2.3 PEH Systems
2.3.2 Flow induced PEH systems
exhibits chaotic characteristics. Friswell et al. [64] proposed a base excited vertical cantilever beam with a tip mass for energy harvesting considering cubic and inertial nonlinearity. Here an improved bandwidth is achieved as compared to linear config- uration. Litak et al. [76] examined the regular and chaotic responses of a vertical beam and a tip mass based vibrational energy harvester by varying the tip mass. A similar model is evaluated under various excitation forces such as purely harmonic, purely random, and combinations of harmonic and random by Bilgen et al. [77].
Apart from the base excitation, the flow energy is also utilized as an energy source to develop PEH systems. The next subsection describes the flow induced PEH systems.
The recent work by Allen and Smits [90], Tang et al. [91], Zhu et al. [92] and Barrero- Gil et al. [84], further inspired the research studies, where galloping instability is utilized to extract energy from wind for energy harvesting. Hobeck and Inman [93]
developed a biologically inspired piezoelectric grass which consists of an array of cantilevers. Abdelkefi et al. [1] studied the performance of PEH system attached with various bluff body shapes, i.e., D section, square and isosceles triangle with 30◦ and 53◦ angle.
Li et al. [94] reviewed recent PEH systems based on flow induced vibrations from the future perspective to use existing harvesting technology in the aerospace field and discussed the drawbacks along with potential implementation challenges. An- drew and Mahmoodi [95] reviewed designs and methodologies of wind excited PEH systems. Hamlehdar et al. [96] reviewed the energy harvesting from fluid flow us- ing piezoelectrics. Flapping foil based flexible flow energy harvesters (Xiao and Zhu [97]) also attracted the researchers. In the review work presented by Abdelkefi [17], recent energy harvesters based on aeroelastic vibration mechanisms i.e. flut- ter, vortex induced vibration, galloping and wake galloping are discussed. In this work, mathematical models and qualitative and quantitative comparisons are also reviewed. Another flow induced phenomenon like vortex induced vibration (VIV) is also explored for energy harvesting in the work of Akaydin et al. [98] and Sun et al. [99]. Sun et al. [99] studied PEH, utilizing flow energy of water by using VIV and galloping, here the galloping is found to be superior to the VIV for energy har- vesting. Flutter [100–103] and wake galloping [104–106] are also explored for energy transduction.
Different shapes of bluff bodies (Abdelkefi et al. [1]) have been explored for better performance of the galloping based PEH (GPEH) system. The galloping of rhombic shaped bluff bodies is investigated by Ibarra et al. [107]. In another study trapezoidal shape is found to be best suited blunt body shape (Kluger et al. [108]) for energy harvesting. The regular shapes such as square and rectangular sections have been studied by many researchers. For example, in the work of Ewere and Wang [109], square and rectangular sections are compared and square is found to be better than rectangular one. The bioinspired bluff body is investigated by Ewere et al. [110], where the galloping velocity can be controlled by wavy profiled bluff body without any gain in the output power. Javed and Abdelkefi [111] analysed the effect of
inclination of bluff body on energy harvesting. Inverted piezoelectric flag (Xiao and Zhu [97], Orrego et al. [112], Shoele and Mittal [113]) is also explored for harvesting purposes with flexible piezopolymers like PVDF. Kwon [103] used a T shaped PEH system. Javed and Abdelkefi [114] found that the geometry of bluff body, angle of attack and aerodynamic force representation impacts the performance of GPEH system.
Galloping is also utilized in electromagnetic (Zhang et al. [115], Vicente-Ludlam et al. [116]) and hybrid (Javed and Abdelkefi [111]) energy harvesters. The concur- rent forced and self-excited hybrid PEH systems [117–122] are also investigated for performance improvement and harnessing bridge vibration along with galloping.
Perturbation methods like the method of multiple scales [23, 123–125], Krylov- Bogoliubov [109] and method of normal form [126, 127] have been used to obtain a closed form solution.
Structural and aerodynamic nonlinearities are exploited in several studies, like, Ab- delkefi et al. [128] investigated the level of harvested power from aeroelastic vibra- tions of a cantilever beam attached with a triangular bluff body and is supported by nonlinear torsional spring. A nonlinear restoring force is considered to improve the performance of GPEH system by Bibo et al. [125]. In most of the studies a quasi steady approximation is used to model the fluid forces while in the work of Yan and Abdelkefi [122] a GPEH system is modeled as nonlinear quasi steady approach. In this work, the GPEH is analysed under combined forces of wind and base excitation.
Periodic, aperiodic, quasi periodic and chaotic responses are observed.
The effect of galloping on a tall prismatic structure is considered by Abdel-Rohman [123]. The beam of square cross section considered having two degrees of freedom (along and across the steady wind). The amplitude in the along wind direction is found to be small as compared to the across wind transverse amplitude. Generally, a steady wind condition is considered for simplicity but realistic wind conditions are mostly turbulent in nature. For more realistic modeling, in the work of Abdel- Rohman [124], a similar system is analysed under unsteady wind environment where a single harmonic component is considered as unsteady component for simplicity.
Also, in the work of Zulli and Luongo [129] and Luongo and Zulli [130], unsteady component of wind with having two frequency components is considered. PEH
under turbulent air flow is also explored by Kwuimy et al. [131] and [98]. Realistic wind data maps [132] may be useful to find the average wind speeds at a particular location, which can help in deciding the design of energy harvesting system.
Many researchers have carried out a literature review on energy harvesting systems in the last twenty years. In the following section the published review papers related to energy harvesting systems are briefly discussed.