Contents lists available at ScienceDirect Applied Energy journal homepage: www.elsevier.com/locate/apenergy Role of the galloping force and moment of inertia of inclined square cylinders on the performance of hybrid galloping energy harvesters U. Javed a , A. Abdelkefi b, ⁎ a Department of Mechanical and Manufacturing Engineering, Saint Cloud State University, Saint Cloud, 56301 MN, USA b Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA HIGHLIGHTS • Hybrid Energy harvesting by inclined square cylinder prone to galloping oscillations is investigated. • A reduced-order model is developed for the beam-cylinder harvester using Galerkin discretization. • The performance of the energy harvester for various inclination angles are carried out. • An upright zero inclined or a slight angle of cylinder is preferable for energy harvesting. • Any backward angle of cylinder is not suitable for attaining high levels of harvested power. ARTICLE INFO Keywords: Hybrid energy harvesting Inclined square cylinders Transverse galloping Aerodynamic force representation ABSTRACT Energy harvesting by a square cross-section cylinder, inclined at different angles from the incoming wind flow, prone to galloping oscillations is investigated. The cylinder is fixed at the tip of a cantilever beam at a definite angle, to which is attached a piezoelectric layer and a permanent magnet placed in the close vicinity of a coil. Existing aerodynamic-coefficient experimental values as a function of the incident angle of attack are utilized for determining the aerodynamic force on each inclined cylinder. Seven-order polynomial is recognized to be a convenient choice for performing the analyses in this study. After establishing the galloping aerodynamic force of each case, a reduced-order model is developed for the beam-cylinder energy harvester using Galerkin dis- cretization. Moment of inertia of each case is calculated using transformation matrix and its impact on the natural frequency is determined. It is shown that the moment of inertia affects the linear characteristics of the galloping-based energy harvester when the inclination of the cylinder is changed. The nonlinear characteristics and performance of the energy harvester for various inclination angles are carried out. It is indicated that an upright zero inclined or a slight angle of cylinder till ten or fifteen degrees towards the wind flow is preferable for energy harvesting. Any forward inclination towards the wind flow greater than that or any backward angle of cylinder away from the wind flow are not suitable for attaining high levels of harvested power. This behavior actually opens the doors for using a movable cylinder at the tip of a beam with lock mechanism that can be tilted at a high forward or backward angle for extreme windy conditions to have reasonable practical power harvesting without damaging the harvester. 1. Introduction Localized energy production is on the rise due to the arrival and applicability of electronic gadgets, microelectro-mechanical systems, actuators [1,2], health monitoring and wireless sensors [3], and med- ical implants [4]. Researchers have shown tremendous interest in both base [5–7] as well as flow-induced vibrations [8–14] for effective en- ergy harvesting. Abdelkefi [15] talks in length about utilizing aeroelastic oscillations, such as flutter exhibited by airfoil sections, galloping vibrations of prismatic cylinders, vortex-induced vibrations (VIV) present in circular cylinders, or wake galloping using different transduction mechanisms including piezoelectric [5–7], electro- magnetic [8,16,17], and electrostatic [18]. The concept of using hybrid transduction comprising of a functional piezoelectric layer and an electromagnet-coil arrangement for aeroelastic oscillations have re- cently been proposed [16,17]. https://doi.org/10.1016/j.apenergy.2018.09.141 Received 25 April 2018; Received in revised form 25 August 2018; Accepted 13 September 2018 ⁎ Corresponding author. E-mail address: abdu@nmsu.edu (A. Abdelkefi). Applied Energy 231 (2018) 259–276 0306-2619/ © 2018 Elsevier Ltd. All rights reserved. T