Amin Bibo Nonlinear Vibrations and Energy Harvesting Laboratory (NOVEHL), Department of Mechanical Engineering, Clemson University, Clemson, SC 29634 Abdessattar Abdelkefi Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003 Mohammed F. Daqaq Nonlinear Vibrations and Energy Harvesting Laboratory (NOVEHL), Department of Mechanical Engineering, Clemson University, Clemson, SC 29634; Visiting Associate Professor Department of Mechanical and Materials Engineering, Masdar Institute of Science and Technology (MIST), Abu Dhabi, UAE e-mails: mdaqaq@clemson.edu; mfdaqaq@masdar.ac.ae Modeling and Characterization of a Piezoelectric Energy Harvester Under Combined Aerodynamic and Base Excitations This paper develops and validates an aero-electromechanical model which captures the nonlinear response behavior of a piezoelectric cantilever-type energy harvester under combined galloping and base excitations. The harvester consists of a thin piezoelectric cantilever beam clamped at one end and rigidly attached to a bluff body at the other end. In addition to the vibratory base excitations, the beam is also subjected to aerodynamic forces resulting from the separation of the incoming airflow on both sides of the bluff body which gives rise to limit-cycle oscillations when the airflow velocity exceeds a criti- cal value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitations is derived using the energy approach and by adopting the nonlinear Euler–Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The resulting partial differential equations of motion are discretized and a reduced-order model is obtained. The mathematical model is validated by conducting a series of experiments at different wind speeds and base excitation amplitudes for excitation frequencies around the primary resonance of the harvester. Results from the model and experiment are pre- sented to characterize the response behavior under the combined loading. [DOI: 10.1115/1.4029611] 1 Introduction In the last decade, the field of energy harvesting has become a focal research topic with the ultimate goal of developing devices that harness energy from their environment to augment small bat- teries that are known for their finite life span and time consuming replacement. The availability of such renewable, cheap, and yet scalable energy systems may permit, on the long run, autonomous operations of low-power electronics including wireless and health monitoring sensors, cameras, data transmitters, and medical implants [1–3]. Researchers have introduced many new concepts to harness wasted energy from the environment with different transduction mechanisms [4–9]. Among such approaches, vibration energy har- vesting and flow energy harvesting have been receiving growing interest. A vibration energy harvester (VEH) transforms mechani- cal motions directly into electricity by exploiting the ability of active materials (piezoelectric and magnetostrictive) and some electromechanical coupling mechanisms (electrostatic and elec- tromagnetic) to generate an electric potential in response to me- chanical stimuli and external vibrations [10–18]. Figure 1 depicts a schematic of a typical VEH implementing a piezoelectric trans- duction mechanism and its associated linear frequency response. The harvester consists of a piezoelectric flexible structure, a beam or a plate, set into resonant motions via external mechanical vibrations applied at its base. Deflection of the structure strains the piezoelectric material producing an electric charge, which can be channeled as an alternating current to an electric load. While flow energy harvesters (FEHs) share the same electrome- chanical transduction mechanisms as VEHs, they differ in the way environmental energy is channeled into the harvester. Typically, a FEH channels energy from a moving fluid to a mechanical oscilla- tor by coupling the dynamic forces culminating from the motion of the fluid past the oscillator to its natural modes of vibration. As a result, the oscillator undergoes large amplitude motions which can be transformed into electricity using any of the aforemen- tioned electromechanical transduction mechanisms. The oscilla- tions arise from distinct fluid-dynamic phenomena/instabilities that can be classified by the nature of the flow patterns or mor- phology around the structure. These patterns depend on the char- acteristics of the structure or the mechanical oscillator such as its shape and dimensions as well as the ongoing flow conditions, e.g., steadiness, velocity, and angle of attack. In general, the efficacy of a FEH depends on the strength of the coupling between the dynamic fluid forces and the restoring forces of the oscillator (harvester). This coupling determines the portion of the kinetic energy of the flow which is converted into elastic energy, and subsequently transformed into electricity via the elec- tromechanical coupling mechanism. The nature and strength of this coupling varies according to the fluid–structure interaction mechanism utilized in the harvester’s design. Figure 2 depicts three different approaches for piezoelectric flow energy harvesting in uniform and steady flow. In the three approaches, the harvester consists of a flexible cantilever beam with a piezoelectric laminate attached to a resistive load, R, and subjected to flow-induced vibrations. The first approach is known as wake-galloping or vortex- induced vibrations and is based on placing the harvester in the wake of a bluff body. When the flow separates on the bluff body, vortices are shed from first one side and then the other forming the so called K arm an vortex street. As the vortices move down- stream, surface pressures are imposed on the beam as shown in Fig. 2(a). The oscillating pressures cause the beam to vibrate in a periodic resonant manner at a frequency that equals the vortex Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 3, 2014; final manuscript received January 4, 2015; published online February 18, 2015. Assoc. Editor: Marco Amabili. Journal of Vibration and Acoustics JUNE 2015, Vol. 137 / 031017-1 Copyright V C 2015 by ASME Downloaded From: http://vibrationacoustics.asmedigitalcollection.asme.org/ on 02/18/2015 Terms of Use: http://asme.org/terms