Effect of Tip Mass Length Ratio on Low Amplitude Galloping Piezoelectric Energy Harvesting

Abstract

Galloping beams were exposed to the wind free stream and is used for sustainable wind-power harnessing. In this paper, the effect of tip mass on the performance of a galloping energy harvester is investigated by simple modeling of the system, which is useful for broad engineering applications of these systems. Here, the piezoelectric layer attached to a cantilever beam with a tip mass exposed to the wind free stream is used as an energy harvester. A fluid–solid interaction model is used to simulate the problem. The fluid–solid interaction model is composed of the experimental data for aerodynamic loads and one-dimensional structural model of piezoelectric and beam material with Euler–Bernoulli beam theory. The governing partial differential equations of the system are solved analytically by use of the approximation method. The resulting model is confirmed by preceding experimental results. The effects of the tip mass length ratio on the onset of galloping, the level of the produced voltage, and the harvested power are determined analytically. As shown by increase of the length of tip mass for the constant beam and piezoelectric length, the inertia of the system increases while the tip displacement and onset of galloping decrease.

Akbari–Ganji Method for Solving Equations of Euler–Bernoulli Beam with Quintic Nonlinearity

“…The results illustrated in this section clearly demonstrate that AGM is very effective and convenient for the nonlinear beam vibration for which the highly nonlinear governing equations exist. This method in comparison with EBM has It is important to have an accurate parametric solution to understand non-linear vibration characteristics [32][33][34][35][36][37]. The results illustrated in this section clearly demonstrate that AGM is very effective and convenient for the nonlinear beam vibration for which the highly nonlinear governing equations exist.…”

“…Table 6 compares the natural frequencies obtained by these three methods for various values of amplitude. It is important to have an accurate parametric solution to understand non-linear vibration characteristics [32][33][34][35][36][37]. The results illustrated in this section clearly demonstrate that AGM is very effective and convenient for the nonlinear beam vibration for which the highly nonlinear governing equations exist.…”

“…The method can be applied for the applications of safety monitoring of warehouse racks, in high bay warehouses and high storage warehouses [34] and evaluate precast pre-post-tensioned concrete bridge beams [35]. The effect of nonlinear galloping piezoelectric energy harvesting which consist of a simple beam and concentrated mass at the end is studied by Abdollahzadeh Jamalabadi [36][37][38].…”

Amplitude resonance response and feedback control of cantilever beams with tip-mass under aerodynamic load

“…Many studies have been carried out on cantilever beams with tuned mass in order to study the influence of tip mass on the dynamics (Payam and Fathipour 2015), invest the energy harvesting (Homayouni-Amlashi et al 1919, Izadgoshasb et al 2018, Ahn et al 2018, Abdollahzadeh 2019 of the system or the influence of the parameters (Payam and Fathipour 2015, Pratiher and Dwivedy 2011, Labdzki et al 2018, Kim et al 2012, Meesala and Hajj 2019a, Warminski et al 1919 of the system on its natural frequency (Mahmoud 2019, Li et al 2013, Payam and Fathipour 2013 and control (Moutlana and Adali 2015, Belhaq and Fahsi 2009, Moutlana and (2-4 December), 2013, Pratiher 2012). Among them, in 2012, Kim et al (2012) study the behaviour of a nonlinear cantilever beam with tuned mass and subjected to an axial force and an electrostatic excitation.…”