1. Introduction
With the development of the Internet of Things (IoT) and big data, the rapid technological revolution has recently necessitated improved micro-energy harvesting systems to power wireless sensors and communication nodes [
1]. This is required to overcome the shortcomings of conventional batteries, including limited life span, capacity, hazardous disposal, and replacement difficulty in several locations. Moreover, in specific practical applications such as implantable medical devices [
2] or cardiac pacemakers [
3], there arises a need for frequent surgeries to replace batteries that seriously threaten the patient’s health. Thus, long-lasting self-powered smart devices driven by micro energy generation systems possess a clear superiority and desirability compared to their battery-reliant counterparts.
Micro energy harvesters are designed to capture ambient energy from surrounding sources and convert it into electrical energy. Numerous studies have introduced various transduction mechanisms, including electrostatic [
4,
5], electromagnetic [
6,
7], triboelectric [
8,
9], and piezoelectric [
4,
10], to harvest energy from various ambient sources. With several prominent characteristics comprising high power density, minimal damping, good scalability, and simplicity of design and implementation, the piezoelectric transduction mechanism has certainly established a unique position compared to the other techniques [
11]. Additionally, the ability of piezoelectric materials to convert mechanical energy directly into electrical energy has piqued the interest of research communities working with vibrating sources [
12], as electrical energy could be generated from various sources including but not limited to wind [
10], ocean waves [
13], structural actions [
14], vehicular [
15] and mechanical motion [
16] with piezoelectric transduction. These sources are widely used in powering remote sensors for structural health monitoring systems and piezoelectric energy harvesting systems [
17,
18,
19]. However, biological action, particularly human motion, has recently been recognised as a vibration source for piezoelectric energy harvesting, bringing up a wide range of possibilities for developing different human-motion-powered devices [
20]. For instance, the ability to make piezoelectric energy harvesters (PEH) on a micro-scale in flexible and stretchable minuscule devices is a big step forward in developing self-powered implanted medical devices.
Conventional linear PEH is a cantilever beam structure bonded with one or two piezoelectric transducers in the form of a unimorph or bimorph harvester, respectively, near the fixed end. This is often preferred by most researchers since the cantilever beam structure can be modified to enhance the performance of the harvester as required [
21]. More often, a proof mass may be attached to the free end of the PEH to tune the resonance frequency of the harvester [
22]. Pillatsch et al. [
23] proposed a PEH that operates under the swing motion of the human arm. The harvester had an eccentric rotating magnetic proof mass and a piezoelectric bimorph with a magnetic tip mass. It was similar to the structure employed in the Seiko kinetic wristwatch. Moving forward, Shukla and Bell [
24] invented a PEH consisting of a rotor pendulum with several strikers and a PVDF unimorph as a piezoelectric system to harness power from the waist motion. Using the lower limb motions, such as leg swings, is more beneficial since they can deliver the most mechanical energy as their torques are higher than those of other body parts [
25]. Pozzi et al. [
26] proposed a wearable knee joint PEH that consisted of seventy-four plectra implanted in a rotating hub with four fixed piezoelectric bimorphs. More recently, Izadgoshasb et al. [
27] invented a device to enhance the productivity of PEH using the double pendulum system coupled with repulsive magnetic force. The harvester performed significantly better than most existing designs. However, unlike high-frequency energy sources, working with ultra-low frequency vibration (1–10 Hz) [
28] sources such as human motion is still challenging due to the intrinsically high resonance frequencies of most conventional linear PEH systems. Besides, the above-mentioned PEH designs are working on a frequency-up conversion method that contains considerable additional weights, magnets, impact stoppers, etc. So far, studies focusing on ultra-low-frequency vibrations with geometrical optimisation of the design are relatively scarce.
Conventional PEH is designed to operate at its first resonance frequency within a narrow operating bandwidth. Hence the effectiveness of the harvester becomes significantly poorer in an environment where abundant ambient vibrations are randomly spread over a wider frequency spectrum. PEH with multiple branches is feasible to attain multiple close resonance peaks. Zhang and Hu [
29] studied a PEH with multiple branches attached to the main cantilever beam. The design performed better in power density than the conventional PEH since a single piezoelectric patch was used to generate multiple resonance peaks. Further studies on the branch beam concept were conducted by Upadrashta et al. [
30], Izadgoshasb et al. [
31] and Piyarathna et al. [
32]. Even though the devices mentioned above were superior to the conventional PEH, they either carried excessive proof masses for performance improvement, were not satisfying for multi-directional ultra-low frequency vibrations, such as human motion, or had limited performance improvement in an ultra-low frequency range.
Another major drawback of conventional PEHs is they cannot generate adequate electricity for most low-power smart electronic devices [
33]. Hence, researchers have studied piezoelectric material improvements [
34,
35], circuitry developments [
36,
37,
38], and structural and mechanical enhancements to improve power output. This paper focuses on the structural aspects of PEH for power improvement. With time, the structure of the conventional cantilever beam has been modified from a rectangular section to different structures, including triangular [
39], trapezoidal [
40], spiral [
41], zigzag [
42], and curved sections [
33]. Among these, curved sections have recently been utilised in PEHs. These curved sections experience uniform stress distribution along the vibrating direction compared to commonly used conventional cantilever beam harvesters (CBHs), which helps to boost the effectiveness of the PEHs in terms of voltage, power, and power density [
33]. Furthermore, the curved PEH is less affected by the charge redistribution effect due to relatively even stress distribution [
33,
43,
44]. However, standalone curved sections cannot widen the PEH’s operating bandwidth. Hence, developing a PEH that can achieve broader operating bandwidth and effective power output simultaneously is challenging.
This paper presents a novel harvester design, which incorporates the curved beam and branch beam concepts together for ultra-low frequency excitations. As per the authors’ knowledge, this was the first time these two concepts had been combined. One of the key objectives of this study was to propose a harvester capable of achieving a few closer resonance peaks in the ultra-low frequency range (0–10 Hz) [
28], i.e., to broaden the operating bandwidth. Having a few more comparable resonance frequencies in the ultra-low frequency range would fit well with most common human motions, from the heartbeat [
45], lung motion, and muscular contraction displacements [
46] inside the human body to external physical motions, including finger movements [
47], walking [
48], and running [
49], which waste an enormous amount of mechanical energy that can be potentially converted into electrical energy. The other objective was to enhance the effectiveness of the harvester in terms of voltage and power output purely through geometrical optimization without any additional accessories (i.e., no magnet/impact stopper penalty). The design was validated by finite element analysis (FEA) and experimental studies. FEA was conducted to assess the operating bandwidth, while the experimental study was focused on evaluating the voltage and power capability of the proposed design. Experimental tests were conducted using a mechanical shaker and human motion to illustrate ultra-low-frequency energy sources. It is worth noting that this paper is focused on an experimental study to prove the workability of combining two concepts (curved beam and branch beam concept). Hence the theoretical study can be considered for advanced development of the harvester in future research.
2. Design of Arc-Shaped Branch Beam Harvester
This study proposed a novel beam design by combining arc-shaped cantilever beam sections with two branch beam sections, as presented in
Figure 1. The arc-shaped cantilever beam acts as the main beam component of the design. A 28 mm × 14 mm × 0.350 mm sized macro fibre composite (MFC—M2814-P2) patch operating under bending mode (
was attached with epoxy near the main beam’s fixed end. Two branches comprising a vertical straight section, arc shape section, and horizontal straight section were attached to the main beam’s free end, allowing a 4 mm gap in between. The proposed arc-shaped branch beam harvester is referred to as ASBBH in the text. A parametric study was conducted to understand the effect of using different beam lengths for ASBBH, presented in
Section 3.1.
The architecture of the branch beam was inspired by the stance phase and swing phase of running motion, as shown in
Figure 2. At this stage, the leg that strikes the ground acts as a shock absorber helping to dissipate the mechanical energy of the body [
50]. This allows the bent leg to enter the swing phase [
50]. The highest knee flexion (i.e., bending of the knee) is achieved during the end of the stance phase and the start of the swing phase for running motion [
51]. Inspired by this phenomenon, the branch beam of the harvester has been designed (
Figure 2b) to achieve higher flexion. However, the design was further modified to
Figure 2c, as a curved joint section helps to distribute the stress evenly compared to straight sections, aiming to increase the durability of the harvester when it experiences excessive deformations. While working under vibrations, the branch beams induce tensile stress along the beam axis. Following this, the branch beam motion causes flexural deformation in the arc-shaped main beam near the clamped end, which tends to generate strain in the MFC attached to the arc-shaped main beam. In this manner, the excitation tends to amplify twice, initially by the branch beams and then by the flexural deformation of the arc-shaped main beam [
52].
Two alternative beam designs (conventional cantilever beam harvester (CBH) (
Figure 3a) and segmented curved beam harvester (SCBH) (
Figure 3b) were also explored in the FEA to evaluate the operating bandwidth and effectiveness of the proposed device. To achieve a fair comparison, the overall horizontal length of ASBBH was considered as the length of the CBH. The equal volume concept was not considered in this scenario to avoid the length of the CBH becoming excessive. The volume of the other counterpart, SCBH, was kept equivalent to the ASBBH. A proof mass of similar weight was attached to the free end of all three harvester designs.
The physical parameters of the aluminium beam and steel proof mass are summarised in
Table 1. Furthermore, the material properties of the MFC transducers used in this study are summarised in
Table 2. These values have been obtained from the Smart Materials Corporation manufacturer’s profile.
3. Finite Element Analysis (FEA)
For the proposed ASBBH, FEA was conducted using the commercially available FEA software package SIMULIA ABAQUS to evaluate its mechanical behaviour. The findings of the FEA study will lead the authors to understand the most suitable beam section lengths, the proximity of natural frequencies, the harvester’s operating bandwidth, and the potentiality of voltage and power generation. CBH and SCBH systems were also examined using FEA for comparison purposes.
Three types of simulations were performed in FEA: parametric study, static analysis, and modal analysis. A fixed constraint was applied at one end for all three harvesters, and a proof mass was attached to the free end. The physical properties adopted for the simulation are presented in
Table 1 and
Table 2. A 20-node quadratic piezoelectric brick element named C3D20RE was used to model the MFC piezoelectric patch attached to each harvester. A 20-node quadratic brick element named C3D20R was used to build the model for the rest of the solid beams and proof masses. Each node possessed three translational degrees of freedom in the polar coordinate system for both elements. The element size chosen was 1 mm after a discretisation and convergence test, which was small enough to produce accurate results without requiring significant processing effort [
31].
3.1. Geometrical Optimisation of the ASBBH—Parametric Study
The natural frequencies (NFs) and modal characteristics of a harvester can be altered by changing the geometrical parameters, including beam length, width, thickness and tip mass. The parametric study was conducted in this research to understand the effect of using different beam lengths for ASBBH. This helps to determine the optimum beam lengths for the different beam sections to operate the harvester below 10 Hz, preferably with one or more NFs. As such, only the beam lengths were changed, while the beam width, thickness and proof mass were kept constant. However, the values of the fixed parameters were selected as below due to the following reasons.
The width of the piezoelectric transducer (MFC) used in the study was approximately 15 mm; thus, the curved beam width was fixed as 20 mm. The thickness of the selected aerospace-graded aluminium material was 0.6 mm; hence beam thickness was fixed at 0.6 mm throughout the harvester. The minimum gap between the branch beams that allowed the branch beams to vibrate without colliding with each other was 4 mm; hence the gap between the branches was set as 4 mm for the whole branch beam section. The minimum arc length considered in the parametric study was 70 mm, considering the length of the MFC patch (30 mm), clamped edge (10 mm) and length of the joint (5 mm). The upper and lower arc beams were kept with the same arc lengths.
Table S1 represents the first three NFs of various design configurations selected in the parametric study. A few of the configurations (arc lengths between (70–120 mm) were not listed in
Table S1 for simplicity. All the design parameters were labelled in
Figure 1.
The desired configuration of the ASBBH with ultra-low, closer natural frequencies was achieved with a 120 mm arc length. Out of the three designs with the respective arc length, designs 5 and 6 work well for the frequency of human motion. However, to avoid hogging the L3 beam (in design 6) due to its excessive length, design 5 was selected as the preferred configuration for ASBBH. However, it is worth noting that these dimensions of the harvester (ASBBH) were chosen as a proof of concept. With the special characteristics of piezoelectric materials, the device can be scalable to use as enlarged or as a microstructure depending on the real-time application.
3.2. Static Analysis
The operating mechanism of a transducer is a critical factor for any energy harvester design. The MFC transducer used for this study, which works under the d
31 mode, relies on the strain generated in the cantilever beam. Hence, static analysis was first conducted in ABAQUS for all three designs to elucidate the highest stress/strain gain. During the analysis, a different magnitude of imaginary loads (1–10 N) was applied at the midpoint of the proof mass attached to the tip of each energy harvester. In the case of ASBBH, the loads were applied only to the top two proof masses out of the four, keeping the sum of the loads equal to the load applied to the other two designs at similar conditions. The two masses on the bottom of the branch beam were not added with any loads as it was unrealistic in actual conditions and did not replicate the same conditions as the other two harvesters, CBH and SCBH, respectively. The results were elaborated on tip deflection and highest stress/strain gain and presented in
Figure 4.
3.2.1. Tip Deflection
This section discusses the tip (free end) deflection of each harvester against the applied load. The deflection of a cantilever beam is linearly proportional to the stress and strain gained. The deflection is proportional to the stress/strain generation, thus, voltage production.
As per the results presented in
Figure 4a, the tip deflection of CBH at all applied loads (1–10 N) remains the lowest. For an instant, the deflection of SCBH and ASBBH was approximately four times and 10 times higher than that of CBH. Moreover, ASBBH achieved about 2.5 times higher deflection than SCBH for all considered cases. This allows us to predict that the achievable stress/strain might follow the same trend in their results. In accordance with the visual observations made during the experiments for voltage generation, the two branches attached to the main beam of ASBBH significantly enhanced the main beam deflection.
3.2.2. Highest Stress and Strain
The main beam’s highest stress/strain generation is crucial for energy generation by the MFC patch.
Figure 4b,c present the highest calculated stress/strain results under different loadings (1–10 N). The highest stress/strain of CBH was generated near the fixed end of the harvester. However, it was noted that the aforementioned stress/strain generation of CBH was the lowest among all three energy harvesters. Compared to the stress/strain generation of CBH, SCBH slightly improved its performance by approximately 1.2 times and 1.3 times, respectively.
In contrast, the proposed ASBBH yielded the highest stress and strain, which were comparatively higher than the other two designs. The stress generation of ASBBH was approximately 3.4 times and four times higher than SCBH and CBH, respectively. Conversely, the strain generation of ASBBH was approximately two times and 2.7 times higher than SCBH and CBH, respectively. Possible reasons for this significant improvement of ASBBH could be the higher tip deflection and the reduced stiffness due to the compact structure. These results emphasised that the proposed ASBBH could potentially generate higher voltage and power when dynamically excited. To sustain the higher stress and strain experienced during the vibration, the ASBBH design is recommended to fabricate with aerospace-graded aluminium 2024. As per the manufacturer’s profile, aerospace-graded Aluminium 2024 has high strength and excellent fatigue resistance compared to aluminium 6061. However, future studies are recommended to focus on assessing the long-term reliability of the ASBBH.
3.3. Modal Analysis and Mode Shapes
3.3.1. Modal Analysis
To identify the first six natural frequencies and mode shapes, three-dimensional (3D) structures for ASBBH, CBH, and SCBH were investigated in SUMULIA ABAQUS. To do so, a linear perturbation analysis was conducted. The software used the following Equation (1) to solve the eigenvalue problem in this analysis, where ω was the frequency of the system while M represented the mass matrix,
φ denoted the mode shape, and
K symbolised the stiffness of the system. The natural frequencies obtained through FEA are presented in
Table 3 and
Figure 5.
As per the results, the first six natural frequencies of CBH spread over a frequency range of 4.6 Hz to 322 Hz. In addition, CBH had only one natural frequency in the desired ultra-low frequency spectrum (<10 Hz). The gap between the first and second natural frequency was approximately 60 Hz, an inherent expanse. Compared to CBH, SCBH has two natural frequencies in the ultra-low range. Further, the natural frequencies’ spread had been lowered from 2.15 Hz to 82.22 Hz. In this case, the gap between the first and sixth natural frequencies was approximately 80 Hz, reflecting that the CBH had a narrower operating bandwidth than SCBH.
In contrast, the proposed ASBBH exhibited significant enhancement compared to CBH and SCBH. For instance, ASBBH achieved six natural frequencies in the desired frequency spectrum (<10 Hz), a six-fold and three-fold improvement over CBH and SCBH, respectively. It is well-known that the PEH could generate the highest output power when the system, particularly the cantilever beam, excites at its natural frequency [
21]. With six natural frequencies in the ultra-low range, ASBBH facilitates the potential to generate high power output compared to other counterparts. In addition, the gap between each natural frequency increment (e.g., NF1, NF2, NF3, NF5 and NF6) did not exceed 1.96 Hz. Thus, most of the frequencies relying on the band gap have the potential to generate considerable power output since they are much closer to natural frequencies. This statement could be further demonstrated in the experimental stage. Moreover, this reduction in gap leads to a lower spread over six natural frequencies of ASBBH within 1.43 Hz to 6.85 Hz, increasing the operating bandwidth of the harvester, solving one of the major issues of CBH.
3.3.2. Mode Shapes of ASBBH
Figure 6 demonstrates that the branches of ASBBH have motions in three-dimensional space. The X-direction is along the harvester length, the Z-direction is along the harvester width, and branches fixed to the curved beam move in the Y-direction. Hence, the proposed ASBBH demonstrates the capability of harvesting energy through multi-directional vibrations. Moreover, the authors visually witnessed this motion of the branches while conducting the experiments. Generally, this motion would be limited for a conventional cantilever beam harvester, having the beam bending along the Y-direction only. Branch beam harvesters proposed in previous studies [
30,
31] also have a limited motion with beam bending along the Y-direction.
In addition, the mode shapes presented in
Figure 6 further demonstrate that the first, second, fifth and sixth mode shapes (
Figure 6a,
Figure 6b,
Figure 6e and
Figure 6f, respectively) were bending dominant as the beam segments experienced deflection in their transverse direction. Having few bending-dominant modes in ASBBH would be beneficial for electricity generation because the D
31 operating mode of MFC used in the proposed harvesters tends to convert strain into electricity, mainly due to the bending in the Y–direction. The third and fourth modes were mainly categorised as torsion-dominant since the beam segments illustrate a rotation around their respective axis. In the early stage of PEH systems, the torsion-dominant mode was frequently averted, believing opposing signs of stress and subsequent charge cancellation in a flat piezoelectric patch. However, this was later proven false, as in the torsion-dominant mode coupling both bending and torsional modes was found to be comparatively effective [
43].
6. Conclusions
This study introduces a novel multimode PEH design combining two design aspects, i.e., curved structure and branch beams, to improve PEH’s energy production potential from ultra-low-frequency vibration sources, including human motion. A numerical study using ABAQUS FEA software, and a series of experiments were conducted to examine the proposed ASBBH’s performance in operating bandwidth, voltage generation, and power generation. The numerical study was mainly undertaken to study the operating bandwidth of the harvester, while the experiment series was focused on voltage/power generation and suitability of the harvester in human motion applications. The mechanical shaker and human motion tests (walking, jogging, and running motions) were conducted in the experiments. Its performance was then compared against traditional PEH, i.e., CBH.
Six closer resonance peaks were obtained by the proposed ASBBH within the ultra-low frequency range of 1–10 Hz, while only one resonance frequency was obtained by CBH, emphasising a significant improvement in the operating bandwidth of the harvester. The mechanical shaker test proved that the ASBBH could generate the highest output voltage of 34 V and power of 1100 μW at its first resonance frequency. The remaining five natural frequencies also performed well with regard to voltage and power output. Out of the six natural frequencies, two natural frequencies were operating under torsion-dominant modes. The experimental results showed they were more effective than the bending-dominant modes, excluding the fundamental bending mode. Thus, the coupling of both bending and torsional motions was comparatively effective. In the human test series, a peak output voltage of 65 V and power of 4000 μW was recorded for jogging motion (1.5 Hz), which was identified as the first natural frequency of the ASBBH, irrespective of the different base accelerations. These improvements are significant for a simple harvester design such as ASBBH, as it works without additional penalties but with purely optimised structural parameters of the energy harvester. It is worth noting that the geometrical parameters of the harvester were chosen as a proof of concept, and the harvester can be manufactured as a miniaturised apparatus as required for practical human motion applications.
Combined with a suitable rectifier circuit for power management, the ASBBH could be utilised as a standalone energy provider for low-power-consuming devices such as medical implants and WSNs. For future work, attempts should be made to develop a comprehensive theoretical model to elaborate the working principles of combined concepts (curved beam and branch beam in the proposed design). Further, effort should be put into understanding the possible nonlinear behaviour of ASBBH under the influence of magnets or mechanical stoppers, aiming to reduce the anti-resonance valleys between obtained natural frequencies.