to overcome such limitations.

Optimum resistive loads for vibration-based electromagnetic energy harvesters with a stiffening nonlinearity

The exploitation of nonlinear behavior in vibration-based energy harvesters has received much attention over the last decade. One key motivation is that the presence of nonlinearities can potentially increase the bandwidth over which the excitation is amplified and therefore the efficiency of the device. In the literature, references to resonating energy harvesters featuring nonlinear oscillators are common. In the majority of the reported studies, the harvester powers purely resistive loads. Given the complex behavior of nonlinear energy harvesters, it is difficult to identify the optimum load for this kind of device. In this paper the aim is to find the optimal load for a nonlinear energy harvester in the case of purely resistive loads. This work considers the analysis of a nonlinear energy harvester with hardening compliance and electromagnetic transduction under the assumption of negligible inductance. It also introduces a methodology based on numerical continuation which can be used to find the optimum load for a fixed sinusoidal excitation.

Modelling and experimental characterization of an energy harvester with bi-stable compliance characteristics

This paper presents a novel design for a vibrational energy harvester. The design uses high permeability magnetic materials which brings about two key advantages. First, it gives strong coupling between the mechanical and electrical domains, thus enabling effective energy conversion. Second, it gives the device a bi-stable compliance characteristic, which gives the harvester a broad-band frequency response. An explicit analytical model is developed using a combination of experimental data and finite element modelling in order to accurately incorporate the magnetic forces. The model is then validated using dynamic tests of the experimental rig. The main features of the dynamic response of the bi-stable oscillator are highlighted and benefits discussed in the context of energy harvesting. Finally, comments are made on the relationship between the complicated behaviour resulting from the bi-stable compliance characteristic and the benefits of increased electrical coupling.

Switched-Mode Load Impedance Synthesis to Parametrically Tune Electromagnetic Vibration Energy Harvesters

Energy harvesters based upon resonant mass-spring-damper systems can only generate useful power over a narrow range of excitation frequencies. This is a significant limitation in applications where the vibration source frequency changes over time. In this paper, an active electrical load is presented which can overcome the bandwidth limitations by parametrically tuning the overall harvester system. The electrical tuning technique synthesizes an optimum reactive load with high-efficiency switch-mode electronics, which also provides rectification, feeding the energy harvested into a dc store. The method is shown to be effective at increasing the power frequency bandwidth of resonant type harvesters and offers the capability of autonomous operation. The theoretical basis for the technique is presented and verified with experiment results. The paper illustrates the challenges of implementing the power electronic converter for a low-quiescent power overhead and in choosing the control architecture and tuning algorithms.

The bandwidth of optimized nonlinear vibration-based energy harvesters

In an attempt to improve the performance of vibration-based energy harvesters, many authors suggest that nonlinearities can be exploited to increase the bandwidths of linear devices. Nevertheless, the complex dependence of the response upon the input excitation has made a realistic comparison of linear harvesters with nonlinear energy harvesters challenging. In a previous work it has been demonstrated that for a given frequency of excitation, it is possible to achieve the same maximum power for a nonlinear harvester as that for a linear harvester, provided that the resistance and the linear stiffness of both are optimized. This work focuses on the bandwidths of linear and nonlinear harvesters and shows which device is more suitable for harvesting energy from vibrations. The work considers different levels of excitation as well as different frequencies of excitation. In addition, the effect of the mechanical damping of the oscillator on the power bandwidth is shown for both the linear and nonlinear cases.

Identifying the significance of nonlinear normal modes

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.

Bandwidth of a Nonlinear Harvester with Optimized Electrical Load

Many researchers have investigated the possibility of amplifying ambient vibrations and converting the associated kinetic energy into usable electric energy. The vast majority of vibration harvesting devices use mechanical oscillators to boost the amplitude of vibration; however, this can result in a rather narrow band of excitation over which the harvesting device is effective. One approach proposed to overcome this limitation is to substitute the conventional linear oscillator with an oscillator featuring a non-linear compliance characteristic: these mechanisms produce broader frequency responses. The design and optimization of nonlinear energy harvesting devices is however not trivial and there is no consensus among the publish works that the benefits of non-linear oscillators can be realized in the energy harvesting context. This work attempts to further develop understanding of nonlinear energy harvesters by investigating the optimum resistive load. The definition of an optimal load for the nonlinear device is first considered, given due consideration to bandwidth and stability of the operating point, and comparisons with linear devices is shown. Finally, the issue of multiple solutions in the frequency response is addressed.