Vibrational energy harvesting by exploring structural benefits and nonlinear characteristics

Abstract

Traditional energy harvesters are often of low efficiency due to very limited energy harvesting bandwidth, which should also be enough close to the ambient excitation frequency. To overcome this difficulty, some attempts can be seen in the literature typically with the purposes of either increasing the energy harvesting bandwidth with a harvester array, or enhancing the energy harvesting bandwidth and peak with nonlinear coupling effect etc. This paper presents an alternative way which can achieve tuneable resonant frequency (from high frequency to ultralow frequency) and improved energy harvesting bandwidth and peak simultaneously by employing special structural benefits and advantageous displacement-dependent nonlinear damping property. The proposed energy harvesting system employs a lever systems combined with an X-shape supporting structure and demonstrates very adjustable stiffness and unique nonlinear damping characteristics which are very beneficial for energy harvesting. It is shown that the energy harvesting performance of the proposed system is directly determined by several easy-to-tune structural parameters and also by the relative displacement in a special nonlinear manner, which provides a great flexibility and/or a unique tool for tuning and improving energy harvesting efficiency via matching excitation frequencies and covering a broader frequency band. This study potentially provides a new insight into the design of energy harvesting systems by employing structural benefits and geometrical nonlinearities.

Introduction

Over the past years, there has been a growing attention in energy harvesting techniques for employing ambient vibrations in surrounding or machines. Traditional solutions for energy harvesting are usually based on linear resonant mechanical structures composed of springs and mass with the transducer through which mechanical energy can be converted to electrical energy based on electromagnetic [1], [2], [3], piezoelectric [4], [5], [6], [7], [8] and electrostatic [9], [10], [11] mechanisms. However, these energy harvesting systems are often effective only if the ambient vibration frequency is close to their resonant frequency. Due to time-varying and broadband properties of ambient vibrations, only a small fraction of mechanical energy can be converted to electrical energy with linear energy harvesting systems. To improve energy harvesting performance, various solutions have been proposed in order that broader range of operating frequencies of energy harvesters can be achieved. Nonlinear energy harvesting techniques, as an alternative method, have been proved to be capable of providing better performance in terms of the amount of energy extracted from a wider range of ambient vibrations [12], [13], [14], [15], [16], [17].

Recently, it has been demonstrated that bistable structure configurations can be used to overcome the bandwidth issues [12], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. In particular, Erturk et al. [21], [22] introduced a piezomagnetic structure for substantial enhancement of piezoelectric power generation in vibration energy harvesting. The bistability could arise because of appropriate placement of the magnets which create a bistable system switching between two stable states. Based on this, Zhou et al. [20], [33], [34] enhanced the broadband frequency responses by tuning the angular orientation of the permanent magnets. Different from this approach, Ando et al. [12] proposed a bistable clamped-clamped polyethylene terephthalate beam and two piezoelectric transducer, and the bistability of their system is created through beam switching due to the environmental vibrations. Arrieta et al. [18], [19] proposed a bistable composite plate with bonded piezoelectric patches for broadband nonlinear energy harvesting. Both analytical investigation and measurement show that the bistable energy harvesting system can provide better energy harvesting performance with board frequency responses. However, because of the dynamic properties of bistable systems, bifurcations and chaos may be generated and leading to unstable risk.

Several other researchers have attempted to apply nonlinear stiffness or nonlinear damping to enhance the energy harvesting performance [14], [35], [36]. Ramlan et al. [37] proposed a system composed of two types of nonlinear springs connected to a mass together with a linear viscous damper. A bigger amount of power harvested using the developed nonlinear device compared to the linear one. Nonlinear cubic damping has been investigated by Tehrani et al. [38] to increase the dynamic range of an energy harvester, and it is noticed that the nonlinear damping also leads to nonlinear stiffness properties.

To optimise energy harvesting performance, some other researchers such as Roundy [39] and Leland [40] attempted to analyse and optimise the effect of design parameters on power output efficiency. For this purpose, Wu et al. [32] developed a tuneable resonant frequency power harvesting device with cantilever beams, from which the resonant frequency can be shifted to match that of the external vibrations. Challa et al. [41] presented an approach which uses the magnetic force to alter the overall stiffness of the energy harvesting device in order to further change the resonant frequency of the device to lower frequencies for better energy harvesting. While successful in enabling energy harvesting over a broader range of frequencies, the amplitude of the vibration may be reduced which may affect the overall efficiency and power output of the energy harvesting device.

This paper present a novel nonlinear energy harvesting system composed by levers and X-shape supporting structures, in which the X-shape structure has been recently proposed for vibration isolation [42], [43], [44], [45]. The equivalent stiffness and damping of the system are nonlinear because of the geometry relationship between the base and platform motions within the structure. The objective is to explore the displacement-dependent nonlinear damping characteristics and the tuneable stiffness characteristics of the X-shape structure for advantageous energy harvesting performance.

In [49], it is shown that the tuneable stiffness of the X-shape structure can be employed for ultra-low frequency energy harvesting and several X-shape structures can be used in parallel to achieve a coupled effect for energy harvesting in a wider frequency band. However, although a single X-shape structure is much simpler to implement in practice, a lower energy harvesting peak frequency by tuning the structure parameters may contradict with higher harvesting peak value and thus only a discounted energy harvesting performance is achieved. To solve this, an easy-to-design lever-type system is applied to the X-shape structure, which can be used for tuning the dynamic responses of the system without compromising the advantageous nonlinear damping effect of the system. Due to the flexibility of the system configuration, the equivalent stiffness and damping can be freely tuned by adjusting several structure parameters for much better energy harvesting performance. The nonlinear energy harvesting system without levers and the corresponding linear ones are investigated for comparisons in order to validate the advantageous performance of the proposed hybrid energy harvesting system.

It is shown that (a) the nonlinear stiffness can be designed easily by structural parameters to achieve low resonance frequency and it is a fairly weak nonlinearity without chaos and bifurcation; This is a special feature of this proposed energy harvesting system, compared with most other nonlinear energy harvesting systems; (b) the displacement-dependent nonlinear damping effect of the X-shape structure is very beneficial and tuneable for vibration based energy harvesting; this is not well discussed in the literature; This presents a unique feature which is potentially more beneficial and practical to vibration energy harvesting; (c) the lever system is very helpful for tuning the dynamic response of the X-shape structure including the resonance peak and frequency (achieving low resonant frequency but high harvesting peak); this is not reported in the literature and provides another special feature of this energy harvesting system.