Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9

River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Shock & Vibration, Aircraft/ Aerospace, and Energy Harvesting, Volume 9 Alfred Wicks Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015 River Publishers

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor TomProulx Society for Experimental Mechanics, Inc. Bethel, CT, USA

River Publishers Alfred Wicks Editor Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9 Proceedings of the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015

Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-913-9 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2015 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Preface Shock & Vibration, Aircraft/Aerospace, Energy Harvesting represents one of ten volumes of technical papers presented at the 33rd IMAC, A Conference and Exposition on Structural Dynamics, 2015, organized by the Society for Experimental Mechanics, and held in Orlando, Florida, February 2–5, 2015. The full proceedings also include volumes on Nonlinear Dynamics; Dynamics of Civil Structures; Model Validation and Uncertainty Quantification; Dynamics of Coupled Structures; Sensors and Instrumentation; Special Topics in Structural Dynamics; Structural Health Monitoring & Damage Detection; Experimental Techniques, Rotating Machinery & Acoustics; and Topics in Modal Analysis. Each collection presents early findings from experimental and computational investigations on an important area within Structural Dynamics. Topics represent papers on practical issues improving energy harvesting measurements, shock calibration and shock environment synthesis and applications for aircraft/aerospace structures. Topics in this volume include: Energy Harvesting Adaptive Support Shock Calibration Operating Data Applications The organizers would like to thank the authors, presenters, session organizers, and session chairs for their participation in this track. Blacksburg, VA, USA Randy Allemang v

Contents 1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes....................... 1 Elvio Bonisoli, Francesco Di Monaco, Nicolò Manca, Maurizio Repetto, and Stefano Tornincasa 2 Issues in Experimental Testing of Piezoelectric Energy Harvesters ............................................... 11 Paulo S. Varoto 3 Innovative Piezoelectric Cantilever Beam Shape for Improved Energy Harvesting............................. 19 Iman Mehdipour and Francesco Braghin 4 Energy Harvesting from Piezoelectric Stacks Using Impacting Beam............................................ 25 Yig˘it Özpak, Murat Aykan, and Mehmet Çalıs¸kan 5 Nonlinear 2-DOFs Vibration Energy Harvester Based on Magnetic Levitation ................................. 39 I. Abed, N. Kacem, M.L. Bouazizi, and N. Bouhaddi 6 Parameter Identification of Riveted Joints Using Vibration Methods............................................. 47 Elif Altuntop, Murat Aykan, and Melin S¸ahin 7 Dynamic Ground Testing: Ground Vibration Tests Through Control Surface Excitation...................... 55 G. Osmond, A. Azzat, S. Leroy, and O. Delverdier 8 Adaptive Support of an Aircraft Panel................................................................................ 61 Manuel Baschke and Delf Sachau 9 Calculating the Impact Force of Supersonic Hail Stones Using SWAT-TEEM................................... 67 Tyler F. Schoenherr 10 Testing and Validation of the Dynamic Inertia Measurement Method............................................ 81 Alexander W. Chin, Claudia Y. Herrera, Natalie D. Spivey, William A. Fladung, and David Cloutier 11 Estimation of Amplitude-Dependent Resonance and Damping in MEMS Shock Accelerometers............. 105 Jason R. Foley, Thomas J. Lagoski, Jontia Brown, and Jonathan Hong 12 Development of a Mapping Function for a Low- to High-Amplitude Input ...................................... 115 Joshua H. Campbell, Janet C. Wolfson, Jacob C. Dodson, Alain L. Beliveau, Jonathan Hong, and Greg Falbo 13 Experimental Study of Glass Fiber Reinforced Polyester Under Repeated Impacts ............................ 129 Ahmed M. Elmahdy, Abdelhalim M. Elhabak, Mahmoud A. Adly, and Mohamed M. Elbawab 14 FE Modeling of Paperboard Material Using Sandwich Structure Method....................................... 137 W. Yang, M.W. Allin, and C.J. Dehenau 15 Evaluation of Seismic Performance of an Excavation Support System............................................ 141 Omer F. Usluogullari, Yalcin Bulut, and Ahmet Temugan 16 Calculating Stress and Strain from Experimental ODS Data ...................................................... 149 Brian Schwarz, Shawn Richardson, and Mark Richardson vii

viii Contents 17 Case Study: Modeling Generator Chassis Responses with ODS Data............................................. 161 Sze Kwan Cheah 18 Shock Calibration with Zero Shift Using a Digital Filter Technique .............................................. 169 Hideaki Nozato, Wataru Kokuyama, and Akihiro Ota 19 Mechanical Shock Environment Synthesis for Structural Failure Elicitation.................................... 175 Cassidy L. Fisher, Kaitlyn S. Kliewer, Gregory M. Naranjo, Stuart G. Taylor, and Kendra Van Buren 20 Natural Frequencies of Layered Beams Using a Continuous Variation Model ................................... 187 Arnaldo J. Mazzei and Richard A. Scott 21 Analysis of H1and H2 Optimal Design Scheme for an Electromagnetic Damper with Shunt Resonant Circuit ........................................................................................................ 201 Wai Kei Ao and Paul Reynolds 22 Orbit Stability Determination of Satellites Using Harmonic Force Excitation Analysis ........................ 213 Joshua Johnson, William H. Semke, Matthew Zimmer, and Ronald Fevig 23 Energy Harvesting Perspectives from Parametric Resonant Systems ............................................. 223 Maryam Ghandchi Tehrani, Elvio Bonisoli, and Matteo Scapolan

Chapter 1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes Elvio Bonisoli, Francesco Di Monaco, Nicolò Manca, Maurizio Repetto, and Stefano Tornincasa Abstract Powering a remote wireless sensor is a challenging task if batteries are not suitable or enough capacious and their substitution is not feasible. In this project a remote wireless sensor is placed inside training shoes with the aim to collect and transmit data to evaluate and track the performance of an athlete. The primary energy source is the impact between the shoe and the ground while walking or running. The harvester has been designed by means of a multi-physics optimization based on an integrated electromagnetic-mechanical-electric-electronic simulator. Thus an automated optimization of the device with respect to volume constraints, magnets dimensions, induction coils placement and sizes and electric/electronic coupling have been performed to increase the average power extracted from the device at different speeds. These parameters are used as starting point for the product development phase in order to obtain a consistent number of prototypes and validate the simulations on these physical demonstrators. Finally, experimental outcomes evince the expected performance and a more than satisfactory agreement with the models, confirming the feasibility of the application. Keywords Magneto-mechanical generator • Design and optimization • Shoe mounted device • Product development Experimental application 1.1 Introduction Powering remote wireless sensors exploiting the energy of the environment with the aim of making their life independent from some energy limited power source like an electrochemical battery, is a challenging task. In addition, batteries are often not suitable or not enough capacious, their substitution is not feasible or simply annoying and they introduce some problems due to the toxicity of their chemicals. Due to the growing of the wearable electronics market, one of the most debated topics in the field of energy harvesting is the power supply of all those devices where the energy source is the human body motion. The present study proposes a wearable device totally powered by an Energy Harvester (EH): an electrically autonomous bluetooth step-counter placed in the sole of training shoes. This sensor allows collecting and transmitting data to a bluetooth receiver device, as a smartphone, to evaluate and tracking the athlete performance. Figure 1.1 schematically represents the working principle: at each step energy is harvested and used to power the electric interface. Two possible strategies are available to collect energy in shoes during a step, usually by piezoelectric or electromagnetic transducers: sole deformation caused by the contact with the ground and shocks due to the impacts of the heel on the ground. Piezoelectric devices using sole deformation are described by [1, 2] while inertial piezoelectric generators, composed by a cantilever beam with a mass on the free end, are described in [3, 4]. References [5, 6] present two linear electromagnetic generators with one or more magnets sliding into a guide placed horizontally in the shoe. These devices do not have any kind of springs. A rotary generator activated by a harm extending under the sole is described in [7]. A generator using a flow between two pumps placed in the front and in the rear of the sole is presented in [8]. The proposed device is an electromagnetic energy harvester that exploits as primary energy source the impact of the heel on the ground during each step of walking or running activity. Differently from the devices presented in [5, 6] this one is placed in the heel with vertical sliding axis. E. Bonisoli ( ) • F. Di Monaco • N. Manca • S. Tornincasa Department of Management and Production Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: elvio.bonisoli@polito.it M. Repetto Department of Energy, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy © The Society for Experimental Mechanics, Inc. 2015 A. Wicks (ed.), Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15233-2_1 1

2 E. Bonisoli et al. Fig. 1.1 Working principle The harvester has been designed by means of a multi-physics optimization based on an integrated electromagneticmechanical-electric-electronic simulator. Thus, an automated optimization of the device with respect to volume constraints, magnet dimensions, induction coils placement and size and electric/electronic coupling have been performed to increase the average power extracted from the device at different walking speeds. These parameters represent the reference configuration for the product development phase in order to obtain a consistent number of semi-industrialized prototypes and validate the simulations on these physical demonstrators. 1.2 Device Description, Design and Optimization The device consists of the main parts: the transducer for the vibrational energy harvesting and the conversion in electric energy, and the electric interface for step monitoring and data sending. 1.2.1 Harvester The transducer is an electromagnetic linear generator. Its layout is shown in Fig. 1.2: a magnet can slide into a guide suspended between two springs and two coils are winded around the guide in opposite direction one each other. Inertial forces, due to the impact between the shoe housing the transducer and the ground during walking or running activity, induce motion in the magnet. The movement of the magnet causes a variation of the flux linkage in the coils and, consequently, a voltage is induced between the ends of the coils. It is possible to represent the device as a single degree of freedom base-excited mass-spring-damper system where the transducer is considered as an inertial device, so that the forces act on its base and the mass vibrates freely. Two differential equations, one for the mechanical and one for the electrical domain, describe the system. In case of a generic electric load the two equations are: ( d2z r dt2 D d2z inp dt2 c m d zr dt k m zr C 0 m i d i dt D R L i CVL L C 0 L d zr dt (1.1) where m is the mass of the moving magnet, k is the sum of the stiffness of the two springs, c is a generic dissipative viscous mechanical damping, zinp is the base motion, zr the relative position between magnet and base, 0 is the derivative of the magnetic flux linkage with respect to the relative displacement, RandLare respectively the resistance and inductance

1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes 3 Fig. 1.2 Transducer layout of the transducer coils, VL(i) is the voltage on the load, and i is the current [9, 10]. An accurate modelling of the system usually requires considering non-linearity of k and œ0 that are function of the relative displacement [11, 12]. 1.2.2 Electric Interface The simplest electric load is a resistor directly connected to the ends of the coils of the transducer. This solution provides the maximum electrical power, but it does not allow energy storage; it follows that the EH can feed an electrical device only when the floating magnet of the transducer is moving. In order to store the recovered energy a capacitor is connected to the coils terminals and, as the provided current is alternating, a rectifier bridge is interposed between the capacitor and the transducer. Although this configuration represents the easiest way for storing, due to the voltage drops in the diodes of the rectifier, it implies very worst performance with respect to the previous case. Moreover, if the voltage between the ends of the rectifier is lower than the voltage of the capacitor, the transducer does not charge it. To overcome the limits characterizing the bridge rectifier, an active electronic interface consisting in a step-up and a buck converter have been developed. The electronics interface is directly connected to the positive and negative terminal of the transducer. It consists of a full wave active boost converter with a transducer current control; this provides an optimum resistive load emulation independently from the signal provided by the transducer (shape and voltage level) and from the voltage stored on the output capacitor. The interactions between the mechanical and electrical phenomena depend heavily on the power transferred by the seismic mass to the electrical load. In linear system response conditions, the optimal matching follows the well known maximum power transfer theorem. For instance, in [13] it has been demonstrated that the energy recovery in response to a sinusoidal vibration input whose frequency matches the resonant frequency of the mechanical system, is maximum in adapted load condition, namely when the resistive load RL is: RL DRADAPT DR (1.2) However, due to the nonlinear effects present in the system, mainly the mechanical dissipative effects and the limited stroke of the floating magnet, the optimal resistor value is different from the one in (1.2) and it is typically larger. A theoretical analysis of this effect is present in [14], while here the best matching resistance value is calculated according to experimental evidences of the maximum power. Thus, the following equation is adopted through experimental evidence: RL DROPT DRADAPT CRADD (1.3) 1.2.3 Application Constraints, Vibrational Input and Energy Requirements The nature of the specific application imposes very stringent dimensional constraints to the device: a cylindrical shape volume of about ˆ27 16 mm that must contain the magneto-inductive energy harvester system for the power supply, the electronic interface for the data sending and the housing for the placing and the protection of the device itself in the sole of the shoe.

4 E. Bonisoli et al. Fig. 1.3 Vertical acceleration experimentally measured in the heel during walking and running activity 0 5 10 15 20 –300 –200 –100 0 100 200 300 Time [s] Acceleration [m/s2 ] Acceleration [m/s2] Running Walking 0 0.05 0.1 0.15 0.2 0.25 0.3 –200 –150 –100 –50 0 50 100 150 200 Time [s] 10th step Running Walking Fig. 1.4 Step counter system current absorption profile (a) and energy demand (b) As Fig. 1.3 shows, the typical input acceleration profile for walking and running consists of a very limited in duration and amplitude excitation at each step comparable to a series of impulses. Figure 1.4 represents the shape of the current consumption of the electric interface for the via bluetooth data transmission at each step, with the energy demand corresponding to each phase. The total energy need of 87 J represents the minimum energy required for the transmission of the step. Considering the harvester interface and electric components efficiency, the energy that the transducer must provide for the step detection is 104 J. 1.2.4 Device Optimization The stringent constraint imposed to the dimensions, the energy requirement of the electric interface for the step detection and the low intensity energy source imply a strict coupling between the mechanical and electrical characteristics upstream and downstream of the transducer with the objective of maximize the average power extracted from the device. The implemented optimization algorithm exploits Pattern Search algorithm [15], a well know 0th order deterministic technique extensively used in the automated optimization environment. Figure 1.5 summarizes the optimization loop steps based on an integrated electromagnetic-mechanical-electric-electronic simulator. This is a complete Matlab/Simulink model made to study the dynamic behavior of the device integrated in the optimization algorithm in order to maximize performance. Starting from the geometrical dimensions all the operative parameters (mass, springs, motion amplitude, dimensions of coils, number of turns in coils) are calculated. Through an automatic FEM model the flux linkage as a function of the magnet position is calculated. Then the system is simulated using a proper acceleration profile to excite the device. A full description of the simulation model is available in previous articles [16, 17]. Finally, the objective function implemented in the optimization algorithm is evaluated. Figure 1.6 shows the evolution of the parameters and the objective function. A consistent improvement of the performance is found mainly due to the tuning of the elastic characteristic. Moreover the magnetic mass is increased by the extension of

1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes 5 Fig. 1.5 Optimization loop Fig. 1.6 Evolution of parameters (a) and objective function (b) the magnet height, reducing the available stroke. The upper-coil length is also slightly increased. The simulation result emphasized the fact that initial device did not exploit all the available length of the stroke. The problem is fixed by softening its elastic characteristic and increasing the magnet height.

6 E. Bonisoli et al. 1.3 Product Development The geometrical parameters resulting from the optimization process represent the reference configuration for the product development phase. The aim is to convert a virtual prototype in a real device ready for the medium-large scale production, fully functional and ready to use when placed in training shoes. In this context, a consistent number of prototypes have been made to experimentally validate the design process and prove the project feasibility. 1.3.1 Virtual Prototype Starting from the reference configuration, a virtual prototype has been developed in according with the manufacturing requirements. The device consists of three plastic components, the case, the cap and the backcap, holding the cylindrical magnet and protecting the coils and the electronic interface. In order to optimize the available space, the elastic characteristic is obtained by means of two conic springs. As the step-counter will be insert in the sole of training shoes, a very important aspect is the design of the housing that must be sufficiently resistant to support the external load during the running and walking activity but, at the same time, not too thick in order to do not subtract space to the functional components. Therefore, 3D modelling, FEM analysis and the selection of the most suitable materials were key aspects in the product development of this device. The geometries that characterize the structural elements have been studied to minimize the internal stresses but always thinking to the ease of mounting. Figure 1.7 shows the section view of the device and an example of FEM analysis result. Device behavior has been simulated in almost ideal condition neglecting friction. Figure 1.8 shows the simulated electrical performance in terms of average harvested power over 22 s of activity with the first step after 2.5 s, voltage trend and energy recovery with respect to the energy requirement of the tenth step. As it can be observed, the energy harvested during the step in this condition is fully sufficient to support the electric interface requirements. 1.3.2 3D Printed Prototypes The first testing phase has been conducted on the 3D printed prototypes shown in Fig. 1.9. Tests have been performed reproducing on a shaker the same vibrational input used for the design process. Experimental evidences revealed that the springs, even if made of ductile iron, due to the strength of the magnetic induction of the floating element, shift on the lateral side of the magnet, precluded the right working of the device. To maintain the spring coaxial to the magnet, two plastic centering rings have been pasted on its flat surfaces. This allows the right linear oscillation of the floating elements but considerably reduces its available stroke resulting in a loss of performance of about 20 % when running as demonstrate by Fig. 1.10. Due to the smaller oscillation caused by the walking input, in this operative condition performance is the same as before; in fact, the stroke reduction do not affect magnet displacement when walking while strongly influence the behavior when running causing violent bumps that dissipate lot of energy. Real performance is much lower than simulated in almost ideal condition due to friction between floating element and guide, materials efficiency, components production uncertainty, assembling imperfection and all the inconvenient that differs the real from the ideal world. In order to overcome the loss due to the stroke reduction caused by the centering rings, ad hoc magnets, characterized by the same overall dimensions of the previous but presenting two centering holes on the flat surfaces, have been used. Exploiting larger stroke balances the smaller flux due to the smaller magnet volume. In addition, little adjustments of the guide component allowed reducing friction extending the magnet oscillation duration and increasing case resistance to the soldering high temperature. 1.3.3 Molded Prototypes A consistent number of molded prototypes have been produced through a semi-industrialized manufacturing process, see Fig. 1.11. Plots in Fig. 1.12 demonstrate the convenience of adopting ad hoc magnets and the effectiveness of the adjustment performed on the main plastic component. No significant differences of the device performance is registered under walking

1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes 7 Fig. 1.7 Prototype layout (a) and example of FEM analysis result (b) 0 2 4 6 8 101214161820 0 0.2 0.4 0.6 0.8 1 1.2 Time [s] Average Harvested Power [mW] Running sim no friction Walking sim no friction 0 0.05 0.1 0.15 0.2 0.25 0.3 –5 0 5 Time [s] Voltage [V] 10th step 0 0.05 0.1 0.15 0.2 0.25 0.3 0 500 1000 Time [s] Harvested Energy [μJ] Running Walking Fig. 1.8 Virtual prototype performance

8 E. Bonisoli et al. Fig. 1.9 3D printed prototypes 0 2 4 6 8 101214161820 0 0.2 0.4 0.6 0.8 1 1.2 Time [s] Average Harvested Power [mW] Running sim no friction Walking sim no friction Running exp Walking exp 0 0.05 0.1 0.15 0.2 0.25 0.3 –5 0 5 Time [s] Voltage [V] 10th step 0 0.05 0.1 0.15 0.2 0.25 0.3 0 500 1000 Time [s] Harvested Energy [μJ] Fig. 1.10 3D printed prototypes performance input, while, when running, a broad increase in the energy harvested is shown, both in simulation and in real test, about 40 %. The experimental recovered energy during a running step is about five times the required for the activity detection and data sending. Storing the energy surplus compensates the difference with respect to the requirements under very low intensity input allowing detecting every step during activity. 1.4 Conclusions With the aim of feeding a bluetooth step-counter placed in the sole of a shoe for walking and running activity monitoring, a semi-industrialized set of EH prototypes with a dedicated electronic interface has been designed, produced and tested in order to demonstrate the feasibility of the project and validate the simulation model. Energy harvesting is performed with a magneto-inductive transducer designed to maximize the recovery in response to the vibrating input due to the impact between the shoe and the ground during walking or running. The electronics interface consists of a step-up and buck converter, and, by means of a full wave active boost converter with a transducer current control, provides an optimum adaptive load emulation independently from the signal provided by the transducer and from the voltage stored on the output capacitor. The device has been designed in according to the manufacturing requirements for a medium-large scale production and taking into account the severe environment in term of external load where it will be placed. Numerical and experimental results show the effectiveness of the developed EH step-counter device demonstrating that the energy recovered during the impact is

1 From Preliminary Design to Prototyping and Validation of Energy Harvester for Shoes 9 Fig. 1.11 Molded prototypes 0 2 4 6 8 101214161820 0 0.2 0.4 0.6 0.8 1 1.2 Time [s] Average Harvested Power [mW] Running sim no friction Walking sim no friction Running exp Walking exp 0 0.05 0.1 0.15 0.2 0.25 0.3 –5 0 5 Time [s] Voltage [V] 10th step 0 0.05 0.1 0.15 0.2 0.25 0.3 0 500 1000 Time [s] Harvested Energy [μJ] Fig. 1.12 Molded prototypes performance maximized and it is sufficient to support the power requirement of the electronic interface allowing the step detection and the data sending also during the walking activity. Considering running activity, the harvested energy at each step is about four times the required. Storing this energy surplus compensates the difference with respect to the requirements under very low intensity input allowing detecting every step during activity. Acknowledgment This work was performed under a research project with STMicroelectronics. The authors would like to thank Dr. Alessandro Gasparini, Dr. Stefano Ramorini and Dr. Alberto Cattani from STMicroelectronics for their enthusiasm and driving force in the project. References 1. Shenck NS, Paradiso JA (2001) Energy scavenging with shoe-mounted piezoelectrics. IEEE Micro 21(3):30–42 2. Rocha JG, Gonçalves LM, Rocha PF, Silva MP, Lanceros-Méndez S (2010) Energy harvesting from piezoelectric materials fully integrated in footwear. IEEE Trans Ind Electron 57(3):813–819 3. Li WG, He S, Yu S (2010) Improving power density of a cantilever piezoelectric power harvester through a curved L-shaped proof mass. IEEE Trans Ind Electron 57(3):868–876 4. Moro L, Benasciutti D (2010) Harvested power and sensitivity analysis of vibrating shoe-mounted piezoelectric cantilevers. Smart Mater Struct 19(11):1–12 5. Carroll D, Duffy M (2012) Modelling, design, and testing of an electromagnetic power generator optimized for integration into shoes. J Syst Control Eng 226(2):256–270 6. Wang C, Miao D, Luk PC, Shen J, Xu C, Shi D (2010) A shoe-equipped linear generator for energy harvesting. In: 2010 IEEE international conference on sustainable energy technologies, Kandy, Sri Lanka, pp 1–6 7. Baghebani R, Ashoorirad M (2009) A power generating system for mobile electronic devices using human walking motion. Second Int Conf Comput Electr Eng 2:385–388 8. Dai D, Liu J, Zhou Y (2012) Harvesting biomechanical energy in the walking by shoe based on liquid metal magnetohydrodynamics. Front Energy 6(2):112–121 9. Nakano K, Elliott SJ, Rustighi E (2007) A unified approach to optimal conditions of power harvesting using electromagnetic and piezoelectric transducers. Smart Mater Struct 16(4):948–958

10 E. Bonisoli et al. 10. Beeby SP, O’Donnell T (2009) Electromagnetic energy harvesting. In: Priya S, Inman DJ (eds) Energy harvesting technologies. Springer, New York, pp 129–161 11. Tornincasa S, Repetto M, Bonisoli E, Di Monaco F (2012) Energy harvester for vehicle tires: nonlinear dynamics and experimental outcomes. J Intell Mat Syst Str 23(1):3–13 12. Tornincasa S, Repetto M, Bonisoli E, Di Monaco F (2012) Optimization of magneto-mechanical energy scavenger for automotive tire. J Intell Mater Syst Struct 23(8):2055–2064 13. Stephen NG (2006) On energy harvesting from ambient vibration. J Sound Vib 293(1–2):409–425 14. Liang J, Liao W (2012) Impedance modeling and analysis for piezoelectric energy harvesting systems. IEEE/ASME Trans Mechatron 17(6):1145–1157 15. Hooke R, Jeeves TA (1961) Direct search solution of numerical and statistic problems. J ACM 8(2):212–229 16. Bonisoli E, Canova A, Freschi F, Moos S, Repetto M, Tornincasa S (2010) Dynamic simulation of an electromechanical energy scavenging device. IEEE Trans Magn 46(8):2856–2859 17. Tornincasa S, Bonisoli E, Di Monaco F, Moos S, Repetto M, Freschi F (2011) Nonlinear dynamics of an electro-mechanical energy scavenger, vol 3, Modal analysis topics. Springer, New York, pp 339–349

Chapter 2 Issues in Experimental Testing of Piezoelectric Energy Harvesters Paulo S. Varoto Abstract The main goal of this article is to discuss current vibration testing procedures and their effects on the dynamics of beam type piezoelectric energy harvesters. The device is a cantilever beam partially covered by piezoelectric material with a mass at the beams free end. Governing equations of motion are derived for the harvester considering the excitation applied at its fixed boundary. Also, we consider the nonlinear constitutive piezoelectric equations in the formulation of the harvester’s electromechanical model. The prototype is subjected to a series of laboratory tests in order to investigate how different testing procedures can affect the overall dynamics of the device under study. Nonlinear effects are also included in order to check their benefits on the harvester’s dynamics in terms of the resulting electrical power as well as increase of usable frequency range. Keywords Energy harvesting • Nonlinear vibrations • Piezoelectric materials • Electromechanical model • Energy scavenging 2.1 Introduction Piezoelectric energy harvesting (PEH) has become a topic of increasing interest among several research areas as well as engineering majors, as it is the case of the aerospace and automotive industries. The possibility of converting certain amount of mechanical energy into usable electrical energy through has enabled the application of fundamental concepts from the theories of mechanical vibration and piezoelectricity in the development of new energy harvesting methodologies and devices, specially dedicated to power small electronics. Despite the difficulties just mentioned, recent contributions have shown promising results for piezoelectric energy harvesting either in employing linear [1–4] and nonlinear [5–8] modeling approaches in the mechanical to electrical conversion process or in developing new transduction and storage circuitry. The well known cantilever beam model is probably the most commonly employed technique to model and design piezoelectric energy harvesters. In this case a metallic beam (substrate), is covered (partially or fully) by piezoelectric ceramic on both sides, forming a bimorph structure. The piezoelectric layers are connected in series or in parallel and are polled in the transverse direction in order to generate electrical signals from the bending vibrations induced to the beam by some external excitation source. The cantilever harvester is then designed to operate at its fundamental natural frequency for optimum electrical energy conversion, although in principle it can also be used to harvest energy from higher order mode shapes. The harvester’s fundamental natural frequency can be tuned to a desired value by using a tip mass that is attached to the free end of the cantilever beam. The value of the tip mass is chosen such that the fundamental natural frequency of the device falls into an usable frequency range covered in most field applications (e.g. 0–100 Hz for environmental vibration signals). From the testing viewpoint, once a prototype of a given energy harvester is available, it is subjected to a series of vibration tests, mostly in the laboratory environment in order to provide experimental data that will be used to validate the device’s mathematical model. In this case, a commonly employed testing technique consists in performing transmissibility base driven tests [9]. The energy harvesting device is mounted on the armature table of an electromagnetic vibration exciter through a test fixture and the overall combined structure (harvester and fixture) is driven by an input signal that covers the frequency range of interest, that must contain at least the harvester’s fundamental natural frequency. The nature of the input signal that can be used to drive the system can be selected from commonly employed excitation signals in modal and vibration testing, as it is the case of harmonic, random, pseudo-random, chirp, among others. Usually the output signals that are measured consist of the cantilever base acceleration and voltage from the piezoelectric layers, which are used to compute the harvester’s voltage P.S. Varoto ( ) Department of Mechanical Engineering, School of Engineering of São Carlos – USP, São Carlos, SP, Brazil e-mail: varoto@sc.usp.br © The Society for Experimental Mechanics, Inc. 2015 A. Wicks (ed.), Shock & Vibration, Aircraft/Aerospace, and Energy Harvesting, Volume 9, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-15233-2_2 11

12 P.S. Varoto FRF relating the output voltage to the input acceleration. The output voltage is usually measured across a load resistor connected in parallel or in series with the piezoelectric layers. By varying the value of the load resistance the performance of the harvesting circuit in terms of the output voltage generation can be assessed. Another common measurement consists of using a laser vibrometer to measure the harvester’s tip velocity, that along with the input base acceleration are used to compute the tip velocity FRF, that can reveal additional important information on the performance of harvesting device. The goal of this paper is to review commonly employed vibration testing procedures used in obtaining experimental data that can be further used to validate analytical model of piezoelectric energy harvesters. Two different test setups, one for linear tests and the second for nonlinear tests are used in order to simulate different test scenarios when testing a specific harvesting device. Experimental results are shown and discussed, and major conclusions and recommendations are taken for future use. 2.2 Analytical Model Description This section presents a very brief description of the analytical models used in the remaining parts of the paper. Two models are employed, as shown in Figs. 2.1 and 2.2. Figure 2.1 shows the linear cantilever harvester model, where the device is grounded at the left end and free at the opposite end of the cantilever. The free end carries a tip mass (Mt) and the substrate is partially covered on both sides by piezoelectric ceramic layers that are, in the present case connected in series, as seen from Fig. 2.1. Piezoelectric layers and the substrate are assumed to have the same width, and as it will be seen in the next section, they are also have the same length, or, the beam will be fully covered by piezoelectric layers. The model shown in Fig. 2.1 is well known and has been widely used in modeling the electromechanical energy conversion process. When the piezoelectric layers are connected in series, it can be shown [7] that the FRF relating the output voltage from the harvester to the input base applied displacement can be written as V wW .!/ D 1 XrD1 8ˆˆˆ< ˆˆ : r ser r 1 XrD1 j! r r !2 r !2 Cj2 r!!r 1 Rl Cj! Cp 2 C 1 XrD1 j! r ser r !2 r !2 Cj2 r!!r 9>>>= >> ; Ur.x/ !2 r !2 Cj2 r!!r (2.1) Mt g(t) x y LP A-A B-B bS h p hS hp hpc bp z y z y A-A B-B a b Rl vser (t) Poling direction Fig. 2.1 Beam type cantilever piezoelectric energy harvesting model Fig. 2.2 Nonlinear cantilever energy harvesting model

2 Issues in Experimental Testing of Piezoelectric Energy Harvesters 13 Equation 2.1 was obtained by using the Euler-Bernoulli model for the cantilever energy harvester, and details on how to obtain this electromechanical FRF can be found in several references [1–3, 10]. Figure 2.2 shows the nonlinear energy harvesting model that is used in the experimental analysis to be further presented. As seen the harvesting device consists of a cantilever metallic beam usually denoted as the substructure and partially covered by piezoelectric ceramic on both sides and carrying a lumped mass at its free end. The piezoceramic layers are connected in series to a load resistor R1 and the input to the system consists of a base input harmonic acceleration that is applied at the harvester’s grounded side. The tip mass consists of a neodymium magnet that is rigidly attached to the substructure’s free end and that oscillates in the vicinity of a second magnet. A repulsive or attractive nonlinear force can be then generated at the beam’s free end, depending on the magnetic polarity of these magnets. This contactless interaction between the magnetic fields of the tip magnets introduces a nonlinear force on the bimorph beam what in turn can generate nonlinear oscillations of the harvesting device. The governing equations of motion of the model shown in Fig. 2.2 can be obtained by applying the Lagrange equations and can be shown to be expressed as [11] R C Qcf P C Q C Qb 3 QcV QdV 2 D F mt cos.!t/ (2.2) PV C V 2R1e D c 4e P 3d 4e 2 P (2.3) Equations (2.2) and (2.3) constitute a system of coupled and nonlinear differential equations and correspond to the electromechanical model for the harvesting system shown in Fig. 2.2. Solution of this system of coupled equations for the harvester transverse displacement and output voltage can be achieved by employing perturbation methods [11]. 2.3 Test Apparatus Two experimental setups are used in order to assess the dynamic behavior of the harvesting systems shown in Figs. 2.1 and 2.2. Figure 2.3 shows a bimorph cantilever energy harvester that is mounted on the vibration exciter’s table through an impedance head (PCB 288D01, 22.4 mV/N, 100 mV/g). The impedance head is used in order to monitor the input signals (force and acceleration) at the interface between the vibration exciter and the system to be tested. As pointed in [9], knowledge of interface forces and motions in base driven tests can be very useful in the model validation. The harvester used in this case is a commercially available bending sensor (Piezo Systems T226-H4-203X ) measuring 26 6.4 0.66mm made of reinforced brass (substructure) and fully covered by piezoelectric layers. The bimorph harvester is mounted on a test fixture [3] designed to proper simulate the fixed-free boundary condition. A tear-drop ICP miniature accelerometer (PCB 352A24, 100 mV/g) is used to measure the input acceleration signal on the clamping fixture and this signal will be further used to estimate the voltage FRF of the harvester. Fig. 2.3 Linear cantilever energy harvesting setup

14 P.S. Varoto Fig. 2.4 Nonlinear cantilever energy harvesting setup: (a) actual test setup; (b) illustration of the test setup showing excitation direction (arrow) The second experimental setup used in this work is shown in Fig. 2.4. A special fixture was constructed in order to test the harvesting device in both linear and nonlinear testing configurations. Figure 2.4a shows an illustration of the testing apparatus and Fig. 2.4b shows an illustrative description of the test setup. A MIDÉ Volture V22BL energy harvester was used in the tests. The sensor is attached to the test fixture through a clamping device that is used to simulate the cantilever boundary condition. A neodymium magnet is attached to the harvester’s free end and a second magnet is mounted on a vertical tower that part of the fixture as shown in Fig. 2.4. The magnetic gap between the tip and fixed magnet can be varied by moving the vertical tower along the longitudinal axis of the test fixture. By varying the linear distance between the two magnets an attractive or repulsive (depending on the relative position of the magnetic poles) contactless nonlinear restoring force can be induced on the transverse motion of the harvester. This nonlinear magnetic force is actually a nonlinear effect that is induced on the harvesting system in order to generate nonlinear dynamic behavior, which can present some benefits in terms of voltage generation and therefore improve the performance of the harvesting system. The test fixture assembly is mounted on the top of linear tracks and attached to the armature of the vibration exciter that in turn will provide the excitation signals to the harvesting system as indicated by the arrow in Fig. 2.4b. An impedance head is also used to monitor the interface signals between the vibration exciter and the harvesting system, as shown in Fig. 2.4a. The miniature accelerometer is mounted on the clamping fixture in order to measure the transverse input acceleration and will be further used to estimate the harvester’s voltage FRF. 2.4 Experimental Results This section presents and discusses experimental results obtained from tests performed according to the setups described in the previous section. Figure 2.5 show results obtained in two base driven tests employing the test setup of Fig. 2.3. Two test scenarios were examined in this case, where the test item, composed of the bimorph harvester and the clamping fixture was mounted in two different locations on the vibration exciter table. First, the test item was positioned on the top of the exciter’s table such that the location of its center of gravity is aligned with the vertical axis of symmetry of the vibration exciter. The importance of this alignment issue relies on the fact that the vibration exciter table moves vertically and significant sources of misalignments can induce rocking motions of the exciter’s table [9], what in turn can affect the resulting measured FRF data. The situation just mentioned can be clearly seen on the results presented in Fig. 2.5. Figure 2.5a shows the resulting transmissibility FRF relating the bimorph output voltage to the input acceleration measured by the miniature accelerometer. In this case the piezoelectric layers were connected in series with a 1 M load resistor. Two curves are shown in Fig. 2.5a, the blue corresponding to what is called symmetric mounting, where the vertical axis passing through the center of gravity of the energy harvesting system and the main vertical axis of the exciter bare table are approximately coincident. This measured voltage FRF is very consistent, noise free and can be used to characterize the energy harvesting dynamic behavior on the 0– 1,000 Hz frequency range used in the experiment. In this case, the system was drive by a pseudorandom excitation signal, that is very useful since it is a periodic signal in the time window, making the use of digital windows unnecessary, and in addition being very cost effective since a reduced number of averages are required in the data acquisition process. The blue curve shown in Fig. 2.5b corresponds to a measurement where the harvester along with its clamping fixture is fixed to an off-center

2 Issues in Experimental Testing of Piezoelectric Energy Harvesters 15 Fig. 2.5 Experimental results for symmetrical (blue) and unsymmetrical (red) assemblages: (a) output voltage FRF related to base acceleration; (b) zoomed FRF; (c) input acceleration frequency spectra; (d) output voltage frequency spectra a b c d Fig. 2.6 Comparison between symmetrical (blue) and unsymmetrical (red) FRFs to theoretical FRF (black) point on the vibration exciter table. In this case the mass moment of inertia of the harvesting system induces significant rocking motions on the exciter table due to the unsymmetrical mounting and the results of this inadequate assemblage significantly affects the resulting measured voltage FRF, as shown in Fig. 2.5a. Figure 2.5b represents a close up on both symmetrical and unsymmetrical measurements on a zoomed frequency range in the vicinity of the harvester’s natural frequency. It can be seen that amplitude discrepancies occur when inappropriate assemblage is used to characterize the harvester’s dynamics. Figure 2.5c, d show similar behavior on the measured input and output frequency spectra signals. Figure 2.6 shows a comparison between the symmetrical and unsymmetrical FRFs and the theoretical voltage FRF computed by Eq. (2.1), in this case used for a single mode representation. Although the natural frequency is sufficiently close to the theoretical value for both measurements the unsymmetrical result shows amplitude discrepancy in relation to the theoretical curve. The experimental results obtained from sine sweep tests using the test setup of Fig. 2.3 are shown in Fig. 2.7. In this case three tests were performed with different input levels, as indicated, and the resulting output voltage to input acceleration transmissibility FRF was measured for each test. Results shown in Fig. 2.7b indicate that different peak amplitudes are obtained and this in principle contradicts the FRF concept, since it essentially reflects the amount of output to each unit of input applied to the test system. Hence, when linearity holds, increasing input levels should in principle lead to proportionally increasing output levels and the ratio between them should remain constant. On the contrary, results shown in Fig. 2.7 not only show different amplitude levels for the measured FRFs but also a slight shift of the harvester’s natural frequency peak. A possible explanation for the amplitude differences observed on the results shown in Fig. 2.7b is the fact that when passing through the resonance, the vibration exciter presents the force drop-off phenomenon [9], and this can be clearly seen on the results for the input acceleration frequency spectrum shown in Fig. 2.7a. A second possibility that can explain both the amplitude differences and the natural frequency deviation is that the system reveals nonlinear behavior, what is usually

16 P.S. Varoto Fig. 2.7 Experimental results from sine sweep tests: (a) input acceleration frequency spectra; (b) FRF a b Fig. 2.8 Nonlinear measurements: (a) repulsive magnetic force; (b) attractive magnetic force observed when sine sweep is used to drive the system under study. In this case, care should be taken in choosing appropriate excitation levels such that the system’s response falls within linear limits. On the other hand, the use of sine sweep signal is suitable for studying nonlinear behavior, and should be preferred in this case in relation to random or pseudorandom excitation signals, since the later tends to smooth nonlinear effects mostly due to the nature of the signal (white noise) and the linearization effects of the Fourier transform used to compute the FRF. Finally, the results shown in Fig. 2.8 were obtained with the test setup shown in Fig. 2.4. In this case the system was driven by a sinusoidal excitation signal that covered a reduced frequency range. The linear distance between the tip magnet attached to the free end of the harvester and the magnet fixed on the vertical tower shown in Fig. 2.4 was varied in order to generate different magnetic forces, thus inducing different nonlinear effects on the dynamics of the harvester. Figure 2.8a show results for a repulsive magnetic force while Fig. 2.8b show similar results but in this case the magnets were inverted such that an attractive magnetic restoring force could be achieved. Results clearly show differences in amplitude and on the location of the resonant peak, indicating that the use of the magnets significantly altered the dynamic behavior of the harvester.

2 Issues in Experimental Testing of Piezoelectric Energy Harvesters 17 2.5 Closing Remarks This paper addressed important issues regarding experimental procedures used in the characterization of piezoelectric energy harvesters in laboratory testing. It was shown that adequate assemblage of the harvesting system on the vibration exciter table during base driven tests is very important in order to obtain meaningful experimental results. It was also discussed the application of different test setups as well as the use of different excitation signals in the process of characterization of the dynamic behavior of piezoelectric energy harvesters. Acknowledgements The author would like to acknowledge the support received from CAPES and University of São Paulo, in Brazil in the development of this work. References 1. Erturk A, Innam DJ (2008) A distributed parameter electromechanical model for cantilevered piezoelectric energy harvesters. J Vib Acoust 130:041002 2. Erturk A, Innam DJ (2008) On mechanical modeling of cantilevered piezoelectric vibration energy harvesters. J Intell Mater Syst Struct 19:1311–1325 3. Erturk A, Innam DJ (2009) An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations. J Vib Acoust 18:025009 4. Erturk A, Hoffmann J, Inman DJ (2009) A piezomagnetoelastic structure for broadband vibration energy harvesting. Appl Phys Lett 94:254102 5. Stanton S, Mcgehee C, Mann B (2009) Reversible hysteresis for broadband magnetopiezoelastic energy harvesting. Appl Phys Lett 95:174103. 3pp 6. Stanton S, Mcgehee C, Mann B (2010) Nonlinear dynamics for broadband energy harvesting: investigation of a bistable piezoelectric inertial generator. Phys D Nonlinear Phenom 10:640–653 7. Abdelkefi A, Nayfeh AH, Hajj MR (2012) Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters. Nonlinear Dyn 67:1147–1160 8. Abdelkefi A, Nayfeh AH, Hajj MR (2012) Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitations. Nonlinear Dyn 67:1231–1232 9. McConnell KG, Varoto PS (2008) Vibration testing: theory and practice, 2nd edn. Wiley, New York 10. Franco VR Optimization techniques applied to piezoelectric energy harvesting. Ph.D. dissertation, University of Sao Paulo, Brazil (in Portuguese) 11. Mineto AT (2013) Energy harvesting from nonlinear structural vibration signals. Ph.D. thesis, University of Sao Paulo, Brazil (in Portuguese) 12. Erturk A, Innam DJ (2008) Issues in mathematical modeling of piezoelectric energy harvesters. Smart Mater Struct 17:065016

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